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 steps of generating a series of incident ultrasonic waves, measuring a canonical reflection matrix R ui(t) defined between the emission base (i) at the input and a reception base (u) at the output, determining a set of responses R of the medium obtained from the canonical reflection matrix R ui(t), at several frequencies and for several points in a region around a reference point, determining a frequency correction law from the responses of the medium at the different points, the frequency correction law being adapted to the reference point and being determined at the frequencies f, determining the corrected responses of the medium by applying the frequency correction law to the responses of the medium around the reference point and for the plurality of frequencies f. Figure for the abstract: FIGURE 5

Description

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

[0001] The present disclosure relates to methods and systems for ultrasonic characterization of a heterogeneous medium. These methods and systems implement an array of transducers placed in contact with a medium, to emit ultrasonic waves into this medium and to measure the waves backscattered by the heterogeneities of this same medium. STATE OF THE ART

[0002] In the field of acoustic imaging, we seek to characterize an environment by actively probing it with ultrasonic waves. This is notably the principle of the ultrasound scanner in medical imaging.

[0003] [Fig. 10] illustrates a conventional process of focusing in a medium to produce an ultrasound image of this medium. The medium in this example comprises an aberrator layer with a sound speed different from the sound speed observed in other parts of the medium. This results in spatial distortion and temporal dispersion (reverberation) of the acoustic wavefront which leads to transverse and axial aberrations of the resulting ultrasound image. These phenomena lead to a degradation of its resolution and contrast as well as the appearance of reverberation artifacts, which are particularly troublesome during a medical examination for example.

[0004] In the diagram on the left of this figure, the transducer array, placed opposite a medium, makes it possible to insonify and image the medium. The conventional method consists of insonifying the medium using emissions focused by a technique called beamforming. A set of appropriate delays r based on a homogeneous velocity model c0 is applied to the signals emitted by each transducer, in order to constructively interfere the waves produced by each transducer at the targeted focal point of spatial position rin. = (xin, z). Due to the physical limits of diffraction, the ultrasound emitted through the aperture of the ultrasound probe is concentrated in an area often called a "focal spot". In addition, the waves passing through the aberrator layer are distorted and reflected several times, which causes a plurality of wave echoes in the direction of the focal point during this emission.

[0005] In the diagram in the center of this figure, the waves reflected at the focal point are returned to the transducer array and then pass through the layer again aberration, which further distorts the ultrasound waves and causes a multiplication of echoes due to multiple reflections. Each diffuser in the medium thus gives rise to several echoes generating several temporal pulses arriving at different times on each transducer, hence a significant temporal dispersion of the ultrasound signals. A path formation process applied to this type of signal makes it possible to construct an ultrasound image with significant axial distortion: the same diffuser appears at several depths as illustrated by the ultrasound image in [Fig. 14]. In addition, the heterogeneous distribution of sound speed in the tissues crossed impacts the quality of the constructed image.

[0006] The diagram on the right of [Fig. 10] explains how, in the case of a single diffuser, one could temporally deconvolve the signals received by each transducer and then reverse them temporally, to optimally focus the ultrasonic waves both spatially and temporally on the diffuser in question. This time reversal focusing technique remains limited because it requires a medium comprising only a few diffusers. In ultrasound echography, the challenge is quite different since we have media presenting a random distribution of a multitude of under-resolved diffusers generating an ultrasonic speckle.

[0007] Thus the usual assumption of a homogeneous medium with a constant sound speed c0 of conventional imaging is often not respected. The waves are then reverberated with multiple internal reflections on the path of the waves towards a focal point. This results in a spatio-temporal distortion of the acoustic wavefront which leads to significant aberrations of the ultrasound image, and therefore to a degradation of its resolution and contrast. These aberrations can be such that they compromise the ultrasonic characterization.

[0008] Document WO 2020 / 016250 proposes a technique for correcting aberrations in ultrasound imaging based on post-processing manipulation of the reflection matrix of the medium. However, the method described in this document only considers IQ ultrasound signals temporally windowed around the expected ballistic time. The phase shift applied to these signals to correct the aberrations is therefore equivalent to an application of temporal delays, these delays also having to be of amplitude lower than the temporal resolution of the ultrasound signals. The technique of document WO 2020 / 016250 therefore applies to relatively low-order aberration corrections without temporal dispersion. It therefore cannot be used to correct reverberation or multiple scattering problems which require determining different delay laws for each frequency component of the ultrasound signal. SUMMARY

[0009] The present disclosure aims to improve the methods of probing by known ultrasounds, in particular to correct aberrations.

[0010] The present disclosure relates, according to a first aspect, to an ultrasonic characterization method for medical analysis of a medium, the method comprising the steps of:

[0011] - generation of a series of incident ultrasonic waves in an area of ​​said medium, by means of an array of transducers, said series of incident ultrasonic waves being an emission base (i); and

[0012] - measurement of a canonical reflection matrix Rui(t) defined between the basis emission (i) at the input and a reception base (u) at the output, the coefficients of this canonical reflection matrix corresponding to the signals received by the transducers and induced by the ultrasonic waves reflected in the medium.

[0013] The method further comprises the steps of:

[0014] - determination (S 130) of a set of responses R of the medium which are obtained by a focusing process for several frequencies / and for several points of spatial position r = (x, z) of a region around a reference point of spatial position rp = (Xp, zp) from the canonical reflection matrix Rui(t) for a sound speed model c0,

[0015] - determination (S140) of a frequency correction law ® from the responses from the middle to the different spatial position points (x,z), the frequency correction law being adapted to the reference point and being determined at the frequencies /

[0016] - determination (S 180) of the corrected responses R of the medium by application of the law of frequency correction *0 to the R responses of the medium around the reference point and for the plurality of frequencies /

[0017] Thanks to these provisions, the method advantageously makes it possible to locally probe the medium to obtain a local estimate of a frequency correction law adapted to correct the ultrasonic focusing process. This correction makes it possible to reduce or eliminate aberrations, for example due to multiple reflections of the waves generated by one or more aberrant zones in the medium.

[0018] These estimates are made by calculation from measurements made and recorded in a canonical reflection matrix. These estimates can thus be calculated independently of the measurement acquisition phase, in particular by modifying various calculation parameters, which makes it possible to carry out various ultrasonic characterization analyses either in real time or a posteriori.

[0019] These correction calculations benefit from local information extracted around a reference point and local frequency information from the environment.

[0020] The method can be used in medical or veterinary imaging as well as in any field of ultrasound imaging.

[0021] According to various embodiments of the method, it is possible to optionally use in addition to one and / or the other of the following provisions.

[0022] According to a variant, the method further comprises a step of:

[0023] - determination (S190) of an intensity Ic of a cor echographic image point responding to the spatial position reference point rp by combining the corrected responses at several frequencies / of this reference point.

[0024] According to a variant:

[0025] - the determination (S 130) of the set of responses R of the medium comprises the determination mination of responses which are obtained by the focusing process between a first point of spatial position rin= (xim z) corresponding to a virtual input transducer and a second point of spatial position rout= (xout, z) corresponding to a virtual output transducer, the first point and the second point being identical (rin = fout), and

[0026] all the responses R being recorded in a confocal reflection matrix R whose coefficients are written according to R = [^(xz, f) ],

[0027] - the determination (S 140) of the frequency correction law <1* is carried out by cor relationship of the responses of the medium to the different points of spatial position (x, z) around the reference point, and whose coefficients are written (]) = [¢( / , rp)]

[0028] - the determination (S 180) of the corrected responses R around the reference point, by application of the frequency correction law to each frequency / by performing the term-by-term product between the confocal reflection matrix R and the phase conjugate of the frequency correction law *0. that is to say by:

[0029] R' = Ro

[0030] where

[0031] all the corrected responses R are recorded in a corrected confocal reflection matrix R whose coefficients are written according to R — y ^ / ) ]

[0032] the symbol 0 is the Hadamard product, such that:

[0033] R (x, z, f) = R (x, z, rp}

[0034] According to a variant, the method further comprises a step of:

[0035] - determination (S190) of an intensity Ic of an ultrasound image point of spatial position (x, z) by combining the corrected responses R of this point at several frequencies / i.e. by: [00361 4Uz) = |E / n*V)| 2

[0037] According to a variant:

[0038] the determination of a frequency correction law (S 140) comprises

[0039] the construction of a correlation matrix (S 141) C from the confocal reflection matrix R(z,f), and

[0040] an analysis (S 142) of the correlation matrix C to determine the frequency correction law <B.

[0041] According to a variant:

[0042] the correlation matrix C is determined in the frequency domain, by:

[0043] C(f, f) = ^(x, 2. f) R\x, z, f')

[0044] where R is the confocal reflection matrix,

[0045] x, z are the coordinates of the points of the region around the reference point,

[0046] * is the conjugation operator.

[0047] According to a variant:

[0048] the correlation matrix C is determined in a basis of image points of spatial position (x, z), by: C( {x, z), (x', z'} ) zn^x', z, f)

[0050] where R is the confocal reflection matrix,

[0051] x, z are the coordinates of the image points in the region around the reference point,

[0052] * is the conjugation operator.

[0053] According to a variant:

[0054] the analysis (S 142) of the correlation matrix C is a decomposition into eigenvalues ​​of the correlation matrix C and the frequency correction law is the first eigenvector Uj of the correlation matrix C.

[0055] According to a variant:

[0056] the analysis (S 142) of the correlation matrix C is the resolution of an equation involving the correlation matrix C and the frequency correction law *1*, this resolution of the equation corresponding to an iterative time reversal or an iterative phase reversal.

[0057] According to a variant:

[0058] the determination (S140) of the frequency correction law is carried out by an optimization algorithm maximizing the confocal intensity of an ultrasound image in the region around the reference point.

[0059] According to a variant:

[0060] the steps (S 140, S180) of the correction processing are iterated several times, and

[0061] in which at each iteration, the corrected confocal reflection matrix R is used \z,f) obtained in the previous iteration instead of the focused reflection matrix R(

[0062] According to a variant:

[0063] at each iteration, the size of the region around the spatial position reference point rp is reduced.

[0064] According to a variant:

[0065] the determination (S 130) of the confocal reflection matrix R(z, / ) comprises a compensation for the time attenuation of the signals.

[0066] According to a variant:

[0067] - the determination (S 130) of the set of responses R of the medium comprises the determination mination of responses which are obtained by the focusing process between a first point of spatial position rin= (xim z) corresponding to a virtual input transducer and a second point of spatial position rout= (xout, z) corresponding to a virtual output transducer, the first point and the second point being located in the region at the same depth z, the transverse positions xin and xoul of the first and second points forming a focused base (x) at each depth z, and

[0068] the set of responses R being recorded in a focused reflection matrix R ^(z,f) whose coefficients are written according to R„(.7,. / ) = [R(-X;„, xout^ z, / )],

[0069] - the determination (S 140) of the frequency correction law db includes sub- steps performed at each depth z and each frequency / , of:

[0070] - determination (S150) of a dual reflection matrix R / zJ) by forward projection of the focused reflection matrix Rxx(z, / ) towards a correction basis (c),

[0071] - calculation (S 160) of the frequency correction law ® from the matrix of dual reflection Rc(z, / ), said frequency correction law being determined on the basis of correction (c), O = [ / (c, f, I / )], so that said frequency correction law dh is a spatio-frequency correction law,

[0072] - determination (S 170) of a corrected dual reflection matrix R< around the point of reference and whose coefficients are written according to r;u / ) = [s4.X, C, f, z ) ] ' determined by carrying out the term-by-term product between the dual reflection matrix Rc (z, / ) and the phase conjugate of the frequency correction law, that is to say by:

[0073]

[0074] where

[0075] the symbol * denotes a phase conjugation operation

[0076] the symbol ° is the Hadamard product, such that:

[0077] Rc(Rc(xc, f, z)&(X, C, f, z)

[0078] - the determination (S 180) of the corrected responses R of the medium around the point of reference includes the determination of a corrected focused reflection matrix R / ) by back projection of the corrected dual reflection matrix R'c(zJ) to the focused base (x).

[0079] According to a variant, the method further comprises a step of:

[0080] - determination (S 190) of an intensity Ic of an ultrasound image point of spatial position (x, z), by combining the diagonal coefficients of the corrected focused reflection matrix R'xx(z, / ) of this point, at several frequencies / , that is: 100811

[0082] According to a variant:

[0083] the forward projection (150) is carried out by a matrix product between a passage matrix and the focused reflection matrix Rxx(z, / ), that is to say:

[0084] K(z, / ) = P(z, / ) / )

[0085] where: P(z, f ) = [P(c, x, z, / ) ] is the passage matrix at each frequency / between the focused base (x) at depth z and the correction base (c).

[0086] According to a variant:

[0087] the correction base (c) is an input correction base or an output correction base.

[0088] According to a variant:

[0089] The calculation of the frequency correction law (S 160) includes:

[0090] the construction of a correlation matrix (S161) C from the dual reflection matrix Rc(z,f), and

[0091] an analysis (S 162) of the correlation matrix C to determine the frequency correction law <&.

[0092] According to a variant:

[0093] the correlation matrix C is determined in the correction basis (c) and in the frequency domain, by:

[0094] C ( {c, f} J cf '} ) = (

[0095] where Rc is the dual reflection matrix,

[0096] Rref is a model reflection matrix of a model medium in which the velocity of the its is c0 expected sound speed of the medium and in which a plane reflector is positioned at depth z,

[0097] x, z are the coordinates of the points of the region around the point rp,

[0098] * is the conjugation operator.

[0099] According to a variant:

[0100] the correlation matrix C is determined in a basis of image points of spatial position (x, z), by:

[0101] Crr( {x, z}, {x; z'] ) = Ec fRc(x, c, Z, f)Rref(x, C, Z, / ) Rc(x\ C, z', / ) Rref(x', C, z\ f)

[0102] where Rc is the dual reflection matrix,

[0103] Rref is a model reflection matrix of a model medium in which the velocity of the its is c0 expected speed of sound of the medium and in which a plane reflector is positioned at depth z,

[0104] x, z are the coordinates of the image points in the region around the point rp.,

[0105] * is the conjugation operator.

[0106] According to a variant:

[0107] the analysis (S 162) of the correlation matrix C is a decomposition into eigenvalues ​​of the correlation matrix C and the frequency correction law<!----> is the first eigenvector U1 of the correlation matrix C.

[0108] According to a variant:

[0109] the analysis (S 162) of the correlation matrix C is the resolution of an equation involving the correlation matrix C and the frequency correction law, this resolution of the equation corresponding to an iterative time reversal or an iterative phase reversal.

[0110] According to a variant:

[0111] The calculation of the frequency correction law (S 160) is carried out by an optimization algorithm maximizing the confocal intensity of an ultrasound image in the region around the reference point.

[0112] According to a variant:

[0113] the steps (S140, S180) of the correction processing are iterated several times, and

[0114] in which at each iteration, the forward projection (S 150) uses the corrected focused reflection matrix R'xx(zJ) obtained during the return projection (S 180) of the previous iteration instead of the focused reflection matrix R^^J).

[0115] According to a variant:

[0116] at each iteration of the forward projection (S 150), we alternate between a forward projection in an input correction base and an output correction base.

[0117] According to a variant:

[0118] at each iteration, the correction base (c) of the forward projection (S 150) is different.

[0119] According to a variant:

[0120] at each iteration, the size of the region around the spatial position reference point rp is reduced

[0121] According to a variant:

[0122] the determination (S 130) of the focused reflection matrix R^, / ) includes compensation for the time attenuation of the signals.

[0123] The present disclosure relates, according to a second aspect, to an ultrasonic characterization system for analyzing a medium, for example in the medical context, and configured for implementing methods as described previously. The system according to the second aspect comprises:

[0124] - an array of transducers adapted to generate a series of ultrasonic waves in incident in an area of ​​the medium, and to measure as a function of time the ultrasonic waves backscattered by said area; and

[0125] - 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

[0126] 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:

[0127] Figures 1(a) to 1(h) illustrate transmission / reception sequences used for ultrasonic imaging and characterization of a medium;

[0128] [Fig.2] illustrates usual confocal imaging and matrix imaging with the synthesis of a focused reflection matrix containing the responses between distinct virtual transducers synthesized at each depth by channel formation;

[0129] [Fig.3] illustrates an example of an ultrasonic characterization system for implementing the method according to the present disclosure;

[0130] [Fig.4] shows the definitions used in the method according to the present disclosure;

[0131] [Fig.5] is a diagram of the ultrasonic characterization method according to the present disclosure, in which a frequency correction law is determined from responses at several points in the medium and at several frequencies and the responses of the medium are corrected by applying this frequency correction law;

[0132] [Fig.6] is a diagram of an embodiment of the step of determining a frequency correction law of the method of [Fig.5], by projection of the focused reflection matrix into a correction base;

[0133] [Fig.7] illustrates a particular calculation of the frequency correction law of [Fig.6], by construction and analysis of a correlation matrix;

[0134] [Fig.8] illustrates a particular calculation of the frequency correction law of [Fig.6] by local ultrasound image optimization;

[0135] [Fig.9] illustrates a diagram of an embodiment of the step of determining a frequency correction law of the method of [Fig.5], by construction and analysis of a correlation matrix, in the case of a confocal reflection matrix;

[0136] [Fig. 10] illustrates the problem of an aberrator layer in ultrasound imaging;

[0137] [Fig. 11] illustrates the first embodiment of the method according to the present di popularization in matrix version which solves this problem of reverberations, generalizing to the “speckle” case the process described in [Fig. 10] in the case of an isolated diffuser;

[0138] [Fig. 12] illustrates the second embodiment of the method according to the present di- popularization in confocal version which solves this problem of reverberations;

[0139] [Fig. 13] illustrates an experimental ultrasound phantom type medium on which the method of the present disclosure is tested;

[0140] [Fig. 14] shows an ultrasound image of an area of ​​interest in the middle of [Fig. 13], an ultrasound image presenting particularly visible reverberation artifacts, notably at the level of the echogenic diffusers of the calibrated experimental medium;

[0141] [Fig. 15] illustrates a frequency correction law expressed in the time domain and obtained in a region B1 of the image of [Fig. 14];

[0142] [Fig. 16] shows an ultrasound image without correction in [Fig.16](a) and an image obtained with the correction of the method according to the present disclosure in [Fig. 16](b);

[0143] [Fig. 17] shows the same ultrasound image as [Fig. 14] with three regions selected to apply the method locally according to the present disclosure;

[0144] [Fig. 18] illustrates the spatio-frequency correction laws obtained in regions C1, C2 and C3 of the image of [Fig. 17];

[0145] [Fig. 19] shows an ultrasound image without correction in [Fig.l9](a), an ultrasound image obtained with global correction in [Fig.l9](b), and an ultrasound image obtained with correction in the three regions C1, C2 and C3 in [Fig. 19] (c).

[0146] In the various embodiments described with reference to the figures, similar or identical elements bear the same references unless otherwise stipulated. DETAILED DESCRIPTION

[0147] 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 disclosure.

[0148] The various embodiments and aspects described in the present disclosure may be combined or simplified in multiple ways. In particular, the steps of the various methods may be repeated, interchanged, and / or executed in parallel, unless otherwise specified.

[0149] The present disclosure 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, provide precise information on the medium studied, detect unhealthy or inactive areas and / or tissue. damaged. For example, these data are very useful for medical applications such as identifying lesions in the breast area, damaged muscle tissue, or degradation of liver tissue. These characterization techniques are notoriously non-invasive for the environment, which is advantageously preserved in particular in its nature and integrity. Usual approach to ultrasound imaging

[0150] In the field of ultrasound imaging, we often seek to construct an image of the reflectivity of a medium from the echoes backscattered by heterogeneities of the medium. This is the principle of the ultrasound scanner used in medical imaging, which in particular makes it possible to visualize the internal anatomy of an object, an individual or an animal. For the purposes of simplification, to allow the construction of an ultrasound image, the medium is considered to be homogeneous, with a constant sound propagation speed c0.

[0151] Conventional ultrasound methods generally use an array of piezoelectric transducers that can emit and / or receive ultrasound signals independently or quasi-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 construct a representative image of the medium in different ways. A conventional method consists of insonifying the medium using emissions focused by a technique called beamforming. This method consists of applying to the signals emitted by each transducer a set of appropriate delays r(uin, xin, z, c0) based on a homogeneous velocity model c0, in order to constructively interfere the wavelets produced by each transducer at the targeted focal point of spatial position (%in, z).Due to the physical limitations 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.

[0152] In order to subsequently construct an ultrasound image illustrating the characteristics of the medium studied, a digital focusing step is also carried out in reception. The echoes captured by the transducers of the network are put back in phase by shifting them temporally. The delays r(uo„„ xout, z, c0) are identical to those applied to the emission, 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 used corresponds to the reality of the medium studied. In reception, the signals coming from this same point (xoul = x,„) interfere by summation of the signals at the echo time t = 2zJc0. This summation makes it possible to obtain the final result of the focusing in reception. This confocal method with double focusing at emission and reception makes it possible to image directly the reflectivity of the medium with a lateral resolution ôx and good contrast. However, this method is time-consuming because it requires physically focusing the emission at each of the points of the medium or at least at a given depth, on each of the lines of the image that will be constructed representative of the medium. Matrix approach to ultrasound imaging

[0153] A matrix approach to ultrasound imaging has been developed in recent years by the applicant. This approach is based on the construction of a canonical reflection matrix of the medium studied. This canonical reflection matrix is ​​determined by experiment or by calculations or numerical simulation, reproducing an experiment.

[0154] A first proposal to create this canonical reflection matrix is ​​to successively emit an ultrasonic pulse from each transducer of the network whose position is identified by the coordinate uin, as shown schematically in [Fig.l] (a). This gives rise to a divergent cylindrical (or spherical) incident wave. This wave is reflected by the diffusers of the medium and the backscattered field is measured by each of the transducers as a function of time as shown in [Fig.l] (b). By repeating this operation with each transducer used successively as a source, we determine the canonical reflection matrix Ruu(t) = [R(uout, uin, / )] expressed in the base of the transducers, composed of the set of impulse responses R(uout, uim t) between each transducer. This matrix is ​​then rich in quantity of information describing the medium studied.However, the method assumes that the medium remains fixed throughout the measurements, which is difficult especially in the case of medical examinations carried out on living patients. In addition, the recorded signals have a poor signal-to-noise ratio because the medium is insonified by a single transducer.

[0155] A second alternative to construct this canonical reflection matrix is ​​to insonify the medium with focused waves, successively at a multitude of points in the medium, as is generally the case in standard ultrasound scanners. [Fig.l](c) illustrates this focused illumination at emission. A delay law is applied to each signal at emission for this focusing. The reception illustrated in [Fig.l](d) is measured by all the sensors of position uout for each focused illumination, and the responses form the canonical reflection matrix R(uout, rin , t). However, this method of focusing at multiple points is still too slow.

[0156] A third way of constructing this canonical reflection matrix consists of insonifying the medium with a series of plane waves. This method makes it possible to overcome most of the problems inherent in the method presented previously. [Fig.l] (e) illustrates the principle of this plane wave illumination. A delay law r' is applied to each signal at transmission to form a wavefront inclined at an angle 6in relative to the transducer array. At reception, as illustrated in [Fig.l] (f), the field backscattered by the medium, R(uout, 0in , t), is measured by all sensors at positions uout for each incident plane wave 0in. All of these responses form a canonical reflection matrix Ruü(t) = [7? (uout, 0in, t)]. The double focusing method described above can be realized numerically by temporally shifting the measured signals before summing them coherently. This method gave rise to ultrafast imaging, and to elastography, and is for example described in the document:

[0157] “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).

[0158] A third alternative to create this canonical reflection matrix consists of insonifying the medium with a base of diverging waves, as represented in [Fig.l] (g) and [Fig.l] (h), which makes it possible to illuminate the acoustic field more broadly than via the use of plane waves. This technique, used in particular in super-resolution imaging, is explained in the document:

[0159] “Ultrafast imaging of the heart using Circular Wave Synthetic Imaging with Phased Arrays”, Couade et al., IEEE International Ultrasonics Symposium (2009).

[0160] 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.2] (a).

[0161] Matrix imaging consists of dissociating the focal points at emission and reception, for the same echo time t, as represented in figure 2 (b). Thus, a focused reflection matrix Rxx(r) = [R(xin, xout, z, r)] is determined, this focused reflection matrix being composed of the responses between virtual input transducers and virtual output transducers of respective spatial positions rin = (xin, z) and rout = (xout, z) corresponding to focal spots synthesized at input and output at different spatial positions, and whose expected depth z is dictated by the echo time t: z=cot / 2. ​​T here represents the time in the focused base such that t = t-2z! cG. The origin of this time T corresponds to the instant when the virtual source emits the ultrasonic pulse. The focused reflection matrix is ​​obtained by focusing (e.g. by channel formations) from the canonical reflection matrix Rui(t).This matrix allows access to more information characteristic of the studied environment than the information obtained via the method used in confocal image mode of conventional imaging. This focused reflection matrix can be synthesized in the time domain by delay laws (path formations) or in the frequency domain by applying . appropriate phase shifts.

[0162] The focused reflection matrix has been described in particular in the document:

[0163] “Reflection Matrix Approach for Quantitative Imaging of Scattering Media”, William Lambert, et al., Phys. Rev. X 10, 021048, (2020),

[0164] then in the document

[0165] “Ultrasound Matrix Imaging - Part I: The Focused Reflection Matrix, the F-Factor and the Role of Multiple Scattering”, William Lambert, et al., IEEE Trans. Med. Pic. 41, 3907-3920, (2022).

[0166] In these publications, the focused reflection matrix R^fe r) was considered between virtual transducers at ballistic time r = 0 (t=2z / c0) While the diagonal coefficients (xout = x,„) of the matrix Rxx(z, t=0) allow us to construct the synthetic confocal image at depth z, its off-diagonal coefficients inform us about the potential aberration and multiple scattering effects likely to alter the quality of this same image.

[0167] In the patent application publication WO2020 / 016250, the focused reflection matrix was considered at ballistic time and studied in particular to correct aberration problems. However, the correction applied corresponds to the application of time delays, these delays having to be of amplitude lower than the time resolution of the ultrasonic signals. The technique of document WO 2020 / 016250 therefore only applies to aberration corrections of relatively low order and without temporal dispersion. It cannot therefore be used to correct reverberation or multiple scattering problems which require determining different delay laws for each frequency component of the ultrasonic signal. Ultrasonic characterization system

[0168] [Fig. 3] illustrates an example of an ultrasound imaging system 1 for implementing methods for ultrasound imaging of a medium such as a heterogeneous medium M, according to the present disclosure. This system and method allow the formation of an ultrasound image of at least a portion (area of ​​interest or field of view) of the medium.

[0169] System 1 comprises:

[0170] - a probing device 20 or probe 20,

[0171] - a calculation unit 30 for calculating an image from the signals received from the probe20,

[0172] - a control panel 40 connected to the computing unit 30, this control panel comprising for example buttons 41 and a touchpad 42,

[0173] - a display device 50 for viewing an image and various elements or measures.

[0174] The probe 20 is connected to the computing unit 30 via a cable 21 or via a wireless connection, and is capable of emitting ultrasonic waves W into the medium M and receiving ultrasonic waves W from the medium M, said ultrasonic waves resulting from reflections of the emitted ultrasonic waves on diffusing particles or diffusers inside the medium.

[0175] The probe 20 may comprise an array 10 comprising a plurality of transducers 11. The array 10 is for example a linear or curved or two-dimensional or matrix array. The transducers 11 are capable of converting an electrical signal into a vibration and vice versa. The transducers 11 are for example ultrasonic piezoelectric transducers which may be in the form of a rigid bar placed in direct or indirect contact with an external surface of the medium M to be coupled to the medium and to vibrate and emit and receive ultrasonic waves W. The array 10 of transducers 11 of the probe 20 is then associated with the calculation unit 30. The array 10 of transducers may comprise a hundred or more transducers 11.

[0176] The calculation unit 30 may comprise a housing 31 including reception devices for amplifying and / or filtering the signals received from the probe 20, and converters (analog to digital converters, and digital to analog converters) for transforming the signals into data representative of the signal. The data may be recorded in a memory of the calculation unit 30 and / or directly processed to calculate intermediate data (channel formation data or others). The calculation unit 30 may implement any method for subsequently constructing an image from the data of the signals received from the probe 20, such as channel formation.

[0177] The calculated image can be:

[0178] - a middle image (B-mode image) usually in grayscale for vi to standardize organs in the environment, and / or

[0179] - an image showing a velocity or flow in the medium (color image) by useful example for visualizing blood vessels and associated flows in the medium, and / or

[0180] - an image showing a mechanical characteristic of the medium (elasticity, according to the ShearWave® elastography mode) for example useful for identifying tumors inside the medium.

[0181] By "connection" or "link" between the survey device 20, the calculation unit 30 and the display device 50, 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 50 can be of any type, such as a touch screen or non-touch, connected or not.

[0182] The display device 50 is a screen for viewing the image calculated by the calculation unit 30. The display device 50 can also display other information such as the scales of the image, or configuration information for the calculation or processing or any measurement or assistance information. The screen 50 can be articulated on a support arm 51 for better positioning for the user. The screen 50 is usually a large screen (at least 20 inches) for better viewing for the user.

[0183] The control panel 40 is for example a portion of a system box, said portion comprising a panel box having a substantially planar surface 40a inclined towards the user for one-handed operation. As shown in [Fig.3], the control panel 40 may comprise a control screen 49 for viewing various configuration information.

[0184] The calculation unit 30 is configured for the implementation of calculation and / or processing steps, in particular for the implementation of method steps according to the present disclosure. By convention, as represented in [Fig.4] showing an array 10 of transducers 11 on a surface of a medium M, a spatial reference frame of the medium M 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 in the example of a linear array, and the second axis Z corresponds to the depth of the medium M 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 network 10, or to a polar reference frame in the case of a curved network 10, or to any other reference frame adapted and / or dependent on the structure and shape of the network 10 of ultrasonic transducers. Thus, in the remainder of this disclosure, we will use a Cartesian reference frame XZ, corresponding to a linear probe 20, for greater simplicity in the explanations, but a specialist in the field would easily generalize and apply the results to any type of reference frame.

[0185] In the remainder of the disclosure, reference is made to an array 10 of transducers 11 for transmission and reception, it being understood that, in a more general case, several arrays of transducers may be used simultaneously. The transducers 11 may be both transmitters and receivers, or only transmitters for some and only receivers for others. Similarly, an array 10 may consist of one (1) to N translators 11, of identical type or of different natures.

[0186] The network 10 of transducers 11 serves for example as both transmitter and receiver, or is made up of several sub-networks of transducers, some being dedicated to the transmission, others to the reception of ultrasonic waves. By network of transducers means at least one transducer, an aligned or non-aligned sequence of transducers, or a two-dimensional distribution of transducers (for example a matrix of transducers), or any spatial distribution of transducers.

[0187] When in the present disclosure, 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.

[0188] Analysis of a point in the middle by focused reflection matrix

[0189] The present disclosure 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.4]:

[0190] We define in the middle:

[0191] - a first point PI of spatial position rin in the spatial reference frame of the middle, and

[0192] - a second point P2 of spatial position route in the middle spatial reference frame.

[0193] 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.

[0194] 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. Thus, the spatial positions of the points PI and P2 are respectively rin = (Xtm z) and rout (Xoub z\

[0195] 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.

[0196] The ultrasonic characterization method implemented by the calculation unit 30 of the system 40 comprises the steps of:

[0197] - generation of a series of incident ultrasonic waves 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

[0198] - measurement or construction of a canonical 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 canonical reflection matrix corresponding to the signals received by the transducers and induced by the ultrasonic waves reflected by diffusers in the medium;

[0199] - determination of a focused reflection matrix Rxx(z) comprising responses of the medium calculated by focusing from the canonical reflection matrix Rui(t) between a virtual input transducer TVin of spatial position rin and a virtual output transducer TVout of spatial position rout.

[0200] The canonical reflection matrix Rui(t) obtained 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”).

[0201] The focused reflection matrix RM 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. These expressions can also 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 point designated as a reference point. The technician in the field will be able to make the necessary changes of variables in the expressions presented.

[0202] The responses of the medium are calculated by focusing from the canonical reflection matrix Rui(t).

[0203] The responses of the focused reflection matrix R^^) correspond to an acoustic pressure field calculated between all the points of the middle of lateral positions xin, and x out, located at the expected depth z and at an echo time t, and for an assumed speed of sound c0. In other words, this focused reflection matrix Rxx(z) is defined by: Rxx(z) [^(¾ Xout* Z)]

[0204] The parameters of depth z in the medium and sound speed c0 influence the delay laws used in the focusing process.

[0205] 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 disclosure of figures 2(a) to 2(f).

[0206] The reception base u is for example the base of the transducers 11. In an alternative, another reception base can be used in reception, for example the plane wave base (or spatial Fourier base), or any other base allowing a measurement of the ultrasonic field in an intermediate plane between the ultrasonic probe and the focal plane considered by an adequate process of channel formation in reception.

[0207] 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.

[0208] In the measurement step, the canonical 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 denoted with the index "in" refer to the emission (i.e. the input) and the elements denoted with the index "out" refer to the reception (i.e. the output). This canonical matrix can also be recorded and / or stored, for example in the memory of the calculation unit, or on any other medium, removable or not, allowing permanent or temporary storage.

[0209] At the stage of determining the focused reflection matrix Rxx(z) can be obtained by:

[0210] - an input focusing process from the canonical reflection matrix Rui(t) which uses a time of flight on the outward journey of the waves 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,

[0211] - an output focusing process from the canonical reflection matrix 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.

[0212] These input and output focusing processes form an input-output focusing process, referred to in the remainder of this disclosure as focusing process or more simply focusing.

[0213] 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 in their spatial positions Ar = rout - rin. In the present case, they are separated only along a lateral axis, of Ax = xouf 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, that is to say 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 real depth.

[0214] Furthermore, the focused reflection matrix Rxx(z) can be determined or calculated:

[0215] - either in the time domain, in which case it can be explicitly noted with the time parameter t, i.e. denoted Rxx(z, t), and

[0216] in practice the data of the focused reflection matrix R^fe t) are calculated between two predetermined time instants;

[0217] - either in the frequency domain, in which case it can be noted explicitly with the pulsation parameter eu which corresponds to a frequency / by eu = 2n / f, that is to say noted Rxx(z, eu), and

[0218] in practice the data of the focused reflection matrix R^fe eu) are calculated between two pulsations eu, of a frequency bandwidth, for example between a lower pulsation eu- and a higher pulsation a>+, for a central pulsation euc.

[0219] Thus, the rest of the calculations of the method can be carried out in the time domain or in the frequency domain.

[0220] In the first case of calculation in the time domain, the focused reflection matrix R^z, t) of the medium between the virtual input transducer TVin and the virtual output transducer TVout is obtained by focusing by a channel formation calculation at the inputs and outputs. The coefficients of this focused reflection matrix R„L, t) can be determined by: [0221 ] / C( X^p ... f ) ) AolJl (

[0222] (J)

[0223] in which:

[0224] Nin is a first normalization coefficient,

[0225] Noul is a second normalization coefficient,

[0226] Rui(t) is the confocal reflection matrix, of which

[0227] R(uout, iin, t) is the element of the confocal 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, to which the delay times rin and roul have been applied;

[0228] Ain ( xinz ) and Aout ( uOMf, Xout, z ) are apodization coefficients which are predefined, for example to keep a constant numerical aperture both on transmission and on reception;

[0229] The first normalization coefficient Nin can for example be defined by: N ( y = V A. ( i. y - i Similarly, the second normalization coefficient- Noul lization can be defined by: v ( xz) = FA fnr ~ )

[0230] rin( ijn, Xùr z) is the expected flight time for each incident wave i;,, to reach the first focal point of spatial position ( xjn, z) in a model medium of sound speed c0

[0231] r„w(u„„„ is the expected time of flight for a wave reflected from the second spatial position focal point ( xmit, z ) to the position transducer u««f.

[0232] These delay times rin and rout are usually calculated by a person skilled in the art from an established model of sound speed. A relatively simplifying assumption is to assume a homogeneous medium with a constant sound speed c0 in the medium. In this case, the flight times are directly obtained from the distances between the probe transducers and the virtual transducers. Thus, these delay time calculations are a function of the wave type, the assumed sound speed, and the geometry of the transducer array.

[0233] 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).

[0234] The previous path-forming formula is therefore a double sum of the time responses recorded in the canonical 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 out, z). The result of this path-forming formula is therefore a time signal for these two spatial coordinates (rin, rout) or for these two lateral positions xin, x OUt*

[0235] Finally, the focused reflection matrix Rxx(z, t) expressed in the time domain, can be transformed in the frequency domain into a focused reflection matrix R„L, û?) by a Fourier transform, that is to say by:

[0236] +f

[0237] (2)

[0238] This Fourier transform can be implemented by any type of discrete Fourier transform, normalized or not.

[0239] In the second case of calculation in the frequency domain, the canonical reflection matrix Rui(t) expressed in the time domain, since it is made up of the signals received by the transducers, can be transformed in the frequency domain into a canonical reflection matrix Rui(co) by a Fourier transform, that is to say by:

[0240] V «,„■(<■>) = MR^)^'

[0241] (3)

[0242] This Former transform can be implemented by any type of discrete Fourier transform, normalized or not.

[0243] Thus, the focused reflection matrix Rxx(z) or R„C, eu) of the medium can be obtained by focusing by the matrix calculation below, substantially equivalent to the focusing by the time channel formation explained previously, that is to say by the following matrix product:

[0244] R„(z, W) = GLU 01)^( W)

[0245] (4)

[0246] in which

[0247] the matrix Rf / i ( a? ) is the Fourier transform of the canonical reflection matrix R^f),

[0248] the matrix G(M.(-, ut) is the reception passage matrix adapted for the passage from the reception base (u) to the focused base (x) at the depth z and at the pulsation

[0249] the matrix Pv (Z, w) is the emission passage matrix adapted for the passage from the emission base (i) "i" to the focused base (x) at the depth z and at the pulsation a\

[0250] The symbols * and f denote respectively the matrix operations of conjugation and transposition-conjugation. Aberration correction process

[0251] The method S100 according to the present disclosure aims to correct aberrations in the ultrasonic characterization of the medium M, these aberrations being for example due to variations in structures in the medium which induce variations in sound speed and variations in reflectivity.

[0252] The method S100 according to the present disclosure is illustrated in [Fig.5], and this method implemented by the computing unit 30 of the system 40, comprises the steps of:

[0253] - generation SI 10 of a series of incident ultrasonic waves 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

[0254] - measurement or construction S120 of a canonical 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 canonical reflection matrix corresponding to the signals received by the transducers and induced by the ultrasonic waves reflected by diffusers in the medium.

[0255] These steps S110 and S120 correspond to the respective generation and measurement steps previously described.

[0256] The method S100 according to the present disclosure further comprises a step of:

[0257] - determination S130 of a set of responses R of the medium.

[0258] This step S130 is similar to the step of determining a focused reflection matrix Rx / z / / but this step is distinguished by the fact that the responses are not necessarily organized in a matrix. They can correspond to the confocal signal alone, i.e. only to the diagonal of the focused reflection matrix. Furthermore, these responses are calculated at several frequencies / and at several points of spatial positions r = (x, z) of a region (analysis region) located around a reference point of spatial position rp = (Xp, Zp) ■ The responses around the point of the reference point at several frequencies make it possible to analyze this region around this reference point, which makes it possible to perform a local correction of the aberrations and / or the dispersion and / or the reverberations induced by the medium upstream of the focal plane.

[0259] In particular, the method thus comprises a step of:

[0260] - determination S130 of a set of responses R of the medium which are obtained by a focusing process for several frequencies / and for several points of spatial positions r = (x, z) of a region around a reference point of spatial position rp = (xp, Zp) from the canonical reflection matrix Rui(t) for a sound speed model c0.

[0261] The method S100 according to the present disclosure then comprises a correction processing comprising steps of:

[0262] - determination S140 of a frequency correction law *1* from the responses of the medium at the different spatial position points (x, z), the frequency correction law being adapted to the reference point and being determined at the frequencies /

[0263] - determination S180 of the corrected responses R of the medium by application of the law of frequency correction <0 to the R responses of the medium around the reference point and for the plurality of frequencies /

[0264] Thanks to these provisions, the method advantageously makes it possible to locally probe the medium and to correct the focused reflection matrix with respect to the aberrations, in particular by determining a correction law for each point of the medium M of spatial position rp, and for each frequency / of the ultrasonic wave.

[0265] Furthermore, the method may comprise a step of:

[0266] - determination S190 of an intensity Ir of a point of the ultrasound image cor responding to a point of spatial position r = (x, z) by combining the corrected responses at several frequencies / of this reference point.

[0267] In particular, this intensity is calculated by quadratic sum of the corrected responses R at the spatial position point r = (x, z) and for at least part or all of the frequencies / previously calculated. For example, the calculation can be limited in a predetermined frequency band for ultrasonic characterization of the medium. 1 - First embodiment

[0268] A first embodiment of the method S100 of the present disclosure performs matrix calculations by performing focusing processes between virtual input transducer points and virtual output transducer points which may or may not be distinct from each other. Thus, a large number of responses of the medium are calculated which allows very in-depth analyses and therefore specific correction processing for the characterization of the medium M.

[0269] [Fig. 11] illustrates this method according to the first embodiment of the present di popularization. The network of transducers, placed opposite a medium, makes it possible to insonify and image a region of a medium with random reflectivity of the “speckle” type.

[0270] In the first diagram (A) of this figure 11, a plurality of waves are emitted successively into the medium using focused emissions towards several focal points of spatial positions rl, r? and by a technique called path formation or focusing. The waves pass through an aberrator layer and induce focal spots distorted both spatially and temporally around the focal points. The temporal dispersion of the focused waves is induced here by the frequency dependence of the speed of sound within the aberrator layer and / or the multiple reflection echoes induced by the latter.

[0271] In the following three diagrams (B) of the figure, during the return journey, the waves reflected at each focal point again pass through the aberrator layer, which again distorts both spatially and temporally the ultrasonic waves, with in particular a new multiplication of echoes induced by the multiple reflections within the aberrator layer. The temporal signals received by the transducers are therefore very complex and then all include numerous echoes linked to the multiple reflections.

[0272] As shown in the fifth diagram (C), by performing an average or correlation processing of the echoes induced by the plurality of focal points in the region around the spatial position reference point rp, a temporal response is obtained such as it would be generated by a virtual coherent reflector. This calculation makes it possible to determine a spatio-frequency correction law (here illustrated with the base of the transducers u).

[0273] The sixth diagram (D) of this figure explains how one can use this deconvolved and temporally reversed virtual response as an optimal delay law to be applied in order to correctly focus on each focal point while compensating for problems of aberrations and / or dispersion and / or reflections. multiples.

[0274] The method of this first embodiment is described in more detail below.

[0275] The step of determining S130 a set of responses R of the medium comprises determining responses which are obtained by the focusing process between a first point of spatial position rin= (xim z) corresponding to an input virtual transducer and a second point of spatial position rout = (xout, z) corresponding to an output virtual transducer, the first point and the second point being located in the region around the reference point, and are located at the same depth z, the transverse positions xin and xoul of the first and second points forming a focused base (x) at each depth z.

[0276] The responses R are then for example recorded in a focused reflection matrix R^, / ) whose coefficients are written as follows according to RXXL~, f) = [R( -L / '' ^aut^ <■» f )].

[0277] Determination of the frequency correction law0 (S140)

[0278] The step S140 of determining a frequency correction law 0 as illustrated in [Fig.6], then comprises sub-steps carried out at each depth z and each frequency / , of:

[0279] - determination S150 of a dual reflection matrix Rc(zJ) by forward projection of the focused reflection matrix Rxx(z, / ) towards a correction basis (c),

[0280] - calculation S160 of the frequency correction law 0 from the matrix of dual reflection Rc(z, / ), said frequency correction law being determined on the basis of correction (c), 0 = [ / (c, f, r / )], so that said frequency correction law 0 is a space-frequency correction law,

[0281] - determination S170 of a corrected dual reflection matrix R around the point of reference and whose coefficients are written according to / ) = GZ, f ) ]' determined by performing the term-by-term product between the dual reflection matrix Rc(z, / ) and the phase conjugate of the frequency correction law 0, that is to say by:

[0282] R; = Rco0

[0283] where

[0284] the symbol * denotes a phase conjugation operation

[0285] the symbol 0 is the Hadamard product, such that:

[0286] X-(x, f} = fc, ' f)-

[0287] The step S180 of determining the corrected responses R of the medium around the reference point then comprises the determination of a corrected focused reflection matrix Rr^ fj by return projection of the corrected dual reflection matrix R'c(z,f) towards the focused base (x).

[0288] Thanks to these provisions, the method advantageously makes it possible to locally probe the medium and to correct the focused reflection matrix with respect to the aberrations, in particular by determining a correction law for each point of the medium M of spatial position rp, and for each frequency / of the ultrasonic wave.

[0289] This correction is carried out in a correction base c adapted to the aberrations to be corrected. The correction base c is an input correction base or an output correction base.

[0290] Basic examples of correction are:

[0291] - a plane wave basis or spatial Fourier basis,

[0292] - a base of the transducers u,

[0293] - a base corresponding to the supposed location of the aberrators in the medium, that is to say for example a plane between the transducer plane (transducer base u) and the focusing plane (focusing base x),

[0294] - a base corresponding to a plan determined by optimization, for example by a correlation matrix whose first eigenvalue is maximum.

[0295] Dual reflection matrix Rc(z, / ) (S150)

[0296] According to an embodiment of the method of the present disclosure, the forward projection S150 makes it possible to determine a dual reflection matrix Rc(z, / ). This forward projection S150 can be carried out by:

[0297] a matrix product between a passage matrix P and the focused reflection matrix R^, / ), that is to say:

[0298] R,(z, / )=P(z, / )xR„fc / )

[0299] where: P( z, f) = [P(c, X, z, / ) ] is the passage matrix at each frequency / between the focused base (x) at depth z and the correction base (c).

[0300] The passage matrix P depends on the correction base c used.

[0301] In the case of a correction basis corresponding to a plane wave basis (c=k), the passage matrix P is the Fourier transform operator.

[0302] In the case of a network 10 of transducers 11 of linear type to generate a two-dimensional image, the coefficients of this passage matrix P can be written as:

[0303] P (kx, x, z, f) = P (k^ x} -exp{- ikxx)

[0304] where kx, the transverse component of the wave vector k associated with each plane wave.

[0305] In the case of a network 10 of transducers 11 of matrix type to generate a three-dimensional image, the coefficients of this passage matrix P can be written:

[0306] P(k^p, z,f) = P(k^p,z, f) =exp(-ik^p)

[0307] where

[0308] is the transverse component of the wave vector k associated with each plane wave, and

[0309] p = (x, y), the transverse position vector.

[0310] In the case of a correction base corresponding to a base of the transducers (c=u ), the coefficients of the passage matrix P correspond to the normal derivative of the Green function connecting each focal point of spatial position (x, z) and each transducer 11 of spatial position (u, 0).

[0311] In the case of a network 10 of transducers 11 of linear type to generate a two-dimensional image, the coefficients of the passage matrix P can be written as:

[0312] P(ux,z,f)=V,G2D(u,r,f)

[0313] where Vz is the projected gradient along the depth direction z, and

[0314] G2£>( U, r ) is the 2D Green function that relates each transducer u = (u, 0) to each point r of the middle M, with:

[0315] =

[0316] where = In f / Cq is the wave number,

[0317] Ho is the first-order Hankel function whose asymptotic expression is as follows:^^^.^^ = vy£o|ur|

[0318] In the case of a network 10 of transducers 11 of matrix type to generate a three-dimensional image, the coefficients of this passage matrix P can be written:

[0319] P(u,x, z, / ) = VÆ3D(u,r, / )

[0320] where G3d(u,r) is the 2D Green function that connects each transducer U = (wA, 0) at each point r = (p, z) of the midpoint M, with: [0321 ] exp( -('A:0^u.pp+z2 ) l / ) =.............-

[0322] The coefficients of the passage matrix P are therefore written in this case as follows:

[0323] exp / -dÀi-pp+ÿ I P(u,x,zf) = -i^........Vr.........Z u |up| Space-frequency correction law (S160)

[0324] According to a first embodiment illustrated in [Fig.7] of the step of calculating the spatio-frequency correction law S160, this calculation step S160 comprises:

[0325] the construction of a correlation matrix S161 C from the dual reflection matrix Rc(z,f), determined in the forward projection step S140, and

[0326] analysis S162 of the correlation matrix C to determine the correction law spatio-frequency <&.

[0327] The spatio-frequency correction law makes it possible to correct the dual reflection matrix Rc(zJ) in the correction basis c, to obtain a corrected dual reflection matrix R'c(zJ). This correction in the correction basis c is then applied to the focused basis x by the return projection S180 of the corrected dual reflection matrix R'c(zJ) in order to obtain a corrected focused reflection matrix R* / 7, f\ Correlation matrix (S161)

[0328] According to a first variant of step S161, the correlation matrix C is determined in the correction base c and in the frequency domain, by the following calculation of the elements of the correlation matrix C = Ccc:

[0329] = C, Z, f) Rref{x, C, Z, f) Rc(x, C, Z, f) Rre / (x, c\Z, f '

[0330] where Rc is the dual reflection matrix,

[0331] Rref is a model reflection matrix of a model medium in which the sound speed is c0 the expected sound speed of the medium and in which a plane reflector is positioned at depth z,

[0332] x, z are the coordinates of points in the region around point rp,

[0333] * is the conjugation operator.

[0334] The addition of a reference matrix Rref to the reflection matrix Rc in the previous equation makes it possible to compensate for the geometric component of the reflection matrix predicted by the sound speed model coet to isolate the distorted and reverberated components of the wavefront. Seen from the focal plane, this operation amounts to virtually moving each focusing point (x, z) to the origin of the reference frame. For a random reflectivity medium (ultrasonic speckle) and a sufficient number of focusing points (x, z) in the region around the spatial position reference point rp, the correlation matrix obtained is equivalent to that which would be measured in the correction base for a coherent virtual reflector whose extent is defined by the focal spot induced by the focusing process in said region.This virtual reflector constitutes a guide star which will be used later to determine an optimal spatio-temporal focusing law in the region around the reference point rp.

[0335] According to a second variant of step S161, the correlation matrix C is determined in the correction base c and in the frequency domain, by the following calculation of the elements of the correlation matrix C = Ccc:

[0336] c( {c, f}, {cf ') ) = £v(x, c, z, f ) x Dc*(x, c, z, / )

[0337] where Dc is a dual distortion matrix obtained by

[0338]

[0339] which can be expressed in terms of calculating the coefficients of this matrix by:

[0340] Dc c, z, f) = Rc(x, c, z, f^R^x, az, / )•

[0341] where Rc is the dual reflection matrix,

[0342] Rref is a model reflection matrix of a model medium in which the velocity of the its is c0 expected sound speed of the medium and in which a plane reflector is positioned at depth z,

[0343] x, z are the coordinates of points in the region around point rp,

[0344] * is the conjugation operator.

[0345] This second variant is equivalent to the first variant. It involves an intermediate calculation of the dual distortion matrix Dc. It is therefore less direct than the first variant, but allows a focusing law to be extracted directly by a simple decomposition into singular values ​​of the matrix Dc.

[0346] Compared to previous work which only considered a distortion matrix temporally windowed at the single central frequency, the originality of the distortion matrix considered here is its frequency dependence which allows access to a complex spatio-temporal focusing law going beyond a simple time delay law. This in fact makes it possible to advantageously compensate, in addition to the classic aberrations, the problems of reverberation and frequency dispersion.

[0347] According to a third variant of step S161, the correlation matrix C is determined in a base of image points of spatial position (x, z), by the following calculation of the elements of the correlation matrix C = Crr:

[0348] C( {X, Z}, {X', Z.'} ) =ZcjRc(x C, Z, f)Rref(x, C, Z, f)Re(.X', C z' / ) Rref(x', C, Z, / )

[0349] where Rc is the dual reflection matrix,

[0350] Rref is a model reflection matrix of a model medium in which the velocity of the its is c0 expected sound speed of the medium and in which a plane reflector is positioned at depth z,

[0351] x, z are the coordinates of the image points in the region around the point rp.,

[0352] * is the conjugation operator.

[0353] The addition of a reference matrix Rref to the dual reflection matrix Rc in the previous equation makes it possible to compensate for the geometric component of the reflection matrix predicted by the sound speed model coet to isolate the distorted and reverberated components of the wavefront. Seen from the focal plane, this operation amounts to virtually moving each focal point (x, z) to the origin of the reference frame, thus forming a set of incoherent guide stars whose amplitude distribution is dictated by the support of the focal spot but also modulated by the random reflectivity of the medium. The calculation of the correlation matrix C in the base focused allows to determine the phase shift between each realization of guide star in the medium and will be used later to determine the way in which these different realizations can be rephased between them and be combined in order to be able to generate a coherent guide star.

[0354] According to a fourth variant of step S161, the correlation matrix C is determined in a base of image points of spatial position (x, z), by the following calculation of the elements of the correction matrix C = Crr:

[0355] C({x,z), {x'.z'J) = ï.cJDc(x,c,z,f) XD^x', c, z', f)

[0356] where Dc is a dual distortion matrix obtained by

[0357] f] = fy

[0358] which can be expressed in terms of calculating the coefficients of this matrix by:

[0359] dc (xc, z, f) = Rc(x, azf) Rref(x, c, z,

[0360] where Rc is the dual reflection matrix,

[0361] Rref is a model reflection matrix of a model medium in which the velocity of the its is c0 expected sound speed of the medium and in which a plane reflector is positioned at depth z,

[0362] x, z are the coordinates of points in the region around point rp,

[0363] * is the conjugation operator. Analysis (S162)

[0364] According to a first variant of step S162, the analysis of the correlation matrix C is carried out by a decomposition into eigenvalues ​​of the correlation matrix C, and the spatio-frequency correction law ® is the first eigenvector of the correlation matrix C in the correction basis (c), i.e. C = Ccc.

[0365] The correlation matrix being Hermitian _ ^ ), its eigenvalues ​​are real and positive.

[0366] The correlation matrix Ccc can thus be written:

[0367] Ccc = EpapUpf4

[0368] or in terms of matrix coefficients:

[0369] €({& / ).

[0370] with Uz? corresponding to the eigenvectors of the correlation matrix C

[0371] aP corresponding to the real and positive eigenvalues ​​of the correlation matrix Ccc arranged in decreasing order: > 02 > ••• >

[0372] We then have the spatio-frequency correction law which is equal to the first eigenvector, ie <p(rp) = Uj ; ou à sa version normalisée, <j>(rp) = exp( / argjüj ), i.e. a spatio-frequency correction law whose coefficients are of unit amplitude but whose phase is equal to that of U? (the symbol arg{ X} designates the phase of the vector X; or to an inverse filter type correction, O(ip) — exp (jarg {Uj}) / | Uj | • The first option is to be preferred if we are in the presence of a poor signal to noise ratio (matched filter). In general, the second option will however be preferred so that the correction does not act as an amplitude filter but allows the correction of only phase distortions. Finally, the third option is relevant when the aberrant medium inhomogeneously attenuates certain components and / or frequencies of the field that we wish to enhance in order to have a more faithful estimator of the reflectivity in fine.

[0373] According to a second variant of step S162, the analysis of the correlation matrix C is carried out by a singular value decomposition of the dual distortion matrix Dc defined above in the second variant of step S161. The eigenvalue decomposition of the correlation matrix Ccc carried out in the first variant of step S162 is in fact equivalent to the singular value decomposition (SVD) of the dual distortion matrix Dc when its coefficients are organized according to the following definition:

[0374] Uz})]

[0375] The singular value decomposition applies to rectangular matrices, and applied to the dual distortion matrix Dc, it is written as follows:

[0376] I)C = Y^VPV'P

[0377] or in terms of matrix coefficients:

[0378] {x,z})=E^Xar)v;Uz)

[0379] with Up — [ Up(c, / ) ] corresponding to the singular vectors of the dual distortion matrix Dc in the correction basis, or equivalently, to the eigenvectors of the matrix Ccc as defined in the first variant of step S162

[0380] VP = [ Vp(x, z) ] corresponding to the singular vectors of the dual distortion matrix Dc in the focused basis,

[0381] corresponding to the singular values ​​of the dual distortion matrix Dc which are, by definition, equal to the square root of the eigenvalues ​​of the correlation matrix C as defined in the first variant of step S162:

[0382] Thus, the spatio-frequency correction law C* is equal to the first singular vector of the dual distortion matrix Dc, i.e. rp) — ; or to its version normalized, ¢( rp) = exp( jarg{ Uj ), i.e. a spatio-frequency correction law whose coefficients are of unit amplitude but whose phase is equal to that of Uj (the symbol arg{X} designates the phase of the vector X); or to an inverse filter type correction, <D(rp) = exp(jarg{Ul}) / |U1| •

[0383] The interest of the singular value decomposition of the dual distortion matrix Dc with respect to an eigenvalue decomposition of the correlation matrix Ccc is the speed of calculation of the numerical algorithms of the singular value decomposition.

[0384] This search for the spatio-frequency correction law is also equivalent to solving the following equation:

[0385] a0(rp) =Cccx0(rp)

[0386] where x is the matrix product and a is a constant

[0387] iteratively by the following expression, which corresponds to an iterative time reversal calculation:

[0388] ®„1(rp)=Cccx "(rp),

[0389] with 0o an arbitrary wavefront, for example 0^ = [ 1 ■ ■ ■ 1 ]

[0390] Then, the space-frequency correction law 0 is obtained by:

[0391] 0 (rp) = lim0„ (rp),

[0392] or its standardized version:

[0393] 0 _ exp( | Hm0„ ( rp ) | ) '

[0394] or its inverse filter version:

[0395] expf / arg|Iim0„(rp) | ) ,

[0396] For n the iterative time reversal algorithm converges to the same first singular vector Uj of the matrix Dc. In practice, there may be an advantage in using an iterative time reversal algorithm rather than an SVD because it can converge after a few iterations, hence a faster calculation.

[0397] According to a third variant of step S162, the analysis of the correlation matrix C cc is carried out by solving the following equation:

[0398] 0(rp) = exp(j arg{Cccx 0(rp)})

[0399] iteratively by the following expression, which corresponds to a calculation by iterative phase reversal:

[0400] 0w+1 (rp) = exp (j arg {Cœ x 0„ (rp)})

[0401] where x is the matrix product,

[0402] with: 0q an arbitrary wavefront, for example 0 — p ... ] j T.

[0403] Then, the space-frequency correction law 0 is obtained by:

[0404] 0 (rp) = lim0„ (rp), This

[0405] Or its inverse filter version: (rp) = lime <t>B(rp)

[0407] The advantage of an iterative phase reversal algorithm compared to the previous alternatives is that it is a more reliable estimator of the phase of the correction law ^(rp) and therefore ultimately achieves better compensation for the phase distortions induced by the aberrator.

[0408] According to a fourth variant of step S162, the analysis of the correlation matrix Crr is carried out by solving the following equation:

[0409] W = exp(j arg{Crr x W))

[0410] where x is the matrix product,

[0411] iteratively by the following expression:

[0412] W„+1(rp) -exp(j arg{Crrx W„(rp)})

[0413] where x is the matrix product,

[0414] with Wo an arbitrary wavefront, for example yy = [ 1 ■ ■ ■ 1 ]

[0415] which makes it possible to obtain the following vector W:

[0416] W = HmWfl

[0417] This vector W = [ W(x, z)] defined in the focused basis contains the phase of each incoherent guide star synthesized by focusing in the region around the reference point rP.

[0418] The phase conjugate of this vector W can then be used to rephase each incoherent virtual star so as to be able to recombine them coherently and thus obtain an estimator of the spatio-frequency correction law *1* unbiased by the random reflectivity of the medium. Mathematically, this operation is written as follows:

[0419] 0(G f, rp) = exp{jx C / ) c- / )}}

[0420] The advantage of this approach compared to an SVD of the distortion matrix Dc (second variant of step S162) or of the iterative phase reversal algorithm (third variant of step S162) is to converge towards a correction law that is as isoplanatic as possible, i.e. efficient for each point of the region around the reference point rP. Space-frequency correction law (S160)

[0421] According to a second embodiment illustrated in figure 8 of the step of calculating the spatio-frequency correction law S160, this calculation step S160 is carried out by an optimization algorithm S163 maximizing the intensity or confocal intensity of an ultrasound image in the region ^p around the spatial position reference point rp.

[0422] In other words, the spatio-frequency correction law is determined by the following maximization:

[0423] (p (c, f, rp) = argmax {z)} ^(c, / ,Fp)

[0424] where z) is the intensity of the ultrasound image in the region Qp for the spatio-frequency correction law <p(c, f, rp) appliquée en entrée et en sortie.

[0425] This ultrasound image is for example determined by a triple sum on the frequency values / , on the input correction base cin and on the output correction base cout.

[0426] With the definitions previously given, we can for example have the following calculation:

[0427] 1(^,) = f, rp) A a; z,f, x, z)exp(-i4>(coat, f, rp) ) j"

[0428] The previous calculation includes a dual reflection matrix Rcc(c,„, cout, f) which is obtained by forward projection S150 into an input correction basis cin and an output correction basis cout, and whose coefficients can be expressed by:

[0429] R^C^ Cout) Z, f'} ​​f ' . / J» Xout, z)

[0430] This method of determining the spatio-frequency correction law is iterative with ultrasound image calculations. Even if these ultrasound images are limited to the region around the spatial position reference point rp, the iterations of the optimization algorithm can be computationally expensive.

[0431] However, this method has the advantage of determining the spatio-frequency correction law more accurately because it takes into account the reciprocity of the aberration corrections to be applied on the outward path and on the return path of the ultrasonic waves. Corrected dual reflection matrix (S 170)

[0432] According to the embodiment of the method of the present disclosure, illustrated in Figure 6, the corrected dual reflection matrix S170 r4 / ) = C, f,z) is determined by performing the term-by-term product between the dual reflection matrix Rc(z, f) and the phase conjugate of the space-frequency correction law O, i.e. by:

[0433] r; = Rco 0*

[0434] where the exponent * represents the phase conjugation operation

[0435] the symbol ° is the Hadamard product, that is to say the term-by-term matrix product of matrix coefficients, such that

[0436] £ (f,z)= Rc (X, C, X, C, f^z)' Corrected reflection matrix (S180)

[0437] According to the embodiment of the method of the present disclosure, a corrected focused reflection matrix R'v^, fj is then determined by back projection S180 of the corrected dual reflection matrix towards the focused base (x).

[0438] The return projection is carried out by a matrix product between the passage matrix P defined above and the focused reflection matrix r'. (z,f), that is to say: 104391 R„(4 f) -Pù. f)

[0440] Where the exponent t denotes the matrix trans-conjugation operation. Iterations of the correction treatment (Ll)

[0441] According to the embodiment of the method of the present disclosure illustrated in [Fig.5], the steps of the correction processing, i.e. the steps of:

[0442] - S140 of determining the frequency correction law ¢, said step S140 possibly comprising steps S150 of determining the dual reflection matrix Rc(z, f), S160 of calculating the frequency correction law d\ and S170 of determining the corrected dual reflection matrix Re(z, f)

[0443] - S180 for determining the corrected focused reflection matrix R^.^ y),

[0444] are iterated multiple times (twice or more than twice), as represented by loop Ll of [Fig.5].

[0445] At each iteration, the forward projection of step S150 uses the corrected focused reflection matrix RVA.(^, / ) obtained during the return projection of step S180 of the previous iteration instead of the focused reflection matrix Rxx(zJ).

[0446] Thus, at each iteration, the spatio-frequency correction law is improved to take into account one or more aberrations of the medium M better and better.

[0447] According to a first variant of this iterative process, at each iteration of step S150 of determining the dual reflection matrix Rc(z, f), a different correction base c is used, for example to correct different aberrations located in different places in the medium.

[0448] For example, the medium M can be discretized or modeled by a succession of layers according to the direction of the depth z, and the correction bases c of the iterations correspond to planes of these successive layers. In other words, corrections corresponding to a plurality of aberrations of the medium M are applied during the iterations.

[0449] For example, the medium M can be spatially segmented into domains, in a predetermined manner or automatically on the basis of a first ultrasound image of the medium M. Each iteration of the iterative process will perform a correction on a correction basis c corresponding to each domain of said medium M.

[0450] According to a second variant of this iterative process, at each iteration of step S150 of determining the dual reflection matrix Rc(z, f), a forward projection is used either towards an input correction basis or towards an output correction basis of the reflection matrix. In the latter case, the projection of the matrix Rxx(z, / ) towards the correction basis is carried out in the following manner:

[0451] R, (z, f) = 1¾. / ) x R |.. / )

[0452] where the symbol I denotes the matrix transposition operation.

[0453] In the succession of iterations, one can alternate between the use of an input correction base and an output correction base. Thus, the spatio-temporal correction law is improved at each iteration, and the correction of aberrations is improved.

[0454] According to a third variant of this iterative process, at each iteration of step S150 of determining the dual reflection matrix Rc(z, f), a region around the spatial position point rp of increasingly smaller size is used during these iterations. In other words, at each iteration the size of the calculation region around the reference point rp is reduced. By size of the region, one can understand the width in the x direction or the depth in the z direction, or both, or any other dimension convention of this region, for example adapted to the scanning mode of the medium M.

[0455] Thus, the law of correction is increasingly better suited to a localized aberration near the spatial position reference point rp. Confocal image (S 190)

[0456] According to one embodiment of the ultrasonic characterization method of the present disclosure, the method further comprises a step of:

[0457] - determination S190 of an intensity Ic(x,z) of an ultrasound image point of spatial position (x, z), from the diagonal coefficients of the corrected focused reflection matrix r' / zJ) integrated over the bandwidth of the ultrasonic signals, i.e. by the combination of the corrected responses R' of the point at several frequencies / . We thus have, for example, the following calculation: 104581

[0459] The previous intensity determined at a plurality of points makes it possible to construct a corrected confocal image of the medium M, which corresponds to a classic ultrasound image freed from the problems of aberrations, reverberations and frequency dispersion of the speed of sound in the medium studied. 2 - Second embodiment

[0460] A second embodiment of method S100 of the present disclosure performs more direct calculations, for example for the purpose of determining primarily a characterization of the medium M in a confocal manner. This simplified embodiment can be useful for determining more simply the intensity lc of an ultrasound image point, in order to more quickly determine an ultrasound image of an area of ​​interest of the medium M.

[0461] In this second embodiment, the focusing processes are determined or calculated only between identical virtual input transducer points and virtual output transducer points. This amounts to determining only the diagonal components of the focused reflection matrix Rxx(z, f) of the first embodiment, and recording them in a confocal reflection matrix R(z, / ), which drastically reduces the number of calculated medium responses.

[0462] [Fig. 12] illustrates this method according to the second embodiment of the present disclosure. The network of transducers, placed opposite a medium, makes it possible to insonify and image a region of a medium with random reflectivity of the “speckle” type.

[0463] In the first diagram (A) of this figure 11, a plurality of waves are emitted successively into the medium using focused emissions towards several focal points of spatial positions r^, r? and by a technique called path formation or focusing. The waves pass through a reverberant layer and arrive at the focal points with multiple reflection echoes induced by the reverberant layer.

[0464] In the following three diagrams (B) of the figure, during the return journey, the waves reflected at each focal point cross the reverberant layer again, causing a new multiplication of echoes induced by the multiple reflections within the reverberant layer. The temporal signals received by the transducers are very complex and then all include numerous echoes linked to the multiple reflections.

[0465] As shown in the fifth diagram (C), by performing an average or correlation processing of the echoes induced by the plurality of focal points in the region around the spatial position reference point rp, a temporal response is obtained such as it would be generated by a virtual coherent reflector. This calculation makes it possible to determine a frequency correction law to be applied to the signals to compensate for the reverberations on the ultrasound image.

[0466] The sixth diagram (D) of this figure explains how one can use this deconvolved and temporally reversed virtual response as the optimal delay law to be applied in order to correctly focus on each focal point while compensating for problems of temporal dispersion and / or multiple reflections.

[0467] The method of this second embodiment is described in more detail below.

[0468] This second embodiment of the method S100 has the following characteristics.

[0469] The step S130 of determining a set of responses R of the medium comprises determining responses which are obtained by the process of focusing between a first spatial position point rin= (xim z) corresponding to a virtual input transducer and a second spatial position point rout= (xout, z) corresponding to a virtual output transducer, the first point and the second point being identical (rin = rout), and

[0470] all the responses R being recorded in a confocal reflection matrix R whose coefficients are written according to R = [ f ) ].

[0471] Thus, in comparison with the first embodiment, the confocal reflection matrix R now only comprises a single lateral position parameter x, instead of the two independent lateral position parameters xin and xouf.

[0472] The step of determining (S 140) the frequency correction law is then carried out directly by correlating the responses of the medium to the different points of spatial positions (x, z) around the reference point, and the coefficients of this frequency correction law are written 0 = [¢( / , r^)]-

[0473] The step of determining (S 180) the corrected responses R around the reference point is then carried out directly by applying the frequency correction law to each frequency / by carrying out the term-by-term product between the confocal reflection matrix R and the phase conjugate of the frequency correction law, i.e. by:

[0474] R = R o <D

[0475] where

[0476] all the corrected responses R are recorded in a corrected confocal reflection matrix r' whose coefficients are written according to R' = [ 'U ^ / )]

[0477] the symbol ° is the Hadamard product, such that:

[0478] R (z,f)= R(x, z, / ) / *( / '

[0479] Thanks to these provisions, the method advantageously makes it possible to locally probe the medium and to correct the confocal reflection matrix with respect to aberrations, in particular by directly determining a correction law for reference points of spatial position rp of the medium M and for several frequencies / of the ultrasonic wave.

[0480] The frequency correction law <1* is calculated more directly and more simply than in the first embodiment, by correlation of the responses received, that is to say without using a correction base, nor a dual reflection matrix. Frequency correction law (S 140)

[0481] According to a first embodiment of the step of determining a frequency correction law S140, illustrated in [Fig.9], this step S140 comprises:

[0482] the construction of a correlation matrix S141 C from the confocal reflection matrix R(z, f), and

[0483] an analysis S142 of the correlation matrix C to determine the frequency correction law

[0484] This step of determining a frequency correction law S140 is then similar to the step of calculating the frequency correction law S140 of the first embodiment. It does not require a dual reflection matrix and it is directly implemented on the confocal reflection matrix. The calculations are thus simplified, but the possible variants of these steps of the method are also similar to those of the first embodiment, as explained below.

[0485] According to a first variant of step S141, the correlation matrix C is determined in the frequency domain by the following calculation:

[0486] C(f, f) = V If tz, / ) «'(* z. f)

[0487] where R is the confocal reflection matrix,

[0488] x, z are the coordinates of the points in the region around the reference point,

[0489] * is the conjugation operator.

[0490] According to a second variant of step S141, the correlation matrix C is determined in a base of image points of spatial position (x, z), by:

[0491] C( {x, z}, {x'.z'J )

[0492] where R is the confocal reflection matrix,

[0493] x, z are the coordinates of the image points in the region around the reference point,

[0494] * is the conjugation operator.

[0495] According to a first variant of step S142, the analysis of the correlation matrix C is a decomposition into eigenvalues ​​of the correlation matrix C and the frequency correction law d> is the first eigenvector U! of the correlation matrix C.

[0496] According to a second variant of step S142, the analysis of the correlation matrix C is the resolution of an equation involving the correlation matrix C and the frequency correction law O, this equation resolution corresponding to an iterative time reversal or an iterative phase reversal, in a manner similar to what was explained in the first embodiment.

[0497] According to a second embodiment of the step of determining a frequency correction law S140, the determination of the frequency correction law is carried out by an optimization algorithm maximizing the confocal intensity of an ultrasound image in the region around the reference point, in a manner similar to what was explained in the first embodiment. Iterations of the correction treatment (Ll)

[0498] As illustrated in [Fig.5], the steps of the correction processing, i.e. the steps of:

[0499] - S140 for determining the frequency correction law and

[0500] - S180 of determination of the corrected confocal reflection matrix R'(z, f),

[0501] are iterated multiple times (twice or more than twice), as represented by loop L1 of [Fig.5].

[0502] At each iteration, the step of determining the frequency correction law of step S140 uses the corrected confocal reflection matrix R(A, f) obtained during the step of determining the corrected responses of step S180 of the previous iteration instead of the confocal reflection matrix R(z,f).

[0503] Thus, at each iteration, the frequency correction law is improved to take into account one or more aberrations of the medium M better and better.

[0504] At each iteration of step S140, a region around the spatial position reference point rp of increasingly smaller size may be used during these iterations. In other words, at each iteration the size of the calculation region around the reference point rp is reduced. By size of the region, one may understand the width in the x direction or the depth in the z direction, or both, or any other dimension convention of this region, for example adapted to the scanning mode of the medium M.

[0505] Thus, the correction law ® is increasingly better adapted to an aberration located near the spatial position reference point rp. Confocal image (S 190)

[0506] According to one embodiment of the ultrasonic characterization method of the present disclosure, the method further comprises a step of:

[0507] - determination S190 of an intensity Ic(x,z) of an ultrasound image point of spatial position (x, z) by combining the corrected responses R' of this point at several frequencies / . We thus have, for example, the following calculation: 105081

[0509] The previous intensity determined at a plurality of points makes it possible to construct a corrected confocal image of the medium M, which corresponds to a classic ultrasound image freed from the problems of aberrations, reverberations and frequency dispersion of the speed of sound in the medium studied.

[0510] Results on a calibrated experimental medium (called “phantom”)

[0511] [Fig. 13] illustrates a calibrated experimental environment called “phantom” generating a ultrasonic speckle with two cylindrical inclusions exhibiting greater reflectivity than the surrounding medium and a plurality of point reflectors (nylon threads) arranged linearly along two lines, one horizontal and the other vertical. Apart from the point reflectors, the speed of sound in this medium is approximately 1540 ms-1. On this phantom is placed a layer of plexiglass corresponding to an aberrator layer, having a speed of sound of approximately 2750 ms-1. On this layer is then positioned the network 10 of transducers 11 of the ultrasonic probe. The medium is insonified by a plurality of plane waves of various angles between -40 and +40 degrees relative to the plane of the transducers. The ultrasonic waves in such a medium pass through media having different sound speeds and undergo multiple reflections (reverberations) between the interfaces of these media before reaching the diffusers of the phantom medium.

[0512] [Fig. 14] illustrates an ultrasound image obtained in an area of ​​interest of the experimental medium of [Fig. 13]. This ultrasound image is obtained with a sound speed assumption of 1540 ms-1, in the volume of the insonified medium. This ultrasound image illustrates the aberration and reverberation problems induced by the plexiglass layer on the image of the point reflectors. First, the image of each point reflector is stretched laterally, which illustrates the degradation of the lateral resolution of the image due to the differences between the sound speed model cO and the actual sound speed distribution in the medium. Second, the image of each point reflector is repeated in the direction of depth z behind each ballistic image of a reflector, which illustrates the reverberations induced by the echoes of multiple reflections within the plexiglass layer.Therefore, the ultrasound image is very disturbed with both lateral and axial distortions of the ultrasound image. In the case of medical imaging, these problems lead to low contrast, low resolution and the appearance of artifacts in the ultrasound image, which seriously hinders the practitioner's diagnosis.

[0513] Figure 1 5 then illustrates a frequency correction law ® obtained by the method according to the present disclosure in the region of the medium B1 of Figure 14. This frequency correction law is obtained according to the second embodiment, by iterative phase reversal of the frequency correlation matrix C=[C( / , / ')] of the confocal signals of each point of the medium. This figure first shows the modulus and the phase as a function of the frequency for this frequency correction law, then the temporal representation of this frequency correction law obtained by inverse Fourier transform. The phase of the frequency correction law corresponds to the phase shifts to be applied to each frequency component of the ultrasonic signals.Equivalently, the time correction law corresponds to the law of time delays which must be convolved to the received ultrasound signals to (partially) compensate for reverberation problems and obtain a more satisfactory ultrasound image.

[0514] The temporal representation of the frequency correction law includes a first high amplitude echo whose echo time less than the ballistic time corresponds to the error of the propagation model on the speed of sound in the medium, and several subsequent echoes corresponding to the multiple reflections in the plexiglass layer. Thus, this frequency correction law makes it possible to correct on average the aberrations in the B1 region of the experimental medium which corresponds to a “speckle” region of the medium. This law is then used in the area of ​​interest for characterizing the medium, and in particular to improve a corrected ultrasound image of this area of ​​interest, as can be seen in [Fig.l6](b) explained below.

[0515] [Fig. 16] illustrates the improvement obtained by the method according to the present disclosure.

[0516] The left image (a) in this figure is the ultrasound image obtained with the focusing method generally used in the prior art of the experimental medium with a sound speed assumption c0 of 1540 ms', and without aberration correction. This image has a low resolution and is of poor quality.

[0517] The right image (b) in this figure is an image obtained by the method described to correct aberrations in sound speed and multiple reflections. There is a significant improvement in the spatial resolution of the image of point reflectors in the medium and the (partial) suppression of echoes from multiple reflections. The background image also shows a greater difference in amplitude between the virtual reflectors and the surrounding speckle. The reverberation compensation process therefore significantly improves the quality, particularly the contrast, of the ultrasound image.

[0518] Figure 17 illustrates, as in figure 16(b), the ultrasound image obtained with respect to an area of ​​interest in the experimental environment of figure 13 after applying compensation for aberrations and reverberations according to the first embodiment, i.e. by applying a spatio-frequency correction CD1 — / )] de terminated in the plane wave basis. This law is obtained by iterative phase reversal of the space-frequency correlation matrix Ckk = C( {kx, / }, {k'x, f'} ​​) obtained by averaging the correlations over all points in the field of view. As in [Fig.l6](b), this global correction only allows partial compensation of aberrations and reverberations. Unlike [Fig.l6](b), three regions Cl, C2, and C3 are identified in this image in order to locally and iteratively apply the method of the present disclosure.

[0519] Figure 18 illustrates the result of the determinations of the spatio-frequency correction law 9b in the first region Cl of Figure 17, in the region C2 of the figure 17, then in region C3 of figure 17. Thus, on the first line (a) of this figure 18, the spatio-frequency correction law ® in the first region Cl is represented by its spectrum (|C^ X as a function of the transverse component kx of the wave vector and the frequency / (left image) and by its phase (arg [<!----> ]) as a function of kx and frequency / (right image). The second line (b) of figure 18, represents with the same formalism, the spatio-frequency correction law *1* in the second region C2. Another spatio-frequency correction law ® is also determined for the third region C3 in the ultrasonic speckle.

[0520] [Fig. 19] then illustrates the improvement obtained by the method according to the present disclosure using the local spatio-temporal correction laws including the corrections C1, C2 and C3.

[0521] The left image (a) in this figure is the ultrasound image with the focusing method generally used in the prior art of the experimental environment with a sound speed assumption c0 of 1540 ms', and without aberration correction. This image has a low resolution and is strongly degraded by the phenomenon of reverberations.

[0522] The center image (b) in this figure is an image obtained by the described method for correcting sound speed and multiple reflection aberrations globally across the entire area of ​​interest in the image. This correction corrects the aberrations on average for this entire area of ​​interest, which already provides an improvement. This image is analogous to that shown in [Fig. 17].

[0523] The right image (c) in this figure is an image obtained by the method described by iterating the calculations of the spatio-frequency correction law locally as illustrated by [Fig.18] for the regions C1, C2 and C3 shown in [Fig.17]. The corrections made to the spatio-frequency correction laws make it possible to significantly improve the spatial resolution of the image and make it possible to largely eliminate the echoes induced by the multiple reflections within the plexiglass layer. Finally, the relative amplitude between the point reflectors and the surrounding speckle is much better, which illustrates the gain in terms of contrast provided by local compensation for aberrations and reverberations. Ultrasonic characterization system

[0524] The system 1 for ultrasonic characterization of the medium M according to the present disclosure is illustrated in [Fig.3]. It comprises:

[0525] - an array 10 of transducers 11 adapted to generate a series of ul- waves incident ultrasonic waves in an area of ​​the medium, and to measure as a function of time the ultrasonic waves backscattered by said area; and

[0526] - a computing unit 30 connected to the transducer network and adapted to implement implements a method comprising steps of:

[0527] - generation SI 10 of a series of incident ultrasonic waves USin in the area of ​​the medium, by means of the network 10 of transducers 11, this series of incident ultrasonic waves being an emission base i; and

[0528] - S120 measurement of a canonical reflection matrix Rui(t) defined between the basis emission base i at the input and a reception base u at the output, the coefficients of this canonical reflection matrix corresponding to the signals received by the transducers and induced by the ultrasonic waves reflected in the medium;

[0529] - determination (S 130) of a set of responses R of the medium which are obtained by a focusing process for several frequencies / and for several points of spatial position r = (x, z) of a region around a reference point of spatial position rp = (Xp, zp) from the canonical reflection matrix Rui(t) for a sound speed model c0,

[0530] - determination (S 140) of a frequency correction law ® from the responses from the middle to the different spatial position points (x, z), the frequency correction law being adapted to the reference point and being determined at the frequencies /

[0531] - determination (S180) of the corrected responses R of the medium by application of the law of frequency correction ® to the R responses of the medium around the reference point and for the plurality of frequencies / < / t> < / j>

Claims

Claims

1. A method for ultrasonic characterization (S100) of a medium, comprising the steps of: - generating (S 110) a series of incident ultrasonic waves (USin) in an area of ​​interest of said medium, by means of an array (10) of transducers (11), said series of incident ultrasonic waves being an emission base (i); and - measuring (S 120) a canonical 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 canonical reflection matrix corresponding to the signals received by the transducers and induced by the ultrasonic waves reflected in the medium;said method being characterized in that it further comprises a correction processing comprising the steps of: - determining (S 130) a set of responses 7? of the medium which are obtained by a focusing process for several frequencies / and for several points of spatial position r = (x, z) of a region around a reference point of spatial position rP = (xp, zp ) from the canonical reflection matrix Rui(t) for a sound speed model c 0, - determining (S 140) a frequency correction law from the responses of the medium at the different points of spatial position (x, z), the frequency correction law being adapted to the reference point and being determined at the frequencies / - determining (S 180) the corrected responses R of the medium by applying the frequency correction law ® to the responses R of the medium around the reference point and for the plurality of frequencies / ;

2. A method according to claim 1, further comprising a step of: - determining (S 190) an intensity Ic of an ultrasound image point corresponding to the spatial position reference point rp by combining the corrected responses at several frequencies / of this reference point.

3. Method according to claim 1 or claim 2, wherein: - the determination (S 130) of the set of responses R of the medium comprises the determination of responses which are obtained by the process of focusing between a first point of spatial position rin = (xin, z) corresponding to a virtual input transducer and a second point of spatial position rout= (xout, z) corresponding to a virtual output transducer, the first point and the second point being identical (rin = rout), and all the responses R being recorded in a confocal reflection matrix R whose coefficients are written according to R = [SUz, / )], - the determination (S 140) of the frequency correction law is carried out by correlation of the responses of the medium at the different points of spatial positions (x, z) around the reference point, and whose coefficients are written (J> = [¢( / , r^)] - the determination (S 180) of the corrected responses R around the reference point, by application of the frequency correction law at each frequency / , by carrying out the term-by-term product between the confocal reflection matrix R and the phase conjugate of the frequency correction law O,that is to say by: R =Ro q* where all the corrected responses R are recorded in a corrected confocal reflection matrix r' whose coefficients are written according to R'=[«W)] the symbol ° is the Hadamard product, such that: R z, f) = R(x, z, rp)-,

4. Method according to claim 3, further comprising a step of: - determining (S 190) an intensity Ic of an ultrasound image point of spatial position (x, z) by combining the corrected responses R of this point at several frequencies / i.e. by: Z.) = Z, / )|2

5. A method according to claim 3 or claim 4, wherein: determining a frequency correction law (S 140) comprises constructing a correlation matrix (S 141) C from the confocal reflection matrix R(z,f), and analyzing (S 142) the correlation matrix C to determine the frequency correction law *1*.

6. Method according to claim 5, in which: the correlation matrix C is determined in the frequency domain, by: c( ff ) R'(x,in where R is the confocal reflection matrix, x, z are the coordinates of the points in the region around the reference point, * is the conjugation operator.

7. Method according to claim 5, in which: the correlation matrix C is determined in a basis of the image points of spatial position (x, z), by: C( (¾z), {y.z') ) = ï.fR(x,z, f) where R is the confocal reflection matrix, x, z are the coordinates of the image points in the region around the reference point, * is the conjugation operator.

8. Method according to one of claims 5 to 7, wherein: the analysis (S 142) of the correlation matrix C is a decomposition into eigenvalues ​​of the correlation matrix C and the frequency correction law O is the first eigenvector Uj of the correlation matrix C.

9. Method according to one of claims 5 to 7, in which: the analysis (S 142) of the correlation matrix C is the resolution of an equation involving the correlation matrix C and the frequency correction law O, this equation resolution corresponding to an iterative time reversal or an iterative phase reversal.

10. Method according to one of claims 3 to 9, wherein: the determination (S 140) of the frequency correction law is carried out by an optimization algorithm maximizing the confocal intensity of an ultrasound image in the region around the reference point.

11. Method according to one of claims 3 to 10, wherein: the steps (S 140, S180) of the correction processing are iterated several times, and wherein at each iteration, the corrected confocal reflection matrix R'(zJ) obtained at the previous iteration is used instead of the focused reflection matrix R(zJ).

12. The method of claim 11, wherein: at each iteration, the size of the region around the spatial position reference point rp is reduced

13. Method according to one of claims 3 to 12, in which: the determination (S 130) of the confocal reflection matrix R(z, / ) includes compensation for the time attenuation of the signals.

14. A method according to claim 1 or claim 2, wherein: - the determination (S 130) of the set of responses 7? of the medium comprises the determination of responses which are obtained by the focusing process between a first point of spatial position rin = (xin, z) corresponding to a virtual input transducer and a second point of spatial position rout= (xout, z) corresponding to a virtual output transducer, the first point and the second point being located in the region at the same depth z, the transverse positions x in and xout of the first and second points forming a focused base (x) at each depth z, and the set of responses R being recorded in a focused reflection matrix Rxx(z, / ) whose coefficients are written according to Rxx(z, f )= [RC-^wp xouti z, / )], - the determination (S 140) of the frequency correction law ® comprises sub-steps carried out at each depth z and each frequency / , of: - determination (S 150) of a dual reflection matrix Rc(z, / ) by forward projection of the focused reflection matrix Rxx(z, / ) towards a correction basis (c), - calculation (S 160) of the frequency correction law <1* from the dual reflection matrix Rc(zJ), said frequency correction law being determined on the basis of correction (c), (J) — f, I / )], so that said frequency correction law <1* is a spatio-frequency correction law, - determination (S 170) of a dual reflection matrix corrected around the reference point and whose coefficients are written according to R.(s. f) = [X( x, c, fi -) ]' determined by performing the term-by-term product between the dual reflection matrix Rc(z, / ) and the phase conjugate of the frequency correction law <1*, i.e. by: R. = Rc° Or the symbol * denotes a phase conjugation operation the symbol 0 is the Hadamard product, such that: Rc(x, c, f, z.Xi c,f,z)^(x. C, f, Z) - the determination (S 180) of the corrected responses R of the medium around the reference point includes the determination of a corrected focused reflection matrix fj by back projection of the corrected dual reflection matrix R'c(zJ) to the focused base (x).

15. Method according to claim 14, further comprising a step of: - determining (S 190) an intensity Ic of an ultrasound image point of spatial position (x, z), by combining the diagonal coefficients of the corrected focused reflection matrix R'xx(z, / ) of this point, at several frequencies / , that is to say: iv~> ' <2 z) — z, / ) |

16. A method according to claim 14 or claim 15, wherein: the forward projection (150) is performed by a matrix product between a pass matrix and the focused reflection matrix Rxx(z, / ), i.e.: where: P (s, f ) = [P(c, x, z^ f) ] is the pass matrix at each frequency / between the focused base (x) at depth z and the correction base (c).

17. Method according to one of claims 14 to 16, wherein: the correction base (c) is an input correction base or an output correction base.

18. Method according to one of claims 14 to 17, in which: The calculation of the frequency correction law (S 160) comprises the construction of a correlation matrix (S161) C from the dual reflection matrix Rc(z,f), and an analysis (S 162) of the correlation matrix C to determine the frequency correction law

19. The method of claim 18, wherein: the correlation matrix C is determined in the correction basis (c) and in the frequency domain, by: C ( [f, / }, ) = L^Rc(x, C, Z, f)Rrej(x, C, Z, / ) R*(.K, C, Z, f) RreJ(x, c', Z, f') where Rc is the dual reflection matrix, Rref is a model reflection matrix of a model medium in which the speed of sound is c0 expected speed of sound of the medium and in which a plane reflector is positioned at depth z, x, z are the coordinates of the points of the region around the point rp, * is the conjugation operator.

20. Method according to claim 18, in which: the correlation matrix C is determined in a basis of the image points of spatial position (x, z), by: C„( {.r, 4, {x', z'} ) c, z, c' M / ) R>^ c'^f) where Rc is the dual reflection matrix, Rref is a model reflection matrix of a model medium in which the speed of sound is c0 expected speed of sound of the medium and in which a plane reflector is positioned at depth z, x, z are the coordinates of the points of the image in the region around the point rp., * is the conjugation operator.

21. Method according to one of claims 18 to 20, wherein: the analysis (S 162) of the correlation matrix C is a decomposition into eigenvalues ​​of the correlation matrix C and the frequency correction law is the first eigenvector of the correlation matrix C.

22. Method according to one of claims 18 to 20, in which: the analysis (S 162) of the correlation matrix C is the resolution of an equation involving the correlation matrix C and the frequency correction law ¢, this equation resolution corresponding to an iterative time reversal or an iterative phase reversal.

23. Method according to one of claims 14 to 22, in which: The calculation of the frequency correction law (S 160) is carried out by an optimization algorithm maximizing the confocal intensity of an ultrasound image in the region around the reference point.

24. A method according to one of claims 14 to 23, wherein: the steps (S 140, S180) of the correction processing are iterated several times, and wherein at each iteration, the forward projection (S 150) uses the corrected focused reflection matrix RJ^z / ) obtained during the return projection (S 180) of the previous iteration instead of the focused reflection matrix Rxx(z,f).

25. The method of claim 24, wherein: at each iteration of the forward projection (S 150), alternating between a forward projection in an input correction base and a correction base output correction.

26. Method according to claim 24, wherein: at each iteration, the correction base (c) of the forward projection (S 150) is different.

27. ​​The method of claim 24, wherein: at each iteration, the size of the region around the spatial position reference point rp is reduced

28. Method according to one of claims 14 to 27, wherein: the determination (S 130) of the focused reflection matrix R^, / ) comprises a compensation for the time attenuation of the signals.

29. System (1) for ultrasonic characterization of a medium (M), the system comprising: - an array (10) of transducers adapted to generate a series of incident ultrasonic waves in an area of ​​interest of the medium, and to measure as a function of time the ultrasonic waves backscattered by said area of ​​interest; and - a calculation unit (30) connected to the array of transducers and adapted to implement the method according to one of claims 1 to 28.

Images