METHOD AND SYSTEM FOR ULTRASONIC CHARACTERIZATION OF A MEDIUM

Abstract

Method and system for ultrasonically characterizing a medium Method for ultrasonic characterization of a medium comprising a step of generating a series of incident ultrasonic waves, a step of generating an experimental reflection matrix R ui(t) defined between the emission base (i) at the input and a reception base (u) at the output, a step of determining a de-scanned reflection matrix R' of the medium between a virtual input transducer calculated from an input focus of the experimental reflection matrix and a virtual output transducer calculated from an output focus of the experimental reflection matrix, these virtual transducers being at the same depth. The method comprises a step of extracting an optimal position deviation or an optimal sound speed model in this focal spot image. Figure for abstract: FIGURE 5

Description

Title of the invention: METHOD AND SYSTEM FOR ULTRASONIC CHARACTERIZATION OF A MEDIUM Technical field

[0001] The present description relates to methods and systems for characterizing a medium by ultrasound, and applies in particular to medical imaging as well as to non-destructive testing of a medium and more generally to all fields which can use a multi-element network of transducers to measure the reflection of a diffusing medium. STATE OF THE ART Limitations of ultrasound imaging

[0002] In the field of ultrasound imaging, we seek to construct an image of the reflectivity of a medium from echoes backscattered by heterogeneities of the medium. This is the principle of the ultrasound scanner used in medical imaging, which allows in particular to visualize the internal anatomy of an individual. Most of the time, to construct an ultrasound image, the medium is considered homogeneous, with a constant speed of sound c0. However, the hypothesis of a homogeneous medium is often not verified in the majority of concrete cases, in particular when it comes to imaging parts of human or animal bodies. For example, in the case of ultrasound of the liver, the acoustic waves pass through a succession of layers of fat and muscles before reaching the targeted organ. The speed of sound can in this case vary for example between 1450 m / s for adipose tissue and 1600 m / s for the liver.The disagreement between the actual distribution of the speed of sound in the medium and the speed model used to construct the ultrasound image can induce fairly strong aberrations in the image thus obtained, compromising for example the practitioner's diagnosis during a medical examination.

[0003] As illustrated in [Fig.l], conventional ultrasound methods use an array of piezoelectric transducers that can emit and / or receive ultrasonic signals independently, each transducer being at a position u in the bar supporting said array. The array of transducers, placed opposite a medium, makes it possible to insonify and image the medium in different ways. The conventional method consists of insonifying the medium using emissions focused by a technique called beamforming. As shown in [Fig.l](a), this method consists of applying to the signals emitted by each transducer a set of appropriate delays i(uin, xin, z, c0) based on a homogeneous velocity model c0, in order to make the wavelets produced interfere by each transducer at the targeted focal point of spatial position (%in, z). Due to the physical limits of diffraction, ultrasound is emitted through the aperture of the ultrasound probe, concentrated in an area often called a "focal spot", of lateral width ôx.

[0004] In order to then possibly construct an ultrasound image, a digital focusing step is also carried out in reception. The echoes captured by the transducers of the network, as shown diagrammatically in [Fig. l](b), are put back in phase by shifting them temporally. The delays xout, z, c0) are identical to those applied to the emission, with the variable uout designating the position of each transducer. In the emission phase, all the signals interfere at the position point (xim z) at the ballistic time t = z / c0 if the velocity model c0 corresponds to reality. In reception, the signals coming from this same point (xoul = x,„) interfere by summing the signals at the echo time t = 2zJc0. This summation gives the final result of the focusing in reception. This confocal method with double focusing at emission and reception, illustrated in [Fig.l], allows to directly image the reflectivity of the medium with a lateral resolution ôx and a good contrast. However, this method is time-consuming because it requires to physically focus the emission at each of the points of the medium or at least at a given depth, on each of the lines of the constructed image representative of the medium. Moreover, this image is often of a low qualitative level when the medium is heterogeneous, in particular with a speed of sound not constant between the various zones constituting the observed medium. [Fig.l](c) and [Fig. l](d) show a medium which includes an aberrator layer with a speed of sound different from the speed of sound observed in the rest of the medium. This results in an aberration of the acoustic wavefront which leads to a distortion of the resulting ultrasound image and therefore to a degradation of its resolution and its contrast, annoying in particular during a medical examination. Matrix approach to ultrasound imaging

[0005] To compensate for these aberration problems, a matrix approach to ultrasound imaging has been developed in recent years. This approach is based on the measurement by the ultrasound probe of an experimental reflection matrix of the medium studied.

[0006] A first proposal for measuring this experimental reflection matrix is to successively emit an ultrasonic pulse from each transducer in the array whose position is identified by the coordinate uin, as shown schematically in [Fig.2](a). This gives rise to a diverging cylindrical (or spherical) incident wave. This wave is reflected by the diffusers in the medium and the backscattered field is recorded by each of the transducers as a function of time as shown in [Fig.2](b). By repeating this operation with each transducer used successively as a source, the experimental reflection matrix Ruu is determined. (t) expressed in the transducer base, composed of all the impulse responses R(uout, uin, t) between each transducer. This matrix is then rich in quantity of information on the medium studied. But, the method assumes that the medium remains fixed throughout the duration of the measurements. In addition, the recorded signals have a poor signal-to-noise ratio because the medium is insonified by a single transducer.

[0007] A second way to construct this experimental reflection matrix consists of insonifying the medium with a base of series of plane waves. This method makes it possible to overcome the previous problems. [Fig.2](c) illustrates the principle of this plane wave illumination. A delay law r' is applied to each signal at the emission to form a wavefront inclined at an angle 6in relative to the transducer array. At the reception, illustrated in [Fig.2](d), the field backscattered by the medium, R(uout, 0in, t), is measured by all the sensors of positions uout for each incident plane wave. All of these responses form an experimental reflection matrix Ruo(t). The double focusing method described previously can be carried out numerically by temporally shifting the measured signals before summing them coherently.This method gave rise to ultra-rapid imaging and elastography, and is for example described in the document: .

[0008] “Coherent plane-wave compounding for very high frame rate ultrasound and transient elastography”, G. Montaldo et al. (IEEE Trans. Ultrason., Ferroelect. Freq. Control 56 489-506, 2009).

[0009] A third way to create this experimental reflection matrix consists of insonifying the medium with a basis of diverging waves, as shown in [Fig.2] (e) and [Fig.2] (f), which makes it possible to illuminate the acoustic field more broadly than by using plane waves. This technique, used in particular in super-resolution imaging, is explained in the document:

[0010] “Ultrafast imaging of the heart using Circular Wave Synthetic Imaging with Phased Arrays”, Couade et al., IEEE International Ultrasonics Symposium (2009).

[0011] Conventional imaging therefore consists of double focusing on emission and reception at the same focal point for each pixel of the image (xin = xoul), as represented in [Fig.3](a).

[0012] Matrix imaging, on the contrary, consists of dissociating the focal points at emission and reception, for the same echo time t, as represented in [Fig.3](b). Thus, a focused reflection matrix R,,(7, Co) is determined, composed of the responses between virtual input transducers and virtual output transducers of respective spatial positions rin = (%in, zin) and rout = (xout, zout) corresponding to focal spots synthesized at input and output at different spatial positions, and whose depth is dictated by the echo time t. This matrix is obtained by channel formations from the experimental reflection matrix Rui(t). This matrix allows access to much more information than the confocal image of conventional imaging. This focused reflection matrix can be synthesized in the time domain by delay laws or in the frequency domain by applying appropriate phase shifts.

[0013] This matrix imaging has been described in the document:

[0014] “Reflection Matrix Approach for Quantitative Imaging of Scattering Media”, William Lambert, et al., Phys. Rev. X 10, 021048, (2020),

[0015] then in the document

[0016] “Distortion matrix approach for ultrasound imaging of random scattering media”, W Lambert, et Al. - Proceedings of the National Academy of Sciences, (2020).

[0017] It should be noted that, in these publications, the focused reflection matrix Rrr(t, c0) was considered between virtual transducers at the expected ballistic depth: zin = Zout = Zt= c0t / 2, zt being the depth of the isochronous volume expected for a sound speed Co, the isochronous volume being the set of points in the medium contributing to the signals received at echo time t. This sub-part of the matrix R,,(7, Co) is denoted Rxx( zh t Co). While the diagonal coefficients (xout = xin) of this matrix Rxx(z,, t, c0) give the synthetic confocal image at depth zt, its off-diagonal coefficients inform us about the potential aberration and multiple scattering problems likely to alter the quality of this same image.

[0018] The reflection matrix focused at ballistic depth, Rxx(z„ t, c0), plays a pivotal role for ultrasound matrix imaging. It was initially studied to probe the transverse evolution of the input and output focal spots, then to compensate for aberrations by determining optimal delay laws (or phase shifts) to be applied at the input and output of the reflection matrix. However, this approach is limited because it only allows aberrations to be probed transversely and does not allow for "repositioning the diffusers at their real depth". Thus, any deviation between the sound speed model c0 and its real distribution c(r) implies a bad positioning of the diffusers imaged in depth as shown in [Fig. 1].

[0019] In particular, as mentioned in patent applications US 2022 / 082693, US 2022 / 084496 and US 2022 / 082527, the focused reflection matrix was studied by the applicant beyond the ballistic depth by scanning in depth the relative position of the virtual transducers. By placing oneself at a constant echo time t (fixed isochronous volume), the focal spot at the input (or output) of the device can be probed locally by scanning the spatial position rout (or rin) of the virtual transducer at the output (or input). A focus defect Az = zout - Zin can thus be measured at each point of spatial position rin of the image and an integrated sound speed map between the probe and each point rin can be deduced from this measurement.

[0020] However, this approach is sometimes not optimal because the virtual spatial position transducer rout (or rin) is also sensitive to aberrations, which biases the estimator of the focal spot at the input (or output). SUMMARY

[0021] The present description relates, according to a first aspect, to a method for characterizing a medium by ultrasound, the method comprising:

[0022] - a step of generating a series of incident ultrasonic waves USin in a area of said medium, by means of an array of transducers, said series of incident ultrasonic waves being an emission base i; and

[0023] - a step of generating an experimental reflection matrix Rui(t) defined between the emission base i at the input and a reception base u at the output, the coefficients of this matrix corresponding to the signals received by the transducers induced by the reflected ultrasonic waves.

[0024] The method further comprises:

[0025] - a step of determining a de-scanned reflection matrix R',

[0026] which includes, for a set of midpoints of abscissa x and echo time t,

[0027] responses of the medium calculated by channel formations from the experimental reflection matrix RUi(t), between a virtual input transducer of spatial position rin = (x, zt+Az) and a virtual output transducer of spatial position rout = (x+Ax, Zr+Az), the two virtual transducers being at the same depth zt+Az, zt being the depth of the isochronous volume expected for a sound speed c0, the isochronous volume being the set of points of the medium contributing to the signals received at echo time t,

[0028] the responses of the unscanned reflection matrix R' being determined for a set of lateral deviation values Ax comprising at least Ax = 0 and for a set of depth deviation values Az,

[0029] said unscanned reflection matrix R' being formed with each row corresponding to an element of a couple zlr = {Ax, Az} which corresponds to a focal spot image and each column corresponding to an element of a couple {x, t}, which is noted:

[0030] - an extraction step in which we determine from each spot image focal, an optimal position deviation zAropt, said optimal position deviation Zlropt = {Axopt , Azopt} close to the maximum in said focal spot image.

[0031] Thanks to these provisions, the method advantageously allows the medium to be probed locally at any point and in any direction relative to a ballistic time. of propagation of the ultrasonic wave in the medium.

[0032] This method provides access to a large amount of local information on the medium, which makes it possible to characterize the process of focusing the ultrasonic wave locally, and thus to estimate the Azopt depth focusing defect.

[0033] This estimation is then very useful for improving the focusing and quality of the ultrasound image. This optimization of the ultrasound images is carried out by calculation without requiring iteration of new emissions and / or acquisitions, which is an important advantage in particular during in vivo measurements. The optimizations can in fact be carried out in real time or later, possibly on a different and optionally remote system.

[0034] In various embodiments of the method, one and / or the other of the following arrangements may optionally be used in addition.

[0035] According to a variant, the method further comprises:

[0036] - a step of forming an ultrasound image by calculating the reflectivity in a plurality of medium points, from the unscanned reflection matrix R', the reflectivity of each of these medium points corresponding to the response of the medium between the virtual spatial position input transducer rin = (x, zt+Azopù and the virtual spatial position output transducer rout= r + Aropt = (x+Axopl, zt+Azopt), said reflectivity being defined by: Zj (æ, / ) — Ar = AropJ;r3)? Vl'

[0037] According to a variant, the ultrasound image is transformed into the depth dimension, using the sound speed model c0 by: Zi (y. zt) = Zj (ar, t = 2Wcn) '

[0038] in which zt is the depth of a pixel of the ultrasound image or depth of the isochomic volume.

[0039] According to one variant, the ultrasound image is displayed on a display device.

[0040] According to a variant, the method further comprises before the extraction step:

[0041] - a spatio-temporal averaging step of the unscanned reflection matrix R' in which the values of the unscanned reflection matrix R' are locally averaged, along the lateral dimension x and along the echo time dimension t, for each element of the pair Ar = {Ax, Az}, the focal spot images then being averaged.

[0042] According to a variant:

[0043] in the spatio-temporal averaging step, an incoherent point spread function PSFinc is calculated by the following formula: - yJ / n Ar. {F; H■■■■ .p,f' -

[0044] for a set of lateral deviation values Ax comprising at least Ax = 0 and for a set of depth deviation values Az, noted in the form of the pair Ar = {Ax, Az}, to obtain the focal spot image for the lateral position x and the echo time t,

[0045] in which:

[0046] <.> is an average operator according to the parameters of the pair {x', t'}

[0047] R' is the unscanned reflection matrix,

[0048] W(x\ t') is a spatio-temporal weighting window according to the same parameters, and

[0049] in the extraction step, a maximum point of the focal spot image is sought corresponding to a maximum of the modulus of the points of the focal spot image, and the optimal position deviation Z4ropt is the position of said maximum point in said focal spot image.

[0050] According to a variant:

[0051] in the spatio-temporal averaging step, a singular value decomposition SVD of a local focal spot matrix R(l> is calculated, said local focal spot matrix being expressed from the de-scanned reflection matrix / ?' by: RW({:M}) =- [Bz(Ar, 'AHA - ;rF - F]

[0052] in which:

[0053] R' is the unscanned reflection matrix,

[0054] W(x', t') is a spatio-temporal weighting window according to the same pa meters.

[0055] the singular value decomposition SVD of said local matrix is noted: p

[0056] in which

[0057] are the singular values of said local matrix,

[0058] Up are the output eigenvectors,

[0059] Vp are the input eigenvectors,

[0060] we calculate a coherent point spread function PSFcoh by the following formula: (Ar, {«h 0) ” (Ar, {x Z})

[0061] for a set of lateral deviation values Ax comprising at least Ax = 0 and for a set of depth deviation values Az, noted in the form of the couple Ar = {Ax, Az}, to obtain the focal spot image for lateral position x and echo time t, and

[0062] in the extraction step, we search for a maximum point of the focal spot image corresponding to:

[0063] a maximum of the modulus of the points of the focal spot image, or at

[0064] a maximum of the modulus of the derivative along the depth direction of the points of the focal spot image, or to

[0065] a maximum of the modulus of the derivative along the depth direction of the imaginary part of the points of the focal spot image, and

[0066] the optimal position deviation Zlropt is the position of said maximum point in said focal spot image.

[0067] According to a variant, at the extraction step, the lateral deviation Axopt is considered to be zero, Axopt = 0.

[0068] According to a variant, in the step of determining a de-scanned reflection matrix R', the de-scanned reflection matrix R' is formed only for lateral deviation values Ax of zero value, Ax = 0.

[0069] According to a variant, in the spatio-temporal averaging step, the values of the unscanned reflection matrix R' are averaged according to the lateral dimension x and the echo time t, only for focal spot images corresponding to a zero lateral deviation Ax.

[0070] According to a variant, in the extraction step, the optimal depth difference Azopt is determined from the points of the focal spot image having a lateral difference Ax of zero value, Ax = 0.

[0071] According to a variant, an integrated sound speed Copt is determined from the optimal depth difference Azopt, from the optimal position Zlropt= {Axopt, Azopt}, by:

[0072] this integrated sound speed corresponding to an average sound speed between the transducer network and the depth of the isochronous volume.

[0073] According to a variant:

[0074] we calculate local sound speeds c(r), for a set of pairs {x, t}, from integrated sound speed values ^opt obtained for the focal spot images of said pairs {x, t},

[0075] According to a variant, the method further comprises:

[0076] a step of forming a local sound speed image of the medium from said set of local sound speeds.

[0077] According to a variant:

[0078] we recalculate a de-scanned reflection matrix R' using the local sound speed values.

[0079] According to a variant, the calculations of path formations between the virtual input transducer and the virtual output transducer are carried out from the experimental reflection matrix Rui(t), using a forward delay time of the ultrasonic waves between the emission base (i) and the virtual input transducer, and using a return delay time of the ultrasonic waves between the virtual output transducer and the transducers of the reception base (u).

[0080] According to a variant, the unscanned reflection matrix R' is calculated from the experimental reflection matrix Rui(t) by the following formula: { A;r, A .£}, { x, t}, Q) ) ~ tt—Z— -r / (x, im- + As, qO rr{xr Ar, ït 4- As, c^)) - '■ U t ; WHO .

[0081] in which:

[0082] Nin is the number of elements of the emission base (i)

[0083] Noul is the number of elements of the reception base (u),

[0084] Rui(t) is the experimental reflection matrix, of which

[0085] Rui(uout, iia, t) is the element of the experimental reflection matrix Rui0j recorded by the spatial position transducer uout following the emission of index iin in the emission base (i), at a time t,

[0086] c0 being the expected speed of sound.

[0087] According to a variant, the unscanned reflection matrix R' is calculated from a focused reflection matrix R by the following formula: OAr. HAS ]. {0) 4- A / , as t % AA: i

[0088] in which:

[0089] the unscanned reflection matrix R' is formed with each row formed of elements of a pair {Ax, Az} and each column formed of elements of a pair {x, t}, and

[0090] the focused reflection matrix R is calculated from the experimental reflection matrix Rui(t) by the following formula: A 4- AA - 1 ,• • / u / ( ? $uj ■ 'r '' t --A '” △ ~ t <0 y ' M'ont ■ : Af, 4' a - ) J

[0091] in which:

[0092] Nin is the number of elements of the emission base (i)

[0093] Noul is the number of elements of the reception base (u),

[0094] Rui(t) is the experimental reflection matrix, of which

[0095] Rui(uout, iia, t) is the element of the experimental reflection matrix Rui(t) recorded by the spatial position transducer uout following the emission of index iin in the emission base (i) and at time t,

[0096] c0 being the expected speed of sound.

[0097] According to a variant, a film is formed from a succession of ultrasound images by a first number N of iterations of the steps of the method.

[0098] According to a variant:

[0099] among the N iterations, a second number P, less than N of iterations, does not include the steps of determining the unscanned reflection matrix R', the spatio-temporal averaging steps, and the extraction steps, and

[0100] for these P iterations, at the stage of forming the ultrasound image, the ultrasound image is obtained from an optimal position deviation extracted during a previous iteration.

[0101] The present description relates, according to a second aspect, to a system for ultrasonic characterization of a medium, and configured for the implementation of methods as described previously. The system according to the second aspect comprises:

[0102] - an array of transducers adapted to generate a series of ultrasonic waves in incident in an area of the medium, and to record as a function of time the ultrasonic waves backscattered by said area; and

[0103] - a computing unit associated with the transducer network and adapted to implement implements the method according to the first aspect.

[0104] The present description relates, according to a third aspect, to a method for characterizing a medium by ultrasound, the method comprising:

[0105] - a step of generating a series of incident ultrasonic waves USin in a area of said medium, by means of an array of transducers, said series of incident ultrasonic waves being an emission base i; and

[0106] - a step of generating an experimental reflection matrix Rui(t) defined between the emission base i at the input and a reception base u at the output, the coefficients of this matrix corresponding to the signals received by the transducers induced by the reflected ultrasonic waves.

[0107] The method being characterized in that it further comprises

[0108] - a step of determining a de-scanned reflection matrix R',

[0109] which includes, for a set of midpoints of abscissa x and echo time t,

[0110] responses of the environment calculated by formation of channels according to a model of sound speed c0 from the experimental reflection matrix Ruift), between a virtual input transducer of spatial position rin = (x, zr) and a virtual output transducer of spatial position rout = (x+Ax, zr), both virtual transducers being at the same depth zt, zt being the depth of the isochronous volume expected for the sound speed c0, the isochronous volume being the set of points in the medium contributing to the signals received at time t,

[0111] the responses of the unscanned reflection matrix R' being determined for a set of lateral deviation values Ax comprising at least Ax = 0 and for a set of sound speed models c0,

[0112] said unscanned reflection matrix being formed with each row corresponding to an element of a pair {Ax, c0] which corresponds to a focal spot image and each column corresponding to an element of a pair {x, t}, which is noted:

[0113] - an extraction step in which we determine from each focal spot, an optimal lateral deviation Axopt and an optimal sound speed model Copt, close to the maximum in said focal spot image.

[0114] Thanks to these provisions, the method advantageously makes it possible to locally probe the medium at any point and in any direction relative to a ballistic time of propagation of the ultrasound background in the medium.

[0115] This method provides access to local information about the medium, which makes it possible to characterize the process of focusing the ultrasonic wave locally, and thus to estimate the distribution of sound speed in the medium. This physical parameter is a particularly relevant biomarker in ultrasound imaging because it makes it possible to diagnose certain diseases, such as, for example, liver steatosis.

[0116] This estimation of the speed of sound is also very useful for improving the focusing and quality of the ultrasound image. This optimization of the ultrasound images is performed by calculation without requiring iteration of new emissions and / or acquisitions, which is an important advantage particularly during in vivo measurements.

[0117] In various embodiments of the method, one and / or the other of the following arrangements may optionally be used.

[0118] According to a variant, the method further comprises:

[0119] - a step of forming the ultrasound image by calculating the reflectivity in one plurality of midpoints, from the unscanned reflection matrix R', the reflectivity of each of these midpoints corresponding to the response of the midpoint between the virtual spatial position input transducer rin = (x, zi) and the virtual spatial position output transducer rout= (x+Axopt, zt), zt being the depth of the isochronous volume expected for the optimal sound speed model ^opt and said reflectivity being defined by: j} = A;ropt.(;ï', O, cq = cOi>t (;r. t) {;r,t[)| '

[0120] According to a variant, the ultrasound image is transformed into the depth dimension, using the optimal sound speed model ^opt by: = T^xt = 22 / copt.(x3))'

[0121] in which 2 is the estimate of the depth z of a pixel of the ultrasound image.

[0122] According to one variant, the ultrasound image is displayed on a display device.

[0123] According to a variant:

[0124] - we calculate local sound speeds c(r), for a set of pairs {x, t}, at from the optimal sound speed values C^pt obtained for the focal spot images of said pairs {x, t}.

[0125] According to a variant, the method further comprises a step of forming a local sound speed image of the medium from said set of local sound speeds, and displaying said local sound speed image on a display device.

[0126] According to a variant, a de-scanned reflection matrix R' is recalculated using the local sound speed values.

[0127] According to a variant, the method further comprises, before the extraction step:

[0128] - a spatio-temporal averaging step of the unscanned reflection matrix R' in which the values of the unscanned reflection matrix are locally averaged along the lateral dimension x and the echo time t, for each element of a pair {Ax, Co}, the focal spot images then being averaged.

[0129] According to a variant:

[0130] in the spatio-temporal averaging step, an incoherent point spread function PSFinc is calculated by the following formula: 0) ■■■' ( i Ar, h P [) WOr' — ;r, P -

[0131] for a set of lateral deviation values Ax including at least Ax = 0 and for a set of sound speed model values c0, to obtain the focal spot image for the lateral position x and the echo time t,

[0132] in which:

[0133] <.> is an average operator according to the parameters of the pair {x', t'}

[0134] R' is the unscanned reflection matrix,

[0135] W(x', t') is a spatio-temporal weighting window according to the same pa ramemeters, and

[0136] in the extraction step, a maximum point of the focal spot image is sought corresponding to a maximum of the modulus of the points of the focal spot image, and the optimal sound speed model Copt is the ordinate of said maximum point in said focal spot image.

[0137] According to a variant:

[0138] in the spatio-temporal averaging step, a singular value decomposition SVD of a local focal spot matrix R(1) is calculated, said local focal spot matrix being expressed from the de-scanned reflection matrix R' by: -- xf - / h

[0139] in which:

[0140] R' is the unscanned reflection matrix,

[0141] W(x', F) is a spatio-temporal weighting window according to the same pa meters.

[0142] the singular value decomposition SVD of said local matrix is noted: 0 ' v ; h .r. 0)

[0143] in which

[0144] are the singular values of said local matrix,

[0145] Up are the output eigenvectors,

[0146] Vp are the input eigenvectors,

[0147] we calculate a coherent point spread function PSFcoh by the following formula: FS.Fcoh({eo}, {-F 4) “ ({^3 c0}, {æ, ¢))

[0148] for a set of lateral deviation values Ax including at least Ax = 0 and for a set of sound speed model values c0, to obtain the focal spot image for the lateral position x and the echo time t, and

[0149] in the extraction step, we search for a maximum point of the focal spot image corresponding to:

[0150] a maximum of the modulus of the points of the focal spot image, or at

[0151] a maximum of the modulus of the derivative according to the speed of sound image point codes focal spot, or to

[0152] a maximum of the modulus of the derivative according to the speed of sound encodes the imaginary part of the points of the focal spot image, and

[0153] the optimal sound speed model Copt is the ordinate of said maximum point in said focal spot image.

[0154] According to a variant, at the extraction step, the lateral deviation Axopt is considered to be zero, Axopt = 0.

[0155] According to a variant, in the step of determining a de-scanned reflection matrix R', the de-scanned reflection matrix R' is formed only for lateral deviation values Ax of zero value, Ax = 0.

[0156] According to a variant, in the spatio-temporal averaging step, the values of the unscanned reflection matrix R' are averaged to determine a focal spot image, for each element of a pair {Ax = 0, Az}, according to the lateral dimension x and the echo time t.

[0157] According to a variant, in the extraction step, the optimal sound speed model ^opt is determined from the points of the focal spot image having a lateral deviation Ax of zero value, Ax = 0.

[0158] According to a variant, the calculations of path formations between the virtual input transducer and the virtual output transducer are carried out from the experimental reflection matrix Rui(t), using a forward delay time of the ultrasonic waves between the emission base (i) and the virtual input transducer, and using a return delay time of the ultrasonic waves between the virtual output transducer and the transducers of the reception base (u).

[0159] According to a variant, the unscanned reflection matrix R' is calculated from the experimental reflection matrix Rui by the following formula: "T? Tr 'h 7" » Ai J 1 (-t ~î~ ^4;, 'Uout ; 2')) 'Zj;; J

[0160] in which:

[0161] Nin is the number of elements of the emission base (i)

[0162] Noul is the number of elements of the reception base (u),

[0163] Rui(t) is the experimental reflection matrix, whose

[0164] Rui(uout, iin, t) is the element of the experimental reflection matrix Rui(t) recorded by the spatial position transducer uout following the emission of index iin in the emission base (i), at a time t,

[0165] c0 being the expected speed of sound.

[0166] According to a variant, the unscanned reflection matrix R' is calculated from a focused reflection matrix R by the following formula: qJ. {.r, f} ) ~ R(x 4-

[0167] in which:

[0168] the unscanned reflection matrix R' is formed with each row formed of elements of a pair {Ax, Az} and each column formed of elements of a pair {x, t], and

[0169] the focused reflection matrix R is calculated from the experimental reflection matrix Rui(t) by the following formula:

[0170] in which:

[0171] Nin is the number of elements of the emission base (i)

[0172] Noul is the number of elements of the reception base (u),

[0173] Rui(t) is the experimental reflection matrix, whose

[0174] Rui(uout, iin, t) is the element of the experimental reflection matrix Rui(t) recorded by the spatial position transducer uout following the emission of index iin in the emission base (i) and at time t,

[0175] c0 being the expected speed of sound.

[0176] According to a variant, a film is formed from a succession of ultrasound images by a first number N of iterations of the steps of the method.

[0177] According to a variant, among the N iterations, a second number P strictly less than N of iterations does not include the steps of determining the de-scanned reflection matrix R', the steps of spatio-temporal averaging, and the steps of extracting the optimal sound speed model, and for these P iterations, at the step of forming the ultrasound image, the ultrasound image is obtained from an optimal sound speed extracted during a previous iteration.

[0178] The present description relates, according to a fourth aspect, to a system for ultrasonic characterization of a medium, and configured for the implementation of methods as described previously. The system according to the fourth aspect comprises:

[0179] - an array of transducers adapted to generate a series of ultrasonic waves in incident in an area of the medium, and to record as a function of time the ultrasonic waves backscattered by said area; and

[0180] - a computing unit associated with the transducer network and adapted to implement implements the method according to the first aspect. BRIEF DESCRIPTION OF THE FIGURES

[0181] Other advantages and characteristics of the technique presented above will appear on reading the detailed description below, presented in a non-limiting manner for the purposes of illustration, made with reference to the figures in which:

[0182] Figures 1(a) to 1(d) (already described) illustrate the impact of aberrations in imaging ultrasound, according to the prior art;

[0183] Figures 2(a) to 2(f) (already described) illustrate known transmit / receive sequences for ultrasound imaging and quantification;

[0184] [Fig.3] illustrates usual confocal imaging and matrix imaging;

[0185] [Fig.4] illustrates an example of an ultrasonic characterization system for the implementation implementing methods according to this description;

[0186] [Fig.5] illustrates the definitions used in the method of forming an ultrasound image according to the present disclosure;

[0187] Figures 6(A) to 6(D) illustrate a focusing defect due to a sound speed value error;

[0188] Figures 7(a) to 7(d) illustrate the impact of a sound speed value error on an ultrasound image from simulated ultrasound data;

[0189] Figures 8(al) to 8(a3) show three experimental configurations with different media, a first without an aberrator layer, a second with an aberrator water layer, and a third with an aberrator plexiglass layer;

[0190] Figures 8(bl) to 8(b3) show the ultrasound images obtained without the method of the present disclosure, and corresponding respectively to the middles of Figures 8(al) to 8(a3);

[0191] [Fig.8](c) shows the histogram of the estimated focus defects for the different experimental configurations of Figures 8(al) to 8(a3);

[0192] Figures 8(dl) to 8(d3) show the ultrasound images obtained with a first embodiment of the method which corrects a focus defect, and corresponding respectively to the middles of Figures 8(al) to 8(a3);

[0193] Figures 9(a) to 9(d) illustrate the method of correcting the defocusing error;

[0194] Figures 10(a) to 10(c) show focal spot images (modules) obtained without spatio-temporal averaging in [Fig.l0](a), then with various spatio-temporal averaging variants for the first embodiment of the focus correction method;

[0195] [Fig. 10](d) shows the imaginary part of the space-time averaging variant of [Fig.l0](c);

[0196] [Fig.l0](e) shows an axial evolution curve of the phase of the focal spot image of [Fig.l0](c);

[0197] [Fig. 10](f) shows an axial evolution curve of the imaginary part of the focal spot image of [Fig.l0](c);

[0198] [Fig. 10](g) shows axial out-of-focus search curves on the focal spot images of Figs. 10(b) to 10(d);

[0199] [Fig. 1 l](a) shows an ultrasound image of a liver without the implementation of the method of this disclosure;

[0200] [Fig. 11 ](b) shows a focus defect map (depth deviation / optimal axial) determined by the method of the first embodiment corresponding to the image of [Fig. 1 l](a);

[0201] [Fig. 1 l](c) shows an optimal integrated sound speed map determined by the method of the second embodiment corresponding to the image of [Fig. 11](a);

[0202] [Fig. 11 ](d) shows a local sound speed map obtained from the map of [Fig.ll](c);

[0203] [Fig.l2](a) shows an ultrasound image of a liver without implementing the method of the present disclosure;

[0204] [Fig.l2](b) shows an ultrasound image corrected from the image of [Fig.l2](a) and obtained with the method of the first embodiment;

[0205] Figures 12(c) and 12(d) show enlarged areas of the image of [Fig. 12] (a);

[0206] Figures 12(e) and 12(f) show the same enlarged areas in the corrected image beyond [Fig.l2](b);

[0207] [Fig.l3](a) shows an ultrasound image of a liver without implementing the method of the present disclosure;

[0208] [Fig.l3](b) shows the focused reflection matrix associated with the isochronous volume represented by the gray arc on the ultrasound image of [Fig. 13](a);

[0209] [Fig.l3](c) shows a corrected ultrasound image of the liver of the image of [Fig. 13](a) and obtained by the method of the first focus correction embodiment;

[0210] [Fig.l3](d) shows the focused reflection matrix associated with the isochronous volume represented by the gray arc on the corrected ultrasound image of [Fig. 13] (c);

[0211] [Fig. 13](e) shows the transverse evolution of the focal spot deduced from the focused reflection matrices shown in Figs. 13(b) and 13(d);

[0212] Figures 14(a) to 14(b) show focal spot images (modules) obtained with various spatio-temporal averaging variants for the second embodiment of the sound speed correction method;

[0213] [Fig. 14](c) shows the imaginary part of the focal spot image shown in [Fig.l4](b);

[0214] [Fig.l4](d) shows axial maximum search curves on the focal spot images shown in Figs. 14(a) to 14(c);

[0215] [Fig.l5](a) shows an ultrasound image with the focus defects superimposed (axial / depth deviations obtained);

[0216] [Fig. 15](b) shows a corrected ultrasound image of the liver established from the method of the second embodiment of sound speed correction;

[0217] [Fig. 15](c) shows a corrected and repositioned ultrasound image of the image of [Fig. 15](a) from the method of the second embodiment of sound speed correction;

[0218] [Fig.l6](a) shows an ultrasound image of a liver without implementing the method of the present disclosure;

[0219] [Fig.l6](b) shows the focused reflection matrix associated with the isochronous volume represented by the gray arc on the ultrasound image of [Fig. 16](a);

[0220] [Fig. 16](c) shows a corrected ultrasound image of the liver obtained by the method of the second embodiment of sound velocity correction;

[0221] [Fig.l6](d) shows the focused reflection matrix associated with the isochronous volume represented by the gray arc on the corrected ultrasound image of [Fig. 16] (c);

[0222] In the various embodiments described with reference to the figures, similar or identical elements bear the same references unless otherwise stipulated. DETAILED DESCRIPTION

[0223] In the following detailed description, only certain embodiments are described in detail to ensure clarity of the disclosure, but these examples are not intended to limit the general scope of the principles emerging from the present description.

[0224] The various embodiments and aspects described in the present description may be combined or simplified in multiple ways. In particular, the steps of the different methods may be repeated, interchanged, and / or executed in parallel, unless otherwise specified.

[0225] The present description relates to methods and systems for ultrasonic characterization of a medium, and applies in particular to medical imaging of living or non-living tissues. The medium is for example a heterogeneous medium that one seeks to characterize in order, for example, to identify and / or characterize heterogeneities. Optionally, these methods and systems can be applied to the non-destructive testing of products, such as mineral, metallic or other parts. These characterization techniques are notoriously non-invasive for the medium, which is then preserved.

[0226] [Fig.4] illustrates an example of an ultrasound imaging system 40 for implementing methods of ultrasound imaging of a medium such as a heterogeneous medium 20, according to the present description. This system and method is useful for enabling the formation of an ultrasound image of at least a portion (area of interest or field of view) of the medium. The system 40 comprises at least one array 10 of transducers 11, for example a linear or two-dimensional or matrix array; the transducers are for example ultrasonic piezoelectric transducers which may conventionally be in the form of a rigid bar placed in direct or indirect contact with the medium 20. The transducer array is for example part of a probing device 41 (usually called a probe); the transducer array is connected to a computing unit 42, which may itself be connected or associated with a display device 43; the computing unit emits and records electrical signals to and / or coming from each of the transducers 11. The ultrasonic transducers then transform these electrical signals into ultrasonic waves and vice versa. By "connection" or "link" between the probing device 41, the computing unit 42 and the display device 43, we mean any type of wired connection of the electrical or optical type, or any type of wireless connection using any protocol such as WiFi™, Bluetooth™ or others.These connections or links are one-way or two-way. The associated display device 43 can be of any type, such as a touch or non-touch screen, connected or not.

[0227] The calculation unit 42 is configured for the implementation of calculation or processing steps, in particular for the implementation of method steps according to the present description. By convention, a spatial reference frame of the medium 20 is defined, by taking a first axis X and a second axis Z perpendicular thereto. For simplification, the first axis X corresponds to the transverse direction in which the transducers 11 are aligned for a linear array, and the second axis Z corresponds to the depth of the medium 20 relative to this array 10 of transducers 11. This definition can be adapted to the context and thus for example extended to a three-axis spatial reference frame in the case of a two-dimensional array 10, or to a polar reference frame in the case of a curved array 10, or to any other reference frame adapted and / or dependent on the shape of the array 10 of ultrasonic transducers.Thus, in the remainder of this description, we will use a Cartesian XZ reference frame, corresponding to a linear probe, for simplicity in the description, but a specialist in the field would generalize or apply the results to any type of reference frame.

[0228] In [Fig.4] as in the rest of the description, reference is made to a network of transducers for transmission and reception, it being understood that, in a more general case, several networks of transducers may be used simultaneously. Similarly, a network may consist of one (1) to N translators, of identical type or of different natures. The transducers may be both transmitters and receivers, or only transmitters for some and only receivers for others.

[0229] The transducer array serves, for example, as both a transmitter and a receiver, or is made up of several sub-arrays of transducers, some being dedicated to the transmission, others to the reception of ultrasonic waves. By transducer array, we mean at least one transducer, an aligned or non-aligned sequence of trans- transducers, or a matrix of transducers.

[0230] When in the present description, reference is made to calculation or processing steps for the implementation in particular of method steps, it is understood that each calculation or processing step can be implemented by software, hardware, firmware, microcode or any appropriate combination of these technologies or neighboring technologies. When software is used, each calculation or processing step can be implemented by computer program instructions or code which can be for example interpreted, or executed. These instructions can be stored or transmitted to a storage medium readable by a computer (or computing unit) and / or be executed by a computer (or computing unit) in order to implement these calculation or processing steps.

[0231] Analysis of a point in the middle by focused reflection matrix

[0232] The present description describes methods and systems for ultrasonic characterization of a medium. In practical cases, the medium is assumed to be heterogeneous. These methods and systems are based on definitions represented in [Fig.5]:

[0233] We define in the middle:

[0234] - a first point PI of expected spatial position rin in the spatial reference frame of the middle, and

[0235] - a second point P2 of expected spatial position rout in the spatial reference frame of the medium.

[0236] These spatial positions rin and rout are noted in bold, to signify that these elements are position vectors, vectors taken in the spatial reference frame of the medium (X, Z). Other representations and definitions of the positions of the points are possible and accessible to any ultrasound technician.

[0237] In the present disclosure, the first point PI has a lateral position noted, xin. The second point P2 has a lateral position noted xout. The two points PI, P2 have the same expected depth zin = zout, also noted z which is controlled by the echo time t considered. For a medium of homogeneous sound speed, this depth z would be equal to the expected depth zt = c0t / 2. Thus, the spatial positions of the points PI and P2 are respectively rin = (% / n, z) and rout = (xout, z).

[0238] These two points PI and P2 are chosen at a relatively short distance from each other, that is to say a few millimeters from each other, and for example twenty (20) millimeters or less.

[0239] As shown in [Fig.5], the ultrasonic characterization method implemented by the calculation unit 42 of the system 40 comprises:

[0240] - a step of generating a series of incident ultrasonic waves USin in a area of said medium, by means of an array 10 of transducers 11, said series of incident ultrasonic waves being an emission base i; and

[0241] - a step of generation (construction / measurement) of an experimental reflection matrix rimental Rui(t) defined between the emission base i at the input and a reception base u at the output;

[0242] - a step of determining a focused reflection matrix Rxx(t, z, c0) which includes responses from the medium between a virtual input transducer TVin of spatial position rin and a virtual output transducer TVout of spatial position rout.

[0243] This focused reflection matrix Rxx can be expressed in different ways. In the expressions of the present disclosure, the first point PI of spatial position (xin, z) is taken as a reference. But, these expressions can be established with respect to the second point P2 of spatial position (xout, z) or with respect to a midpoint between PI and P2, of spatial position ((xin+xout) / 2, z) or with respect to any reference point. The technician in the field will be able to make the necessary changes of variables in the expressions presented here.

[0244] The responses of the medium are calculated by forming channels from the experimental reflection matrix RUi(t).

[0245] The responses of the focused reflection matrix R^t, z, c0) correspond to an acoustic pressure field calculated between all the points of the middle of lateral positions xin, and xout, located at the expected depth z and at an echo time t, and for an assumed sound speed c0. In other words, this focused reflection matrix R^t, z, co) is defined by: Rxx(t, z, c0) = [R(xout, xin, t, z, c0)J

[0246] The parameters that are the depth z in the medium, and the speed of sound c0 control the delay laws used in the process of forming paths (i.e. focusing process).

[0247] The emission base i at the input is for example a base of waves each generated by a single one of the transducers 11 of the network 10 or a base of plane waves of angular inclination 0 relative to the X axis or a base of virtual sources, as described previously in the description of figures 2(a) to 2(f).

[0248] The reception base u is for example the base of the transducers 11. Optionally, another reception base can be used for reception, for example a frequency or spectral base.

[0249] Thus, the step of generating the ultrasonic waves is understood between the emission base i and the reception base u. This step of ultrasonic generation is therefore defined for any type of focused or non-focused ultrasonic waves, such as plane waves.

[0250] In the matrix generation step, the experimental reflection matrix Rui(t) is defined between the emission base i at the input and a reception base u at the output. This matrix contains all the temporal responses of the medium, measured at time t by each transducer 11 of spatial coordinate uout and for each emission iin. It is understood that the elements named with the index "in" refer to the emission (i.e. the input) and the elements named with the index "ont" refer to the reception (i.e. the output). This experimental matrix can also be recorded and / or stored, for example in the memory of the computing unit, or on any other medium, removable or not, allowing permanent or temporary storage.

[0251] More precisely, in the step of determining the focused reflection matrix Rxx(t, z, c0), we apply:

[0252] - an input focusing process from the reflection matrix exp rimental Rui(t) which uses a time of flight on the way between the emission base i and the virtual input transducer TVin and which creates a so-called input focal spot around the first point PI of spatial position rin, said input focal spot corresponding to the virtual input transducer TVin,

[0253] - an output focusing process from the reflection matrix exp rimental Rui(t) which uses a return flight time of the waves between the virtual output transducer TVout) and the transducers of the reception base u and which creates a so-called output focal spot around the second point P2 of spatial position rout, said output focal spot corresponding to the virtual output transducer TVout.

[0254] These input and output focusing processes actually form an input-output focusing process, referred to in the remainder of this description as the focusing process.

[0255] In other words, in this ultrasonic characterization method, the virtual input transducer TVin corresponds to an ultrasonic "virtual source" located at the spatial position rin in the medium and the virtual output transducer TVout corresponds to an ultrasonic "virtual sensor" located at the spatial position rout. This virtual source and sensor are spatially separated by the difference of their spatial positions Ar = r out - fin- In the present case, they are simply separated laterally by Ax = xout - xin. Their expected depth is the parameter z used in the focusing law for a sound speed model c0. Their actual depth is dictated by the axial position (in depth) of the isochronous volume, i.e. by the echo time t and by the sound speed distribution c(r) in the medium. The lateral dimension of the virtual transducers is dictated by the focal spot produced by focusing at this actual depth.

[0256] For example, a calculation of the focused reflection matrix Rxx(t, z, Co) of the medium between the virtual input transducer TVin and the virtual output transducer TVout by said input and output focusing processes, is an improved path forming method, which can be expressed by the following simplified formula: i : t ■ CA)) ~ 2viui';oiit . fe,K,rt .- (.toxit * ^out tt"- t Gq})

[0257] (1)

[0258] in which

[0259] Nin is the number of elements of the emission base i,

[0260] Noul is the number of elements of the reception base u at output, t + / (^3ùu GD / ) + 7-ÛW- «ont < R <d)) eSt rélément de la experimental reflection matrix Rui(t) recorded by the transducer uout following the emission iin to which the delay times r and r' have been applied, and - On. £. ) is the delay time or time shift that must be applied at the emission to constructively interfere each incident wave iin at the first focal point of expected spatial position (xin, z) for a sound speed model c0- This time shift is deduced from the outward flight time of the ultrasonic wave between the transducers of the emission base i and the virtual input transducer TVin of expected spatial position rin (first point PI). r(;rfntt.• 'Wont- -, G) ) is the time delay or time shift that must be applied to the signals measured by each output transducer uout to constructively interfere the echoes coming from a diffuser located at the expected spatial position (%o„„ z) for the same velocity model c0. This time shift is deduced from the time of flight on the return of the ultrasonic wave between the virtual output transducer TVout of spatial position rout (second point P2) and the transducers of the receiving base u.

[0261] These delay times r and r' are calculated from a sound speed model. The simplest hypothesis is to assume a homogeneous medium with a constant sound speed c0. In this case, the flight times are directly obtained from the distances between the probe transducers and the virtual transducers.

[0262] For example, in the particular case of a plane wave with an emission angle 0in:

[0263] - the emission delay time r' can be obtained by: sin( / Àn j -r .¾ œsfftj .¾ G) Gj

[0264] in which Zà / co is the time to reach the virtual input transducer.

[0265] - the reception delay time r can be obtained by: y2: - 2 , , , , --Sout V I4:out -ont- ' ('U-out ; «ut ? <'0 / — *t.ofvMout-» ^out « G) / — v................G) G) G) Flight Time Delay

[0266] in which zou / c0 is the time to reach the virtual output transducer.

[0267] Thus, these examples of delay time calculations clearly show that they are a function of the type of wave and the speed of sound, assumed here to be constant in the medium.

[0268] The number of elements of the transmission base Nin is for example greater than or equal to one (1), and advantageously greater than or equal to two (2). The number of elements of the reception base Nout is for example greater than or equal to two (2).

[0269] This improved path-forming formula is therefore a double sum of the time responses recorded in the experimental reflection matrix Rui, a first sum according to the emission basis i translating a focusing at emission and a second sum according to the reception basis u linked to a focusing at reception, this calculation being carried out for the spatial coordinates of the two points PI and P2, that is to say the respective points of expected spatial positions rin = (xin, z) and rout = (x ot(„ z). The result of this improved path-forming formula is therefore a time signal for these two spatial coordinates (rin, rout) or for these two lateral positions xin, xout.

[0270] Such a channel-forming formulation can also be supplemented by input and output weighting terms, often called transmit and / or receive apodization.

[0271] The recorded experimental reflection matrix Rui(t) may be a “real” matrix, i.e. composed of real coefficients in the time domain, the electrical signals recorded by each of the transducers being real numbers. Alternatively, this matrix may be a “complex” matrix, i.e. composed of complex values, for example in the case of demodulation for in-phase and quadrature channel formation (known in English as “IQ beamforming”).

[0272] Thus, it is possible to deduce from this temporal response after channel formation, a line of the ultrasound image of the medium by considering the absolute value of the confocal signals characterized by identical lateral positions at the input and output (xin = xout) and at the ballistic depth z = zt= c0t / 2. Thus, to construct an ultrasound image, one can scan or choose a set of lateral positions x = xin = x out which correspond to a set of lines of the ultrasound image. The ultrasound image J can then be constructed from the diagonal coefficients of the focused reflection matrix, by: T(x, zt) = l(x, tyou Z(xJ) ----- C()£ / 2H (2)

[0273] The axial dimension of the ultrasound image is thus dictated by the time of flight t of the echoes. If the velocity model c0 coincides with the speed of sound in the medium, The ultrasound image illustrates a reliable estimate of the reflectivity of the medium allowing the depth of the diffusers to be assessed.

[0274] However, in real conditions (in-vivo in medical imaging), the sound speed model c0 often does not coincide with the sound speed distribution c(r) in the medium which can also be often heterogeneous or even very heterogeneous. To understand the impact that the mismatch between c0 and c can have, the analogy between the formation of pathways and a digital time reversal experiment can be enlightening. The latter is described in [Fig.6] where we seek to re-propagate by time reversal the wave backscattered by a diffuser 5 in a medium of sound speed c, as illustrated in [Fig.6](a) and [Fig.6](b), in a new medium of sound speed c0-

[0275] If c = c0, the refocusing plane, z = Zf, of the time-returned Fonde coincides with the depth of the diffuser zs and with the position of the isochronous volume, zt = cotH, as shown in [Fig.6](c).

[0276] For c < c0 (or reciprocally c > Co), the focusing of the wave takes place upstream (or reciprocally downstream) at a depth z / , such that: Zf - (3)

[0277] under the paraxial approximation while the isochronous volume associated with the target's time of flight appears downstream (or reciprocally upstream) of the focal plane, at a depth zt, such that: .¾ ~ ” s^eo / c (4)

[0278] Thus the ultrasound image shows the diffuser at the wrong depth (zt zs) and its image is degraded because the wave is totally defocused at the level of the isochronous volume (z. / ^ zi) as can be seen in [Fig.6](d). In other words, the depth of the isochronous volume zt which depends on the flight time t and the speed of sound cO is different from the focusing depth zj of the ultrasonic wave in this specific example.

[0279] [Fig.7] illustrates the impact of a poor sound speed model on the ultrasound image by means of a k-wave simulation of an acoustic phantom (c = 1700 m / s) mimicking the properties of soft tissues (ultrasonic speckle) and presenting echogenic diffusers allowing the contrast and resolution of the image formed to be appreciated.

[0280] If the sound speed model c0 is incorrect, as shown in [Fig.7](b) in which a sound speed c0 of 1850 m / s is used, the scatterers appear at the wrong depth compared to [Fig.7](a) which represents the simulated medium model. Furthermore, the dissociation between the focusing depth z / and the isochronous volume depth zt generates an enlarged and distorted focal spot, hence the poor transverse / lateral resolution of each bright point in this image 7(b).

[0281] Thus, there is an uncertainty for each ultrasound image on the axial dimension of the image which is governed by the echo time t and which makes any distance measurement hazardous. Furthermore, any disagreement between the sound speed model c0 and the actual sound speed distribution c(r) generates significant aberrations on the ultrasound image. The resolution and contrast of the latter are then unsatisfactory for use of the image, in particular in medical imaging.

[0282] To solve these problems, we will consider two methods:

[0283] 1) According to a first embodiment of the method for forming an echo image graphically, we use a first approach which consists of dissociating the depth z of the virtual transducers from the echo time t in order to make the focal plane and the isochronous volume coincide. The coincidence is obtained for each point of the image by optimizing the confocal spot with respect to the parameter z which controls the curvature of the applied delay laws.

[0284] 2) According to a second embodiment of the method for forming an echo image graphic, we use a second approach which consists of varying (scanning) the sound speed model c0. The coincidence between the focal plane and the isochronous volume is obtained by optimizing the confocal spot with respect to the sound speed model c0.

[0285] 1) Compensation for a focus defect / foca position defect lization

[0286] The first approach of the first embodiment of the method for characterizing the medium by ultrasound is for example adapted to the following situation: the imaging of a medium whose tissues have a homogeneous sound speed c and equal to the speed model (c = Co) but whose ultrasound image is degraded by the presence of several layers of tissues of different sound speed cp1 upstream of these tissues; (i) is an index in a plurality of layers, and (l) means layer or "layer" in English.

[0287] [Fig.8] illustrates the problem we are facing. The results of three experiments are reported there. The first experiment in [Fig.8](ai) consists of a reference experiment on an ultrasonic phantom mimicking the acoustic properties of a medium whose effective sound speed is substantially homogeneous (c = 1540 m / s). This phantom contains a random distribution of under-resolved scatterers generating an ultrasonic speckle, such as in a soft tissue (agar-agar in our example), as well as several echogenic scatterers (nylon threads) and a cylinder with acoustic characteristics different from the surrounding speckle (symbolized by the 5 points and the black disk in Figures 8(ai) to 8(a3)).

[0288] In the other two experiments (figures 8(a2) and [Fig.8](a3)), a first aberrator layer is introduced between the transducer network (the probe) and the phantom (the medium).

[0289] In [Fig.8](a2) it is a single layer of water with a uniform sound speed C / = 1480 m / s and in [Fig.8](a3) it is a single layer formed from a plexiglass plate with a uniform sound speed C / = 2690 m / s.

[0290] Although the sound speed pattern c0 coincides with the sound speed in the phantom in the present case, the first layer (water) degrades the resolution of the ultrasound image compared to the reference image, as evidenced by the impaired resolution of the bright spots and the degraded speckle contrast of the corresponding ultrasound image in [Fig.8](b2) compared to the reference image in [Fig.8](bi). Due to a significantly different sound speed than the phantom, the plexiglass plate causes a stronger aberration on the ultrasound image and spurious echoes related to multiple reverberations as represented by the corresponding ultrasound image in [Fig.8](b3).

[0291] To understand the nature of the aberration induced by a layer whose sound speed is different, we take up the analogy of [Fig.6] between channel formation and digital time reversal, and we represent this illustration of the associated reasoning in [Fig.9] in the case of a multi-layer medium (two layers).

[0292] A diffuser s at depth zs is associated with echo time ts = 2. [fe - zi) / c0 + z / ci]

[0293] It therefore appears at depth zt on the image of [Fig.9](c): .¾ - Co^ / 2 + .¾}.¼

[0294] The image of the diffuser is strongly aberrated due to the mismatch between the sound speed model used and the sound speed distribution upstream of the diffuser because of the first aberrator layer C / . Under a paraxial approximation, it is known that the position of the focusing plane is indeed given by: (6)

[0295] with — I —-----I \ Qs UJ

[0296] with Zi the thickness of the first aberrator layer.

[0297] The parameter ^zj can be considered as a defocusing defect represented in [Fig.9](c). Remarkably, the latter does not depend on the position zs of the diffuser in the second layer of the medium if the sound speed model is exact and equal to c0: c =c0.

[0298] To correct this “focusing defect” or in other words focusing position defect, the method of the present disclosure proposes to vary the depth of z focusing independently of the time of flight t while these two parameters are generally intrinsically linked in a classical beamforming process.

[0299] We can then construct a de-scanned reflection matrix R', from the focused reflection matrix R by rearranging the rows and columns to obtain a two-dimensional matrix, for the purpose of easier and less expensive matrix calculations, particularly in terms of their duration, which is an important advantage in the context of real-time or quasi-real-time use of the system. Each column of the de-scanned reflection matrix corresponds to an element of a pair {x, t] and each row corresponds to an element of a pair {Ax, Az}. This new de-scanned reflection matrix is therefore defined by: Ax. Ac}, (xf}C

[0300] In other words, the unscanned reflection matrix R' is expressed in a reference base of the first point PI of spatial position (xin, z„) with xin = x, Zm = zr + Az and with the second point P2 of spatial position (xouf zouf) referenced relative to the first point PI, i.e. xouf = x + Ax, Zout = zt + Az. This expression can also be written in another base, such as that of the second point P2 or of the point located in the middle of PI and P2, or of any other reference point, by a simple change of variable accessible to a technician in the field.

[0301] This de-scanned reflection matrix R' makes it possible to easily extract for each point {x, t} of the medium, a local image of the focal spot in the dimensions {Ax, Az}, with:

[0302] Ax = xoul - xin, the lateral gap between the input and output transducers; and

[0303] Az the defocus value between the depth of focus z and the expected depth zt of the isochronous volume for a medium of sound speed c0.

[0304] Thus, the unscanned reflection matrix R' is constructed from the focused reflection matrix R by: {Ar, A.A. {x, 0) + Ax, x, A .¾ A Ci (8>

[0305] To simplify the expressions, we can introduce a position deviation as the pair comprising the lateral deviation and the depth deviation: Ar = {Ax,Az}.

[0306] We can also construct the unscanned reflection matrix R', directly from the experimental reflection matrix Rui. Thus, the unscanned reflection matrix includes the path-forming calculation of the focused reflection matrix R, and we can note: .R-({Ax,A^}, {xAp <C

[0307] (8')

[0308] In other words, in all cases, the method according to the first embodiment comprises a step of determining a de-scanned reflection matrix R',

[0309] which comprises, for a set of midpoints of abscissa x and echo time t,

[0310] responses of the medium calculated by channel formations from the experimental reflection matrix Rui(t), between a virtual input transducer of expected spatial position rin = (x, z,+AzJ and a virtual output transducer of expected spatial position rout = (x+Ax, zr+Az), the two virtual transducers being located at the same expected depth zt+Az, zt being the depth of the isochronous volume expected for a sound speed c0, the isochronous volume being the set of points of the medium contributing to the signals received at echo time t,

[0311] the responses of the unscanned reflection matrix R' being determined for a set of lateral deviation values Ax comprising at least Ax = 0 and for a set of depth deviation values Az,

[0312] said unscanned reflection matrix R' being formed in such a way that each row corresponds to an element of a coupler = {Ax, Az} which corresponds to a focal spot image and each column corresponding to an element of a pair {x, t}, which is noted: R / = J.rU})]-

[0313] [Fig.l0](a) shows an example of an image which represents the apparent focal spot for a point {x, t} in the field of view which can be visualized from the previous unscanned reflection matrix. This image corresponds to a column of the unscanned reflection matrix R', shown in a two-dimensional image form with the lateral deviation Ax on the abscissa and the depth deviation Az on the ordinate.

[0314] The method further comprises:

[0315] An extraction step in which an optimal position deviation Aroptclose to the maximum in said focal spot image is determined from each focal spot image.

[0316] This optimal position deviation Aropt = {Axopt, Azopt} corresponds substantially to the defect in focusing or a defect in the focusing position of the path formation processes.

[0317] The maximum in the focal spot image is the point in this focal spot image having a maximum modulus value relative to the entire focal spot. This means that this maximum corresponds to the point in this focal spot image with the largest modulus value. By "close to the maximum" we mean that we extract a position close to the position of this maximum point. In fact, we can take a point as close as possible, or for example another point according to different criteria such as a point having a zero lateral deviation Ax (Ax = 0), or another point between these two, or by another criterion of maximum point neighborhood. The neighborhood can be defined for example from a desired spatial resolution.

[0318] This apparent focal spot, for example as illustrated in [Fig.l0](a), is modulated both by the random reflectivity of the medium and noisy by the multiple scattering echoes occurring upstream of the isochronous volume.

[0319] To overcome these speckle problems and to have a more precise estimator of the focal spot and therefore of the focusing quality, an average can be performed on the adjacent speckle grains. For this, we consider a spatio-temporal window of dimension (L„ L,) on which we will average incoherently the focal spot around each virtual transducer of spatial position rin.

[0320] Thus, the method according to the first embodiment may optionally comprise, before the extraction step:

[0321] a spatio-temporal averaging step of the de-scanned reflection matrix R' in which the values of the de-scanned reflection matrix R' are locally averaged, along the lateral dimension x and along the echo time dimension t, for each element of a pair Ar = {Ax, Az}, the focal spot images then being averaged.

[0322] Thus, the spatio-temporal averaging step makes it possible to average or smooth the focal spot image from the de-scanned reflection matrix, in order to more correctly extract the position of the maximum in this image, a position which corresponds to a deviation to be used to correct the calculation of the ultrasound image, as will be explained later.

[0323] This spatio-temporal averaging step can be implemented in various ways, based on various weighted or unweighted averaging formulas, with or without normalization.

[0324] According to a first variant of spatio-temporal averaging, represented in [Fig. 10] (b), we use an incoherent point spread function PSFinc (or “incoherent point spread function” in English) which can be calculated by: / ------------------------------------------------------------(9) PSF,jAr. { <M}) ~ ÿ

[0325] in which

[0326] < > is an average operator, which calculates an average according to the parameters { you}

[0327] W(x', t') is a spatio-temporal weighting window.

[0328] For example, the spatio-temporal weighting window is of rectangular type, of

[0329]

[0330]

[0331]

[0332]

[0333]

[0334]

[0335]

[0336]

[0337]

[0338] Hanning type or Gaussian type. The rectangular spatio-temporal weighting window can be defined by: W(x\ t') = 1 for l%'l < L / 2 and It'l < L / 2, and (10) W(x\t') = 0 otherwise The previous incoherent point spread function PSFinc provides for a set of lateral deviation values Ax including at least Ax = 0 and for a set of depth deviation values Az, denoted in the form of the pair Ar = {Ax, Az}, values corresponding to a focal spot image for the lateral position x and the echo time t. This focal spot image is smoothed of speckle and multiple scattering effects, as shown in [Fig.l0](b). The depth position of the maximum of this focal spot image, Azopt, constitutes a first relevant estimator of the defocusing error Azj sought in equation 7. In this case, the position of the maximum in the depth direction, Azopt, can be estimated by the position of the maximum of the modulus of the point spread function PSFinc. More generally, the position of the maximum Aropt(inc) can be estimated by the position of the maximum of the modulus of the point spread function PSFinc. ! . ....... , (11) Ar..,A ' / ! — argrnax l / SLit / Ar. jxA] H With a. __ / a Thus, the maximum position deviation Aropr (inc) can be extracted by this same formula 11, i.e. the maximum position in the focal spot image (focal spot image by spatio-temporal averaging). This maximum position corresponds to the defect in focusing or defect in focusing position by the processes of formation of pathways, due to variation of the speed of sound in the medium, i.e. medium presenting inhomogeneities in the speed of sound of the different tissues composing it. In this way, during the extraction step, a maximum point of the focal spot image is sought corresponding to or close to a maximum of the modulus of the points of the focal spot image calculated by the incoherent point spread function, and the optimal position deviation Aropt is the position of said maximum point in said focal spot image, or a position close to this maximum point, as explained previously. Note that in practice it is not always necessary to calculate or prepare the complete image of the focal spot, and in particular it is often not necessary to scan the points following the transverse direction Ax, since the maximum is a priori located on the axis A%= 0 or very close to this axis A%= 0. Indeed, to estimate the defect of focus in the direction of depth, Az, one can be satisfied with studying the axial evolution of the confocal spot, that is to say for a set of points with Ax = 0, ie for only spatial positions xin = xoul as illustrated by the first curve G1 of [Fig.lO](g) which represents the evolution of the values of the focal spot image of [Fig. 10](b) on the axis Ax= 0.

[0339] This estimator is however biased by an incoherent background highlighted by a relatively weak contrast as is visible in [Fig.l0](b) and generates a spread of the peak of the first curve G1 of [Fig.l0](g).

[0340] According to a second variant of spatio-temporal averaging, the confocal spot can be extracted coherently by intelligently recombining the apparent focal spots obtained on each VE window. This makes it possible to obtain a more precise measurement of the depth difference Az, and more generally of the position difference Ar.

[0341] This recombination is carried out in practice using a singular value decomposition SVD of a local matrix of focal spots, Rw({.z, Q) [R(Ar. - x.tf - £)]

[0342] considered for each space-time window W(x, t), and which is expressed by: (12) P

[0343] in which the singular values Xp are arranged for example in decreasing order.

[0344] Each of the singular values Xp is associated:

[0345] - to an output eigenvector {.r. flp defined in a basis focused de-scanned (Ar), and

[0346] - to an input eigenvector VAb; t}) --U t'}, {.r, defined in the conventional focused base, i.e. the pixel base of the ultrasound image.

[0347] Among these eigenvectors, the first eigenspace is of particular interest since:

[0348] (i) the coefficients of Vi({%, t]) directly give the phase shift to be applied on each speckle grain at {x', t'} to put them back in phase;

[0349] (ii) the vector Ui({%, t}) gives the coherent confocal spot resulting from the phase recombination of each apparent focal spot measured around each point {x', t'}:

[0350] Then, a coherent point spread function PSFcoh (or “coherent point spread function” in English) which can be calculated using: {;r. 0) - F{(Ar; {æ, 0) (13)

[0351] Each coherent confocal spot PSFcoh(Ar, {x, / } ) precisely quantifies the focusing process at each point {x, t} of the acoustic field. Due to its coherent nature, this coherent point spread function PSFcoh makes it possible to obtain an image with a much better contrast as illustrated by the image in [Fig.l0](c) (corresponding to the amplitude of the coherent point spread function PSFcoh) than an incoherent average of the confocal spots as illustrated by the image in [Fig.l0](b). The singular value decomposition SVD defined by equation 12 makes it possible to recombine each focal spot by compensating the phase of each speckle grain at the point {x', t'}. In doing so, echoes linked to scattering events outside the focusing point {x, t} are drastically reduced.

[0352] As previously realized from the incoherent point spread function PSFinc (see equation 12), a new estimator of the defocusing error can be constructed by considering the value of the depth deviation Az maximizing the amplitude of the coherent point spread function PSFcoh and illustrated on the curve G2 in [Fig.lO](g).

[0353] More generally, we consider the position of the maximum zJropt (coh) of the coherent point spread function by: [xf) = argmax (|FSF4h(Ar.

[0354] The uncertainty of the estimator is for example given (in the direction of the depth) by the ratio between the depth of field of the imaging system and the square root of the number of speckle grains Ns covered by the spatio-temporal window VF, i.e.: 2A (15)

[0355] More generally, we can extract the maximum position deviation Aropt = {Axopr, Azopr] by this same formula 14, that is to say the position of the maximum in the focal spot image (focal spot image by spatio-temporal averaging). This position of the maximum corresponds to the defect in focusing or defect in focusing position by the processes of formation of paths, induced by the non-homogeneity of the speed of sound in the medium.

[0356] In this way, during the extraction step, a maximum point of the focal spot image is sought corresponding to or close to a maximum of the modulus of the points of the focal spot image calculated by the point spread function. coherent, and the optimal position deviation Aropt is the position of said maximum point in said focal spot image, or a position close to this maximum point, as explained previously.

[0357] According to a third variant of the spatio-temporal movement, one can also use the information contained in the phase of the coherent confocal spot as illustrated in [Fig.lO](d) for example by examining the imaginary part of the coherent point spread function PSFcoh. This makes it possible to obtain a more precise estimator of the depth deviation Az, and more generally of the position deviation dr.

[0358] The phase of the confocal spot indeed presents a phase jump of at the level of the focusing plane as visualized in [Fig.l0](e) which represents the phase of the coherent point spread function PSFcoh on the axcdx= 0. The coherent confocal spot indeed accumulates the Gouy phase jumps (~ x / 2 in a 2D configuration) induced by the focusing processes at the input and output. These Gouy phase jumps result at the depth z + Azj where the transverse confinement of the focused waves is minimal. It therefore constitutes a more reliable estimator of the defocusing error than the modulus of the coherent point spread functions PSFcoh or the incoherent point spread function PSFinc as can be seen on the curve G3 in [Fig.l0](g) which are also sensitive to the geometric decay of the focused wave.To increase the sensitivity of the method, one can also combine the two previous observables, the modulus and the phase of the coherent point spread function PSFcoh, by examining the imaginary part of this function (see curve in [Fig. 10](f) which represents the imaginary part of the coherent point spread function PSFcoh on the axis Ax= 0). Its inflection point, i.e. the maximum of its axial derivative or derivative along the depth direction Az, provides a new estimator of the optimal depth deviation Azopt (see curve G4 in [Fig. 10] (g)).

[0359] This estimator can be generalized by searching for the maximum of the modulus of the complex derivative of the point spread function PSFcoh: Ar

[0360] According to an uncertainty calculation, this estimator significantly improves the determination of Az by a factor v / g, i.e. approximately ~ 2.5 compared to ? of equation 15.

[0361] [Fig.8](c) shows the histogram of the estimated Azopt out-of-focus errors for the three experiments described in [Fig.8](a). While the reference experiment results in an out-of-focus estimate close to zero (0), Azopt is close to its expected value, whether for the water layer (Azopt = -1.4 mm) or for the plexiglass plate (Azopt = +5.5 mm).

[0362] The dispersion of the estimated values of the defocusing defect highlighted by [Fig.8](c) is linked to the paraxial approximation used to establish equation 7 and which is not strictly verified in the experiments of [Fig.8](a).

[0363] More generally, we can extract the maximum position deviation Aropt = {Axopr, Azopr} by this same equation 16. that is to say the position of the maximum in the focal spot image (focal spot image by spatio-temporal averaging). This position of the maximum corresponds to the defect in focusing or defect in focusing position by the processes of formation of paths, because of variation of the speed of sound in the medium.

[0364] In this way, during the extraction step, we search for a maximum point of the focal spot image corresponding to:

[0365] - a maximum of the modulus of the points (values) of the focal spot image, or at

[0366] - a maximum of the modulus of the derivative along the depth direction (direction axial) of the points (values) of the focal spot image, or to

[0367] - a maximum of the modulus of the derivative along the depth direction (direction axial) of the imaginary part of the points (values) of the focal spot image.

[0368] The optimal position deviation Aropt is the position of the maximum point in said focal spot image, or a position close to this maximum point, as explained previously.

[0369] The optimal position deviation Aropf or the optimum depth deviation Azopt can be used to obtain a new, correctly focused ultrasound image, i.e. with correction of the focusing position defect:

[0370] - either from the focused reflection matrix R: ZJ.rA) = \R(x + + A3opt(aU))| <17)

[0371] - either directly from the unscanned reflection matrix R': Zi(;r, f) ~ ^(Ar ~ Aropt(;r. ü).

[0372] Or if we consider that Axopl = 0 or has a negligible value, by: Zi (.r, t) = R' ( ( Aæ = 0. = A^,pt (x. t)}. {;r, t} ) i

[0373] The optimal position deviation Aropf can be advantageously exploited with its two components, as expressed in equation 17 above.

[0374] Thus, the method according to the first embodiment of the method may further comprise:

[0375] a step of forming an ultrasound image by calculating the reflectivity at a plurality of points in the medium, from the unscanned reflection matrix R', the reflectivity of each of these points in the medium corresponding to the response of the medium between the virtual spatial position input transducer rin = (x, zt+Azopù and the virtual spatial position output transducer rout= r + Aropt = (x+Axopt, zt+Azopt), and said reflectivity being defined by: i) = = âr1)pt(x £). OA '

[0376] The ultrasound image presented above is parameterized as a function of the lateral position x and the echo time t.

[0377] This ultrasound image can be transformed to be parameterized according to the lateral position x and the depth z by using the sound speed model c0 to replace the echo time t. This transformation consists of a change of variables or parameters. The resulting image is identical, but with dimensions in distances as usually used, and on which the practitioner can make measurements of the sizes of structures. Then, the ultrasound image is of the type: Ai (æ. ) — Ai f — -A / Ai) '

[0378] in which zt is the depth of a pixel of the ultrasound image or depth of the isochomic volume.

[0379] Either of the preceding ultrasound images may be displayed on the display device 43.

[0380] According to a variant, a film is formed of a succession of ultrasound images by a first number N of iterations of the steps of the method. Thus, the method is iterated to form ultrasound images at a predetermined rate, and to visualize a substantially real-time evolution of the ultrasound image of the medium.

[0381] According to a variant:

[0382] - among the N iterations, a second number P less than N of iterations does not include do not take the steps of determining the unscanned reflection matrix R', the steps of spatio-temporal averaging, and the steps of extracting an optimal position deviation, and

[0383] for these P (particular) iterations, at the stage of forming the ultrasound image, the ultrasound image is obtained from an optimal position deviation extracted during a previous iteration.

[0384] Thus, for a number P of iterations, the calculations of the steps of determining the unscanned reflection matrix R', the spatio-temporal averaging steps, and the steps of extracting an optimal position deviation are advantageously avoided. The method of this variant requires fewer computing resources and / or time while providing a film of a succession of high-quality ultrasound images. Thanks to this arrangement, the rate of determining the ultrasound image can be decoupled from the rate of calculating the optimal position deviation. Thus, it is possible maintain a high ultrasound image rate despite a reduced number of calculations.

[0385] Furthermore, the previous calculations of the method according to the present description can be carried out only in the axial direction (depth direction z). Thus, in the extraction step, an optimal position deviation Aropt = {Axopl, Azopt} is determined. In the present case, it is possible to limit oneself to determining only the second component of the optimal position deviation, in depth, i.e. the depth deviation Azopt. Thus, according to this variant, it is considered that the first component of the optimal position deviation, i.e. the lateral deviation Axopt is zero, Axopt = 0. This makes it possible to simplify the calculation of the ultrasound image and to reduce the overall cost in time and resources.

[0386] Similarly, in the step of determining a de-scanned reflection matrix R', the de-scanned reflection matrix R' can be formed only for lateral deviation values Ax of zero value, Ax = 0. This avoids calculating a complete de-scanned reflection matrix, which greatly reduces the overall cost in time and resources of calculating this de-scanned reflection matrix, but it also reduces the cost of calculating the steps of the method after this step of determining the de-scanned reflection matrix.

[0387] Optionally, at the spatio-temporal averaging step, one can limit oneself to averaging the values of the unscanned reflection matrix R' along the lateral dimension x and along the echo time dimension t, to the elements of the pairs {Ax = 0, Az} of the focal spot images whose lateral deviation Ax is zero (Ax = 0). Thus, the number of averaged focal spot images to be calculated is reduced, and the cost of the calculation is reduced.

[0388] Furthermore, in the extraction step, the optimal depth deviation Azopt can be determined from the points or values of the focal spot image having a lateral deviation Ax of zero value, Ax = 0. Thus, the optimal lateral deviation Axopt is zero, and the optimal depth deviation Azopt has a value determined only with the points of a curve of the focal spot image corresponding to a zero lateral deviation. Thus, the determined optimal spatial position Aropt is slightly different from that of the maximum of the focal image, but remains close to it because in essence the lateral deviation must be small. The computational cost of this variant is thus advantageously very reduced.

[0389] The ultrasound images corresponding to the results of the method of the present description, correcting the defect in focus or defect in the position of the focusing plane, are illustrated in [Fig.8](d). In the case of the first layer of water, the corrected ultrasound image is represented in [Fig.8](d2). This ultrasound image regains the resolution of the reference image of [Fig.8](di), that is to say the ultrasound image obtained without this first layer of aberration. The application of a single correction on the curvature of the focusing laws (which is achieved by present correction) allows the entire ultrasound image to be corrected. The same effect is observed in the case of the first plexiglass plate layer in [Fig.8](d3). This result is spectacular when comparing this corrected ultrasound image to the initial image in [Fig.8](b3). Note, however, that the present correction of the focus defect does not, however, allow the reverberations induced by the first aberrant layer to be fully compensated.

[0390] The results of corrections of the ultrasound images in [Fig.8] are interesting from an academic point of view but they remain limited because these cases only consider a translation-invariant aberrator layer. [Fig. 11] presents an in-vivo ultrasound imaging experiment on a liver in which a natural irregular arrangement of adipose and muscular tissues, and other vessels, alters the quality of the ultrasound image (see [Fig.ll](a)). The method described previously is extended to the case of a curved probe, which amounts to replacing the Cartesian coordinates (x, z) by polar coordinates (0, r). [Fig.ll](b) presents a mapping of the estimated defocusing error at each point of the image, i.e. a mapping of an axial position deviation Ar calculated with the method. Unlike the previous experiments in [Fig.8], this defocusing is not homogeneous over the field of vision.This is particularly related to the lateral (polar AB) variations of the sound speed in the aberrator layers which result in a fairly large lateral variation of the defocusing. The axial variation of the defocusing in the liver is related to the disagreement between the sound speed model c0 and the effective sound speed c in the liver.

[0391] Finally, the above method can be completed to further determine an integrated sound speed Copi from the optimal depth deviation Azopt, from the optimal position Zlropt= {Axopt, Azopt}, by:

[0392] This integrated sound speed corresponds to an average sound speed between the transducer array and the depth of the isochronous volume. This integrated sound speed can be determined for any pair {x, t}, i.e. for any focal spot image, i.e. for any point in the middle or any point of an ultrasound image.

[0393] The local sound speeds c(r) can then be calculated for a set of pairs {x, t], from integrated sound speed values Copt obtained for the focal spot images of the pairs {x, t}. This calculation, allowing the local sound speeds to be deduced from an integrated sound speed field, is generally carried out by an inversion method. An example of an inversion method of this type will be described in more detail later, at the end of the description concerning the second embodiment of the method, more specifically dedicated to the more precise determination of a sound speed model (integrated sound speed model).

[0394] The method may then further comprise a step of forming a local sound speed image of the medium from the set of previously determined integrated sound speeds, and a step of displaying the local sound speed image on the display device 43. This local sound speed image is important for the practitioner, because it is useful for, associated with other information, identifying certain pathological states or diseases, such as fatty liver.

[0395] Having obtained a local sound speed field, it is then possible to iterate the method described above in order to obtain a more precise ultrasonic characterization of the medium, by recalculating a de-scanned reflection matrix R' using the local sound speed values determined in a previous step.

[0396] As described above for this first embodiment of the method, each pixel of the ultrasound image can be corrected from the locally estimated defocus (see equation 17). The result is shown in [Fig.12]. The corrected image of [Fig.l2](b) advantageously shows a gain in terms of contrast and resolution compared to the initial image of [Fig.l2](a). Veins that are difficult to discern in the initial image are clearly revealed after local correction of the defocus on all or part of the pixels of the image. The correction of transverse aberrations is also quantified in [Fig. 13] which shows an example of focused reflection matrices, for illustrative purposes, before and after correction. While initially the backscattered energy extends well beyond the diagonal of the focused reflection matrix Rxx shown in [Fig.l3](b), the out-of-focus compensation "brings back" most of the backscattered energy to the diagonal of the focused reflection matrix Rxx as illustrated in its representation in [Fig.l3](d). This is confirmed by studying the transverse spread of the incoherent point spread function PSFinc before and after out-of-focus compensation as illustrated by the curves in [Fig.l3](e).

[0397] The method presented is particularly effective in compensating for axial aberrations (along the depth direction) of an ultrasound image. However, it does not allow the diffusers to be perfectly relocated to their actual depth; the axial direction of the image remains dictated by the flight time t of the echoes, such that zt = c0t / 2. To this end, the following section proposes to no longer scan the curvature of the focusing laws to determine a focusing defect, but to directly scan the sound speed model in order to map the latter and thus reposition each diffuser to its actual depth on the ultrasound image. 2) Sound speed tomography

[0398] The second approach of the second embodiment of the method for characterizing by ultrasound a medium consists of varying the sound speed c0 of the sound speed model. We then construct a focused reflection matrix Rxx,t(c0) at the ballistic depth zt comprising the different sound speed models c0. The approach is therefore similar to that of the first approach, with the variation of the sound speed model parameter c0, and a technician in the field will be able to take over and adapt the calculation methods.

[0399] Similar to equation 1, this focused reflection matrix can be written by removing the depth parameter z, since now this depth is adjusted to the expected depth of the isochronous volume zt: z—* ” ' ' ' ....... ....... ' ' ' ..... ' ' (18)

[0400] A de-scanned reflection matrix R' can thus be constructed from the focused reflection matrix R, by rearranging the rows and columns of this matrix to obtain a two-dimensional matrix for easier matrix calculations. Each column of the de-scanned reflection matrix corresponds to an element of a pair {x, t} and each row corresponds to an element of a pair {Ax, c0}. Each row of the de-scanned reflection matrix thus corresponds to a focal spot image. This new de-scanned reflection matrix R' is therefore defined by: R' c0}, {4,0)] <19)

[0401] In other words, this unscanned reflection matrix R' is expressed in / according to a reference base of the first point PI of spatial position rin = (xin, Zm) where xin = % and and with the second point P2 of spatial position rout = (xouf, zout), with = x + Ax. We also have zin = zout = zt. This expression can also be written in another base, such as that of the second point P2 or the midpoint or any other reference point, by a simple change of variable.

[0402] This de-scanned reflection matrix R' makes it possible to simply extract for each point {x, t} of the medium, a local image of the focal spot along the dimensions {Ax, c0}, with:

[0403] Ax = xout - xin, the lateral gap between the input and output transducers; and

[0404] c0 the value of the sound speed model.

[0405] Thus, the unscanned reflection matrix R' is constructed from the matrix of focused reflection R (using equation 18) by: ^({Aæ. co E jax / )) ~.H(æ 4' Az, 4, t. en)

[0406] This unscanned reflection matrix R' contains a set of apparent focal spots for each speckle grain {x, t}.

[0407] One can also construct the unscanned reflection matrix R', directly from the experimental reflection matrix Rui. Thus, the unscanned reflection matrix includes the path-forming calculation of the focused reflection matrix R, and can be noted: R' ( { Ci)}, { x, t} ) “ •r;......— 52 «in 3 + A, Ci) + r(;r + Ax. c0))

[0408] In other words, the method according to this second embodiment comprises a step of determining a de-scanned reflection matrix R'.

[0409] which includes, for a set of midpoints of abscissa x and echo time t,

[0410] responses of the medium calculated by channel formations following a sound speed model c0 from the experimental reflection matrix Rui(t), between a virtual input transducer of spatial position rin = (x, zi) and a virtual output transducer of spatial position rout = (x+Ax, zi), the two virtual transducers being at the same depth zt, zt being the depth of the isochronous volume expected for the sound speed c0, the isochronous volume being the set of points of the medium contributing to the signals received at time t,

[0411] the responses of the unscanned reflection matrix R' being determined for a set of lateral deviation values Ax comprising at least Ax = 0 and for a set of sound speed models c0,

[0412] said unscanned reflection matrix being formed with each row corresponding to an element of a pair {Ax, c0] which corresponds to a focal spot image and each column corresponding to an element of a pair {x, t], which is noted: R-

[0413] This unscanned reflection matrix R' makes it possible to obtain an image which represents the apparent focal spot for a point {x, t} of the field of vision. This focal spot image corresponds to a column of the unscanned reflection matrix R', shown in the form of a two-dimensional image with the lateral deviation Ax on the abscissa and the sound speed model c0 on the ordinate.

[0414] The method further comprises:

[0415] - an extraction step, in which we determine from each focal spot, an optimal lateral deviation Axopt and an optimal sound speed model Copt close to the maximum in said focal spot image.

[0416] The optimal sound speed model Copt then corresponds to a sound speed model close to the sound speed distribution in the medium studied.

[0417] This optimal sound speed model is advantageously much closer to the (actual) sound speed of the medium than the commonly used assumption of a constant sound speed in the medium.

[0418] The maximum in the focal spot image is the point of this focal spot image having a maximum value modulus relative to the entire focal spot. This means that this maximum corresponds to the point of this focal spot image with the largest value in modulus. By "close to the maximum", we mean that we extract a point close to this maximum point. In fact, we can take a point as close as possible, or for example another point according to different criteria such as a point having a zero lateral deviation Ax (Ax = 0), or another point between these two, or by another criterion of maximum point neighborhood. The neighborhood can be defined for example from a desired spatial resolution and / or a desired sound speed resolution.

[0419] As in the first embodiment of the method, this apparent focal spot is modulated due to the ultrasonic speckle problem and multiple scattering. A statistical average of these focal spots is performed in a similar manner over a spatio-temporal window of dimension (Lx, F).

[0420] Thus, the method according to the second embodiment also comprises:

[0421] - a spatio-temporal moving step of the unscanned reflection matrix R' in which the values of the unscanned reflection matrix are locally averaged along the lateral dimension x and the echo time dimension t, for each element of a pair {Ax, c0}, the resulting focal spot images then being averaged.

[0422] This spatio-temporal averaging step makes it possible to correctly average or smooth the focal spot image from the de-scanned reflection matrix, in order to more correctly extract the position of the maximum in this image, a position which corresponds to the lateral deviation and the sound speed model to be used to correct the calculation of the ultrasound image.

[0423] This spatio-temporal averaging step can be implemented in various ways, based on various weighted or unweighted averaging formulas, with normalization or without normalization.

[0424] According to a first variant of spatio-temporal averaging, the intensity of the unscanned reflection matrix is locally averaged by calculating the incoherent point spread function PSFinc on virtual input transducers {x', t'} around the point of interest {x, t], for example by the following expression: {;T3}) - ÿ{|.E'({AÆ. Q)}. -

[0425] (20)

[0426] in which:

[0427] <.> is an average operator according to the parameters of the pair {x', t'}

[0428] R' is the unscanned reflection matrix,

[0429] W(x', t') is a spatio-temporal weighting window according to the same pa meters.

[0430] The spatio-temporal weighting window may be of any type as defined in the presentation of the first embodiment.

[0431] This incoherent point spread function provides for a set of lateral deviation values Ax including at least Ax = 0 and for a set of sound speed model values c0, values corresponding to a focal spot image for the lateral position x and the echo time t.

[0432] The incoherent point spread function PSFinc obtained from the k-wave simulation data shown in [Fig.7] of the first embodiment of the method is now illustrated for the second embodiment of the method in [Fig.l4](a).

[0433] The position of the maximum of the incoherent point spread function PSFinc, defined by P57Ln.,( { Ar, ey} {;r. t} ) ' gives at its ordinate an estimator of the integrated speed of sound ie ...fine) f ,x L.pi: FL O at each point {x, t} of the spot image focal length. The abscissa position of this maximum gives an optimum lateral shift. In [Fig.l4](d) is represented a DI curve showing the evolution of the incoherent point spread function for a zero lateral deviation, i.e. Ax = 0; that is to say the evolution of the point spread function on the axis Ax = 0.

[0434] Note that in practice, as for the first embodiment, it is not always necessary to calculate or prepare the complete image of the focal spot image, and it is often not necessary to scan the points along the lateral / transverse direction Ax, since the maximum is a priori located on the axis i% = 0. We can simply study the axial evolution of the confocal spot, i.e. for Ax = 0, which is equivalent to xin = xoul to estimate the integrated speed of sound as represented by the curve DI of [Fig.l4](d) which represents the evolution of the values of the focal spot on the axis i% = 0.

[0435] In this first variant, at the extraction stage, a maximum point of the focal spot image is sought corresponding to a maximum of the modulus of the points of the focal spot image, and the optimal sound speed model Copt is the ordinate of said maximum point in said focal spot image. The abscissa of the maximum point in the focal spot image is then the optimal lateral deviation Axopt, equivalently to the first embodiment.

[0436] Then, we obtain the coordinates of the maximum point in the focal spot image by: -argmax(PSFinc(^^{x^ <21>

[0437] The optimal sound speed model Copt can be extracted from this formula 21, which corresponds to the value of the ordinate of the maximum point in the image of the focal spot produced (focal spot image by spatio-temporal averaging).

[0438] In this way during the extraction step, a maximum point of the focal spot image is sought corresponding to a maximum of the modulus of the points of the focal spot image, and the optimal sound speed model Copt is the ordinate of said maximum point in said focal spot image.

[0439] Optionally, we extract from the maximum point in the image of the focal spot, its abscissa and its ordinate, that is to say respectively the optimal lateral deviation Axopl and the optimal sound speed model Copt.

[0440] According to a second variant of spatio-temporal averaging, the intensity of the unscanned reflection matrix R' is locally averaged by a calculation of the coherent point spread function PSFcoh. This makes it possible to provide a better estimate of the sound speed model, which is an integrated sound speed model P.

[0441] For this, as in the first embodiment, a singular value decomposition SVD of a local matrix of the focal spots is carried out, by the following expression: W - .....' and

[0442] we obtain an expression similar to the previous equation 13.

[0443] The output eigenvectors are then:

[0444] The first output eigenvector, Ui({%, t}) = [Ui({A%, c0], {x, t})] directly gives the evolution of the coherent focal spot with respect to the model sound speed c0 around each point {x, t}, that is: A)}- {«; 0) = ÎAc0}?

[0445] A new estimator of the integrated velocity can be derived from the maximum of the coherent spreading function, i.e. by: £). t)} ~ argmax A' 0 )Ü f<'o,A;

[0446] More generally, the optimal sound speed model can be extracted by formula 23, thanks to the position of the maximum in the image of the focal spot (image of the focal spot by spatio-temporal averaging). ​

[0447] In this way, during the extraction step, a maximum point of the focal spot image is sought corresponding to a maximum of the modulus of the points of the focal spot image, and the optimal sound speed model Copt is the ordinate of said maximum point in said focal spot image. The abscissa of the maximum point in the focal spot image is then the optimal lateral deviation Axopt.

[0448] The focal spot image obtained by the coherent point spread function PSF coh is shown in [Fig.l4](b). This image advantageously has better sensitivity than that obtained by the incoherent point spread function of [Fig.l4](a).

[0449] Indeed, the precision of this estimator of the integrated speed of sound is inversely proportional to the second derivative of the point spread function PSF around its maximum following c0, that is to say: _ , PSF({Ar - 0, / p - (24) ,ix O.co AA})

[0450] Figure 14(d) shows the values of the focal spot images for zero lateral deviation, i.e. Ax = 0, of Figures 14(a) to 14(c). In particular, the curve DI of Figure 14(d) corresponds to the evolution of the values of the point spread function PSFinc at zero lateral deviation of Figure 14(a). The curve D2 corresponds to the evolution of the values of the coherent point spread function PSFcoh at zero lateral deviation of Figure 14(b). We note the sharper or tighter character of this last curve of the coherent confocal spot around its maximum. In other words, the curve D2 has a greater curvature at its maximum point and with a greater signal-to-noise ratio, which is representative of a better estimation accuracy of the integrated sound speed with this estimation variant: ---(cob).

[0451] According to a third variant of the spatio-temporal averaging, the axial derivative of the coherent point spread function PSFcoh is considered as represented in figure 14(c), which makes it possible to obtain an even more reliable estimator of the integrated sound speed g. The double phase jump of Gouy at the focal plane is exploited. For this, a new estimator of the integrated sound speed can be constructed from the maximum of the axial derivative of the coherent point spread function PSFcoh, that is to say by: {' ù- " argmax (MV1 PSE^({Ax. c0 {-, -^.0^) ^25^ b-4q

[0452] This estimator constitutes an excellent estimator of the position of the focal plane, as illustrated by curve D3 of [Fig.l4](d). The second derivative of this observable around its maximum is in fact much larger than that of the modulus of the coherent point spread function PSFcoh and the modulus of the incoherent point spread function PSFinc.

[0453] More generally, the optimal sound speed model can be advantageously extracted using formula 25, thanks to the position of the maximum in the image of the focal spot (image of the focal spot by spatio-temporal averaging).

[0454] In this way, during the step of extracting an optimal sound speed model, a maximum point of the focal spot image is sought corresponding to:

[0455] - a maximum of the modulus of the points (values) of the focal spot image, or at

[0456] - a maximum of the modulus of the derivative according to the speed of sound c0 of the points (of the values) of the focal spot image, or to

[0457] - a maximum of the modulus of the derivative according to the speed of sound c0 of the part imaginary points (values) of the focal spot image.

[0458] The optimal sound speed model Copt is then the ordinate of said maximum point in said focal spot image.

[0459] The value of the optimal (integrated) sound speed model can be used to obtain a new corrected ultrasound image, i.e. with a correction of the sound speed model:

[0460] - either from the focused reflection matrix R: ZafxA)

[0461] - either from the unscanned reflection matrix R':

[0462] Optionally, it is possible to use both coordinates (abscissa and ordinate), i.e. the optimal lateral deviation Axopt and the optimal sound speed model Copt. The ultrasound image is then obtained:

[0463] - either from the focused reflection matrix R: ZaÙr.Zj (.:c 4- A.zy)pt(.r, t), x.

[0464] - either from the unscanned reflection matrix R': ZaÛL / ) ~A;r ~ (xp)}, {4.

[0465] Thus, the method of the present disclosure also comprises:

[0466] a step of forming the ultrasound image by calculating the reflectivity at a plurality of points in the medium, from the unscanned reflection matrix R', the re reflectivity of each of these points of the medium corresponding to the response of the medium between the virtual spatial position input transducer rin = (%, z,) and the virtual spatial position output transducer rout= (x+Axopl, zt), zt being the depth of the isochronous volume expected for the optimal sound speed model Copt and said reflectivity being defined by: 7), in = t)}, 7})^ '

[0467] The ultrasound image above is parameterized according to the lateral position x and the echo time t.

[0468] This ultrasound image can be transformed to be parameterized according to the lateral position x and the depth z, using the sound speed model Copt to replace the echo time t. This transformation is a change of variables or parameters. The resulting image is identical, but with dimensions in distances as usually used, and on which the practitioner can make measurements of the sizes of structures. Then, the ultrasound image is of the type: ÏPx, 2) = r2(x, t = 2i / c opt ix, t)) (26)

[0469] in which Z is the depth of a pixel of the ultrasound image and the estimated depth of the isochomic volume.

[0470] Either of the preceding ultrasound images may be displayed on the display device 43.

[0471] According to a variant, a film is formed of a succession of ultrasound images by a first number N of iterations of the steps of the method. Thus, the method is iterated to form ultrasound images at a predetermined rate, and to visualize a substantially real-time evolution of the ultrasound image of the medium.

[0472] According to a variant:

[0473] - among the N iterations, a second number P less than N of iterations does not include do not take the steps of determining the unscanned reflection matrix R', the steps of spatio-temporal averaging, and the steps of extracting an optimal sound speed model, and

[0474] for these P (particular) iterations, at the stage of forming the ultrasound image, the ultrasound image is obtained from an optimal sound speed model extracted during a previous iteration.

[0475] Thus, for a number P of iterations, the calculations of the steps of determining the unscanned reflection matrix R', the spatio-temporal averaging steps, and the steps of extracting an optimal sound speed model are avoided. The method of this variant requires fewer computing resources, while providing a film of a succession of high-quality ultrasound images. Thanks to this arrangement, the The ultrasound image determination rate can be decoupled from the optimal position deviation calculation rate. This allows a high ultrasound image rate to be maintained with a drastically reduced number of calculations.

[0476] The various variants for reducing the computational cost of the first embodiment are also usable and / or adaptable to the second embodiment, concerning the search for an optimal sound speed model.

[0477] In particular:

[0478] - at the extraction stage we can consider that the optimal lateral deviation Axopt is zero, and / Or

[0479] - at the stage of determining the unscanned reflection matrix R', we can calculate only the values only for a zero lateral deviation Ax; and / or

[0480] - in the spatio-temporal averaging step, the focal spot images are averaged corresponding to the pairs {Ax = 0, Az}, and / or

[0481] - at the extraction stage, the optimal velocity model will be determined from the points of the focal spot image having a lateral deviation Ax of zero value.

[0482] These variants have advantages similar or even identical to those stated in the first embodiment, and make it possible to reduce the calculations at different stages of the method.

[0483] The set of optimal sound speed model values Copt can be assembled to form an integrated sound speed image. This integrated sound speed image can be displayed on the display device 43. However, it will be preferred to calculate the local sound speed values c(r) as explained later.

[0484] Figure ll(c) shows a map of the integrated velocity obtained in a liver imaging experience. This integrated sound speed map can be used to obtain a new ultrasound image whose axial dimension is no longer given by the echo time t but by the actual depth of the scatterers.

[0485] The result of the method according to this second embodiment of the method is illustrated in [Fig. 15]. [Fig. 15](a) shows the initial ultrasound image in which the axial dimension is an effective depth dictated by the echo time t and the sound speed model c0.

[0486] The first step of the correction process consists of considering for each pixel (x, t) of the image the value of the confocal signal obtained for the integrated sound speed model corresponding to (r ^t.

[0487] The image obtained in [Fig.l5](b) demonstrates a much better contrast than the initial image.

[0488] The second step of the process is to reposition each pixel in depth by shifting it axially by a depth / ys __ / 2- The map of corresponding displacement is given in [Fig.l5](a). This image obtained by equation 26 is here a function of the depth and no longer of the echo time t. The interfaces between tissues show better lateral coherence, particularly at shallow depths where the transverse variations in the speed of sound are the strongest and their impact on the quality of the ultrasound image the most significant.

[0489] The correction of axial aberrations of the image is also accompanied by a drastic reduction of transverse aberrations and therefore a significant improvement in the transverse resolution and contrast of the image presented in [Fig.l6](c).

[0490] The resulting integrated sound speed map or image can also be used to estimate a local sound speed map as shown for example in [Fig.ll](d).

[0491] Thus, the method can comprise a step in which local sound speeds c(r) are calculated for a set of pairs {x, t} (i.e. positions in the medium) from the values of the optimal sound speed models Copt obtained for the focal spot images of the pairs {x, t}.

[0492] A local sound speed image of the medium can then be formed, and it is possible to display it on the display device 43. This local sound speed image is important for the practitioner, because it is useful, combined with other information, for identifying certain pathological conditions or diseases, such as fatty liver.

[0493] Finally, having a local sound speed field, it is then possible to iterate the method described above in order to obtain a more precise ultrasonic characterization of the medium, by recalculating a de-scanned reflection matrix R' using the local sound speed values determined in a previous step.

[0494] We will now describe in more detail an example of a method for finding a map or image of the local sound speed c(r) at each point in the image from an integrated sound speed map or image. To this end, we must invert the following equation: gf: d: .....X eu)

[0495] for example, by the method developed in the document

[0496] “Local speed of sound estimation in tissue using pulse-echo ultrasound: Model- based approach. ”, Jakovljevic M, et Al., Journal of the Acoustical Society of America. 2018 Jul;144(1):254.

[0497] Under a paraxial approximation, the previous equation can be rewritten in the following matrix form: A z S - S (27)

[0498] Which can be explained in terms of matrix coefficients as follows: 1 9 1 î 0 1 I ï 4 (1 0 4 0 . 0 , 0 . 1 4 . 0 \ . 0 . 0 . 0 / ^(zzz2)\ ¢7(.2, 2?) .¾) 74. / -. 24 ) / &(x. Z] ) ¢7(4-. .22) ¢7(22 X X3. 24) (29) U i N / zN)j

[0499]

[0500]

[0501]

[0502]

[0503] With / ■ , -if- . \ ~ .. i presenting the local slowness maps (J 2 I — C *7 — C {d., ,<• ; r and integrated. Inversion of matrix A leads to the following relation: £ = A ~sx S (28) Which is rewritten in terms of matrix coefficients in the following form: / a(x. zi) \ / 7 (a*. 22 ) (7{X. 23) a(:r. 24) / ï 0~ 0 0 1 0 0 ( 1 1 $ ) 0 J 0 0 ■> O 0\ 0 0 0 X py / r. 21 )\X'*', 2o) 2 / . .23 ) (29) \crix.zx)) k0 0 0 ( 1 y vX ~X / Inversion of the integrated care velocity map Xpt(i) shown in Fig. ll(c) gives an estimator c 5Î fx, Q of the local sound velocity map c(.r. t) shown in [Fig.ll](d). This local sound velocity map reveals the different tissue layers present in the liver imaging experiment, including the fat layer and muscle tissues which exhibit particularly contrasting sound velocities. Accurate and reliable measurement of sound velocity in the liver is crucial for the detection of diseases such as steatosis. The sound velocity measured here in the patient's liver is particularly low: <c>= 1450 m / s while the speed of sound in a healthy liver is more like 1600 m / s. This patient is in fact suffering from steatosis, which has been confirmed by other, more expensive, long and / or invasive examination methods, a disease which could ultimately be revealed by a simple ultrasound measurement of the speed of sound in the liver according to the disclosure. Note that the inversion method mentioned above is based on a very strong approximation according to which the speed of sound integrated at a point Xx. 2) depends only on the value of the local speed in vertical position (>^ r .7 Other more sophisticated methods can take into account oblique trajectories and refraction phenomena experienced by incident and reflected waves. They can be used to invert the integrated sound speed map obtained with the present method.

[0504] The local sound speed map can be exploited to construct a more sophisticated propagation model than the initial speed model in order to obtain a finer estimate of the reflectivity of the medium via an ultrasound image obtained using delay laws based on the sound speed map.

[0505] Also, the entire method described previously for a uniform velocity model c0 can also be used to optimize a more complex velocity model c0(r) from more sophisticated optimization algorithms seeking to maximize the coherent confocal signal and / or the gradient of the Gouy phase.< / c>

Claims

Claims

1. Method for ultrasonic characterization of a medium comprising: - a step of generating a series of ultrasonic waves in incident (USin) in an area of said medium, by means of an array (10) of transducers (11), said series of incident ultrasonic waves being an emission base (i); and - a step of generating an experimental reflection matrix Rui (t) defined between the emission base (i) at the input and a reception base (u) at the output, the coefficients of this matrix corresponding to the signals received by the transducers induced by the reflected ultrasonic waves; said method being characterized in that it further comprises - a step of determining a de-scanned reflection matrix R', which comprises, for a set of midpoints of abscissa x and echo time t, responses of the medium calculated by channel formations following a sound speed model c„ from the experimental reflection matrix Rui(t), between a virtual input transducer of spatial position rin = (x, zt) and a virtual output transducer of spatial position rout = (x+Ax, zr), the two virtual transducers being at the same depth zt, zt being the depth of the isochronous volume expected for the sound speed c0, the isochronous volume being the set of points of the medium contributing to the signals received at time t, the responses of the unscanned reflection matrix R' being determined for a set of lateral deviation values Ax comprising at least Ax = 0 and for a set of sound speed models Co, said unscanned reflection matrix being formed with each row corresponding to an element of a pair {Ax, c0} which corresponds to a focal spot image and each column corresponding to an element of a pair {x, t}, which is noted: R' 'and - an extraction step in which an optimal lateral deviation Axopt and an optimal sound speed model Copï close to the maximum in said focal spot image are determined from each focal spot.

2. The method of claim 1, further comprising: - a step of forming the ultrasound image by calculating the reflectivity at a plurality of points in the medium, from the matrix of unscanned reflection R', the reflectivity of each of these points of the medium corresponding to the response of the medium between the virtual spatial position input transducer rin = (%, z,) and the virtual spatial position output transducer rout= (x+Axopl, zt), zt being the depth of the isochronous volume expected for the optimal sound speed model Capt and said reflectivity being defined by: = [ / 77{Aa? = A;rcn,t.(;r.£),éo = 7 h {;r7(7 "

3. A method according to claim 2, wherein the ultrasound image is transformed into the depth dimension, using the optimal sound speed model Copt by: Ï2(23 5) = I2(x,t = 2i / copt(Æ.t))' in which Z is the estimate of the depth z of a pixel of the ultrasound image.

4. A method according to claim 2 or claim 3, wherein the ultrasound image is displayed on a display device.

5. Method according to claim 1, in which: - local sound speeds c(r) are calculated, for a set of pairs {x, t}, from the optimal sound speed values Copt obtained for the focal spot images of said pairs {x, / }.

6. The method of claim 5, further comprising a step of forming a local sound speed image of the medium from said local sound speed set, and displaying said local sound speed image on a display device.

7. A method according to claim 5, wherein a de-scanned reflection matrix R' is recalculated using the local sound speed values.

8. Method according to claim 1, further comprising, before the extraction step: - a spatio-temporal averaging step of the de-scanned reflection matrix R' in which the values of the de-scanned reflection matrix are locally averaged along the lateral dimension x and the echo time t, for each element of a pair {Ax, c0}, the focal spot images then being averaged.

9. Method according to claim 8, wherein in the spatio-temporal averaging step, an incoherent point spread function PSFinc is calculated by the following formula: RSFineG Aæ, c0}, {;M}j — {æ\ t / } ) IV (a:' ~ xf - for a set of lateral deviation values Ax including at least Ax = 0 and for a set of sound speed model values c0, to obtain the focal spot image for lateral position x and echo time t, in which: <.> is an averaging operator according to the parameters of the pair {x', t'} R' is the unscanned reflection matrix, W(x', t') is a spatio-temporal weighting window according to the same parameters, and in the extraction step, a maximum point of the focal spot image is sought corresponding to a maximum of the modulus of the points of the focal spot image, and the optimal sound speed model Copt is the ordinate of said maximum point in said focal spot image.

10. A method according to claim 8, wherein: in the spatio-temporal averaging step, a singular value decomposition SVD of a local focal spot matrix R(1) is calculated, said local focal spot matrix being expressed from the unscanned reflection matrix R' by: Ræfe 0.) - Q] in which: R' is the unscanned reflection matrix, W(x', t') is a spatio-temporal weighting window according to the same parameters. the singular value decomposition SVD of said local matrix is noted: in which are the singular values of said local matrix, Up are the output eigenvectors, Vp are the input eigenvectors, we calculate a coherent point spread function PSFcoh by the following formula: qJ, {;a Q) ~ Fi ({A«, co}5 for a set of lateral deviation values Ax comprising at least Ax = 0 and for a set of sound speed model values c0, to obtain the focal spot image for the lateral position x and the echo time t, and in the extraction step, a maximum point of the focal spot image is sought corresponding to: a maximum of the modulus of the points of the focal spot image, or to a maximum of the modulus of the derivative according to the sound speed codes points of the focal spot image, or to a maximum of the modulus of the derivative according to the sound speed codes the imaginary part of the points of the focal spot image, and the optimal sound speed model Cvpt is the ordinate of said maximum point in said focal spot image.

11. Method according to one of claims 1 to 10, in which in the extraction step, it is considered that the lateral deviation Axopt is zero, Axopt = 0.

12. Method according to one of claims 1 to 11, wherein in the step of determining a de-scanned reflection matrix R', the de-scanned reflection matrix R' is formed only for lateral deviation values Ax of zero value, Ax = 0.

13. Method according to claim 8, in which in the spatio-temporal averaging step, the values of the unscanned reflection matrix R' are averaged to determine a focal spot image, for each element of a pair {Ax = 0, Az}, according to the lateral dimension x and the echo time t.

14. Method according to one of claims 1 to 13, wherein in the extraction step, the optimal sound speed model Copt is determined from the points of the focal spot image having a lateral deviation Ax of zero value, Ax = 0.

15. Method according to one of claims 1 to 14, in which the calculations of path formations between the virtual input transducer and the virtual output transducer are carried out from the experimental reflection matrix Rui(t), using a forward delay time of the ultrasonic waves between the transmission base (i) and the virtual input transducer, and using a return delay time of the ultrasonic waves between the virtual output transducer and the transducers of the reception base (u).

16. A method according to claim 1 or claim 15, wherein the unscanned reflection matrix R' is calculated from the matrix of experimental reflection Rui by the following formula: .R'({ Ar cq}, {æ<0) = in which: Nin is the number of elements of the emission base (i) Noul is the number of elements of the reception base (u), Rui(t) is the experimental reflection matrix, of which Rui(uOut, iin, t) is the element of the experimental reflection matrix Rui (t) recorded by the spatial position transducer uout following the emission of index iin in the emission base (i), at a time t, c0 being the expected speed of sound.

17. A method according to claim 1 or claim 15, wherein the unscanned reflection matrix R' is calculated from a focused reflection matrix R by the following formula: + A;e,æ, ^Co) in which: the unscanned reflection matrix R' is formed with each row formed from elements of a pair {Ax, Az} and each column formed from elements of a pair {x, t}, and the focused reflection matrix R is calculated from the experimental reflection matrix Rui(t) by the following formula: ril. / . cq j —■ v A... Ci / -.. Z.:, • ; (--' i,-• rifj <>:.■ C() ) “bi Amrt :, Ci)} J Am Aug- . in which: Nin is the number of elements of the emission base (i) Nout is the number of elements of the reception base (u), Rui(t) is the experimental reflection matrix, of which Rui(uOut, iin, t) is the element of the experimental reflection matrix Rui (t) recorded by the spatial position transducer uout following the emission of index iin in the emission base (i) and at time t. c0 being the expected speed of sound.

18. Method according to one of claims 1 to 17, in which a film is formed of a succession of ultrasound images by a first number N of iterations of the steps of the method.

19. Method according to claim 18, in which among the N iterations, a second number P strictly less than N of iterations does not include the steps of determining the unscanned reflection matrix R', the steps of spatio-temporal averaging, and the steps of extracting the optimal sound speed model, and for these P iterations, in the step of forming the ultrasound image, the ultrasound image is obtained from an optimal sound speed extracted during a previous iteration.

20. System for ultrasonic characterization of a medium (20), the system comprising: - an array (10) of transducers adapted to generate a series of incident ultrasonic waves in a zone of the medium, and to record as a function of time the ultrasonic waves backscattered by said zone; and - a calculation unit (42) connected to the array of transducers and adapted to implement the method according to one of claims 1 to 19.

Images