High-resolution sounding method using diffused waves.

Abstract

The invention relates to an ultrasonic method for constructing a confocal image of an object contained in a medium, the method comprising the following steps: a) acquiring a canonical reflection matrix Rui(t) by insonizing the object via a diffusing screen present in the medium; b) determining a focused reflection matrix by projecting the canonical reflection matrix onto a space-frequency basis ξ; c) determining a corrected reflection matrix; d) determining a reflection matrix associated with the object by projecting the corrected reflection matrix onto a plane of the object; e) constructing an image from the object reflection matrix. The space-frequency basis ξ ensures independence between the spatial and frequency data and allows for the demonstration of a chromatic-angular memory effect associated with the field reflected by the object. The diffusing screen increases the basic resolution of the acquisition probe.Figure for the abridged version: Fig. 1.

Description

Title of the invention: High-resolution sounding method using scattered waves. Technical field

[0001] The present invention relates to a method and a system for constructing a confocal image of a heterogeneous medium.

[0002] The invention is advantageously applicable to the field of medical imaging, but can be applied to any field of ultrasound imaging, whether in air or via a coupling fluid. State of the art

[0003] In the field of acoustic imaging, the aim is to characterize an unknown medium by actively probing it with ultrasonic waves. This is notably the principle of the ultrasound scanner in medical imaging.

[0004] The lateral resolution ôx of an ultrasound image is limited by several phenomena. On the one hand, it is limited by the size D of the probe via the phenomenon of diffraction. The resolution is in fact dictated by the angle 6 subtended by the probe at the point to be imaged, such that

[0005] ôx-Àl ( 2sin0 ) ~ AzM / D,

[0006] with zm the distance between the probe and the point to be imaged.

[0007] Furthermore, due to inhomogeneities in the speed of sound between the different tissues of the human body, ultrasound images can also suffer from both transverse and axial aberrations that degrade their contrast and impair their resolution. Scattering events between the probe and the target point also induce multi-diffusion noise in the image, which limits its contrast.

[0008] To overcome these problems (aberration and scattering), a matrix approach to ultrasound imaging has been developed in recent years. It is based on the acquisition of the reflection matrix and consists of various post-processing algorithms that determine the focusing laws to be applied in order to eliminate aberrations and obtain an image whose resolution is limited only by diffraction.

[0009] We are familiar with the document Bureau, F., Robin, J., Le Ber, A. et al. “Three-dimensional Ultrasound Matrix Imaging.” Nat Commun 14, 6793 (2023), describing a method for compensating aberrations using the concept of a distortion matrix in ultrasound imaging. This technique, based on a time-windowed reflection matrix, does not allow access to a different correction law at each frequency and can therefore only correct low-order aberrations.

[0010] The document by Kwon, Y., Hong, JH, Kang, S. et al., “Computational conjugal adaptive optics microscopy for longitudinal through-skull imaging of cortical myelin,” Nat Commun 14, 105 (2023), is known, describing a method for compensating aberrations using the CLASS algorithm in the plane of an aberrant screen. CLASS stands for “Closed-Loop Accumulation of Single Scattering.” As with the previous method, this technique is also based on a time-windowed reflection matrix and does not allow access to a different correction law at each frequency. It can therefore only correct low-order aberrations.

[0011] The document YR Lee, et al., “Exploiting volumetric wave correlation for enhanced depth imaging in scattering medium,” Nat Commun 14, 1878 (2023), describing a CLASS matrix imaging algorithm in the frequency domain, is known. However, this algorithm operates from the plane wave basis and therefore does not allow for the correction of aberrations induced by a scattering screen.

[0012] Furthermore, in these documents, the algorithms developed do not allow the diffusion process to be exploited to enhance the resolution of the medium. However, it has been shown, through transmission experiments [A. Derode, P. Roux, and M. Fink, “Robust Acoustic Time Reversal with High-Order Multiple Scattering,” Phys. Rev. Lett. 75, 4206, 1995], that any diffusing medium can be transformed into a lens if the focusing laws can be accessed through it. In transmission, this process is relatively easy using methods such as time reversal or the inverse filter.

[0013] However, in imaging, we do not have access to the transmission matrix but to the reflection matrix. The object that we seek to image is therefore hidden behind the diffusing screen.

[0014] The present invention aims at a new ultrasound imaging method in which the scattering processes induced by the scattering screen will be compensated and, even better, exploited to improve the resolution of the ultrasound image and its contrast.

[0015] Another object of the invention is to show how the association of a network of sensors and a diffusing screen (in reflection or transmission) can constitute an intelligent probe having a small number of elements (which limits the cost and complexity of the associated electronics), possibly parsimonious, while allowing imaging of a large field of view at a resolution close to 2 / 2 without prior calibration measurement. Description of the invention

[0016] At least one of the aforementioned objectives is achieved with an ultrasonic method for constructing a confocal image of an object contained in a medium, the method comprising the following steps:

[0017] a) acquisition, by means of a network of transducers and a diffusing screen arranged on the Fonde path between the network of transducers and the object, of at least one canonical reflection matrix R Ui(t)=[7?(u out,i in,t)] defined between an ultrasonic wave emission basis i at the input and a reception basis 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 the object via the diffusing screen; t denoting the echo time;

[0018] b) determination of a focused reflection matrix R'^( w) by projection of the canonical reflection matrix into a space-frequency basis depending both on a position vector in a plane p of the diffusing screen and on an angular frequency co of the ultrasonic waves, this basis being defined by:

[0019] £ = ££ P ¢-0

[0020] where Co is the speed of sound in the medium, a distance between the diffusing screen and the object,

[0021] c) determination of a corrected reflection matrix R”^( w) in the space-frequency basis by application of a matrix imaging algorithm,

[0022] d) determination of a reflection matrix associated with the object R^ ) by projecting the corrected reflection matrix R"^( w) into a plane of the object x located at a distance zM with respect to the transducer array,

[0023] e) construction of an image from the object reflection matrix Rxx ( zM ) •

[0024] In the context of this disclosure, the term angular frequency œ or frequency f will be used interchangeably in the text and in the equations, the two parameters being proportional and well known to the person skilled in the art.

[0025] The invention makes it possible to exploit the diffusing medium as a lens in order to obtain an image of the reflectivity of the medium of interest with a resolution much better than in free space by virtually increasing the angular aperture of the transducer array. This achieves super-resolution.

[0026] The invention further allows the use of larger and therefore more powerful transducers in order to improve the signal-to-noise ratio.

[0027] With the present invention, an object can be imaged via the diffusing screen without calibration experience.

[0028] The method according to the invention is based on the acquisition and projection of the reflection matrix into a spatio-frequency basis whose coordinate = Z combines The spatial coordinate P of the diffusing screen, the angular frequency, and zo, the distance between the diffusing screen and the object. This basis maximizes the input-output correlations of the field associated with the object, which can be used to estimate the transfer function of the diffusing screen. The present invention takes advantage of the chromatic-angular memory effect in reflection associated with the object.

[0029] Once the transfer function of the diffusing screen is known, the angular diversity offered by the diffusion paths induced by the diffusing screen can be exploited and the angle under which the object is seen can be enlarged to obtain a precise image of the latter, with a resolution much better than in free space.

[0030] The association of transducer network - diffusing screen can be carried out in transmission, that is to say with the diffusing screen placed between the transducer network and the object to be imaged ([Fig.1]), or in reflection, that is to say with the transducer network and the object placed on the same side with respect to the diffusing screen ([Fig.2]).

[0031] Preferably, the object to be imaged according to the invention is two-dimensional with a thickness less than the depth of field.

[0032] The field of view is limited by the range of the memory effect associated with the diffusing screen. If this diffusing screen is two-dimensional, the range of the memory effect is valid over the entire angular domain, and the field of view is limited only by the geometric decay of the ultrasonic waves. If the diffusing screen is volumetric, the angular range of the memory effect is on the order of 2 / L in transmission and M'k in reflection, where L is the thickness of the diffusing medium and A' is the mean free path of the wave within the diffusing screen. This range of the memory effect designates the size P of the patch on which the transfer function H(A Q') of the diffusing screen can be considered spatially invariant: P → AzJ L in transmission and P → XzntK. Thus, the estimation of a single transfer function will be necessary if the size of the area to be imaged is less than P.For a given field of view (FOV), the number of transfer functions to be determined is on the order of FOV / P.

[0033] In prior art aberration correction methods, the ultrasonic data are projected onto the plane of the aberrator, and the spatial and frequency dependencies of the aberrator are determined independently. In the present invention, the spatio-frequency basis ensures optimal exploitation of the chromato-angular memory effect associated with the field reflected by the object and allows for a much more reliable estimation of the transfer function of the diffusing screen.

[0034] This unbiased estimation of the transfer function thus improves the focusing quality and a gain in resolution is obtained for confocal images since the insertion of the diffusing screen between the probe and the object allows the aperture to be enlarged of the imaging system and thus obtain super-resolution. The resolution is indeed given by:

[0035] ôx=Àf {IM'y-XzjE

[0036] Where is the angle at which the object sees the diffusing screen and E is the size of the diffusing screen. Since the size E of the screen is much larger than the size of the probe E and the screen is closer to the object to be imaged than the probe, the resolution of the final confocal image is much better than in free space.

[0037] The acquisition step includes measurements of the field reflected by the object via the diffusing screen for a set of incident waves generated by the transducer array, also via the diffusing screen. This set of reflected fields forms the reflection matrix R(t) stored in a memory space. The variable t represents the echo time associated with the signals recorded during the measurement. For each measurement, the amplitude and phase of the ultrasonic signal are acquired.

[0038] According to an advantageous embodiment of the invention, the step of acquiring at least one canonical reflection matrix Ru(t) may include the emission of an ultrasonic pulse from each transducer of the network whose position is located by the coordinate u in, this pulse gives rise to a divergent cylindrical or spherical incident wave which is reflected by diffusers of the medium, these reflected echoes form a backscattered field which is recorded by each of the transducers as a function of time; the canonical reflection matrix Ruu(t) expressed in the basis of the transducers being composed of a set of impulse responses 7?(u out,u in,t ) between transducers.

[0039] A "canonical" matrix is ​​understood to be a matrix obtained following ultrasonic measurements and from which all post-processing is carried out.

[0040] According to one embodiment, the step of acquiring at least one canonical reflection matrix R ui(t) may include an insonification of the medium with a series of plane waves with a delay r'(u) applied to each signal at emission for the formation of a wavefront inclined at an angle 0 in with respect to the array of transducers, a backscattered field by the medium, 7?(u out, 0 ia, t) is measured by all the position transducers u out for each incident plane wave 0 in, the set of responses forming a canonical reflection matrix Ru 0(t)=[ 7?(u out, 0 ia, t)].

[0041]

[0042] According to yet another variant, the step of acquiring at least one canonical reflection matrix R ui(t) may include an insonification of the medium with a series of divergent waves.

[0044] According to one feature of the invention, the diffusing screen can be an element endogenous to the medium. For example, it could be an element naturally present, such as a skull in ultrasound imaging.

[0045]

[0046] The diffusing screen can also be an exogenous element that is introduced into the path between the probe and the object to be imaged before the acquisition step of the canonical reflection matrix. It can be a removable element.

[0047]

[0048] By way of example, step a) may further include a step of applying a time window to the canonical reflection matrix.

[0049]

[0050] According to an advantageous feature of the invention, step b) may comprise the following steps:

[0051] - a first step in determining a focused reflection matrix Rpp( by projecting the canonical reflection matrix R ui(t) onto the basis P of the diffusing screen according to the following equation:

[0052] R,, (“) = ((l)) x (w) x Pfp (w)

[0053] in which the matrix ux ) is the Fourier transform of each canonical reflection matrix R,„- ( t ), +? ; the matrix Gup( œ ) is the R«i (w R«i ( t) The reception transformation matrix is ​​adapted for the transformation from the reception basis (u) to the basis P of the diffusing screen at the pulsation ω of the ultrasonic waves; the matrix ω is the emission transformation matrix adapted for the transformation from the emission basis (i) to the basis P of the diffusing screen at the pulsation ω of the ultrasonic waves; the symbols * and f denote the matrix operations of conjugation and transposition-conjugation respectively; the symbol x denotes a matrix product,

[0054] - a second step of determining a compensated matrix R^p p. , a) j by compensating for the curvature of wavefronts in the plane of the diffusing screen according to the following equation:

[0055] Rip p, - [ / p ^\Rip p., (p.,

[0056] with a parabolic phase term under the approximation paraxial; Pout being a first spatial position point corresponding to a virtual output transducer; Pin being a second spatial position point corresponding to a virtual input transducer,

[0057] - a third step of determining the focused reflection matrix R'^ a') by performing a change of variable defined by:

[0058] = P ci) 40

[0059] from the compensated matrix so as to obtain the following relationship between the coefficients of the matrices R'^ m) and Rw(w):

[0060] b \R(c^bj

[0061]

[0062] These three steps included in step b) can be recombined in the form of the following equation: R'ef(W) = i*(w) 0 [g^(w) xRw(w) xPj(m)]°I*(w)

[0063] With IfO) = [ / (£ w) ]

[0064] etj^^ =ei^,

[0065] The symbol ° represents the Hadamard product

[0066] The symbol x represents the matrix product.

[0067]

[0068] According to one embodiment, in step c), the matrix imaging algorithm can be an iterative CLASS algorithm for "Closed-Loop Accumulation of Single Scattering", this CLASS algorithm comprising the following steps:

[0069] - construction of an estimator F^y]^ ) of angular spectrum of reflectivity of the object by summing hyperdiagonals of the focused reflection matrix R'^( , these hyperdiagonals being defined such that = constant , and The estimator is defined according to the following equation: 100701 iwfj

[0071] n-1 being the number of iterations, (note that in the classic CLASS algorithm, it (there is no sum over w)

[0072] - application of a phase conjugate of the estimator to the reflection matrix focused R'^ ( û) ) so as to make the object virtually coherent (this corresponds to a spatial Fourier transform of the real and positive object): 100731 «')

[0074] d(hi) is a consistent matrix, ^■coh

[0075] - application on a coherent matrix of a temporal window of echoes ultrasonic signals consisting, in the frequency domain, of a convolution with a function whose bandwidth Au is inversely proportional to the duration Af of the time window applied to the ultrasonic signals in the time domain: 100761 «>)

[0077] with B ( of, Am ) the frequency filter of characteristic width Am,

[0078] - determination of two estimators, , of the function of screen transfer diffusing by summing the rows and columns of the filtered coherent reflection matrix r^; 100791 “) = “1U} ) 100801 «') =exp(i argjE^- 1 ^^, ft >) ) )

[0081] - application of the phase conjugates of these two estimators on the matrix of reflection to obtain a reflection matrix R"^1^) for which the phase shift induced by the diffusing screen has been compensated:

[0082] g = H.(£ , . m) \ ' in 5 ouf / in v ' m J \ ' m ' ouf 1 oult ' ouf /

[0083]

[0084] - iterating the steps of the CLASS-type algorithm so as to converge towards a corrected reflection matrix in the plane of the diffusing screen, then reinjection of the parabolic phase terms that had been previously compensated:

[0085] R„ ( w} T ( 0)} or limR”W ( M ) 1 oi ( w )

[0086]

[0087] The frequency filter can typically be a Gaussian function. As iterations progress, the width Am can be decreased in order to correct increasingly complex aberrations by activating a large number of frequency degrees of freedom.

[0088]

[0089] The CLASS-type algorithm, inspired by the classical CLASS algorithm, is applied here in the space-frequency basis (f), whereas the classical CLASS algorithm was developed in the frequency domain only from the plane wave basis, a basis from which no gain in resolution can be expected and which is not suitable for compensating aberrations with a scattering screen. Such a technique according to the prior art is described in YR Lee, et al. Exploiting volumetric wave correlation for enhanced depth imaging in scattering medium. Nat Commun 14, 1878 (2023).

[0090] The compensation of aberrations by the CLASS algorithm in the plane of an aberrant screen is discussed in another article, but on a time-windowed reflection matrix, which does not allow for frequency-based correction of aberrations: Kwon, Y., Hong, JH, Kang, S. et al. Computational conjugate adaptive optics microscopy for longitudinal through-skull imaging of cortical myelin. Nat Commun 14, 105 (2023).

[0091] The algorithm developed according to the invention is iterative. Each iteration is broken down into several steps, the result of which is a new estimation of the reflection matrix associated with the object. At iteration 0, the initial reflection matrix corresponds to the one measured: ^0) / ^ . >

[0092]

[0093] Preferably, step d) of projecting the corrected reflection matrix onto the plane of object x may further include a summation of the results on the frequencies according to the following equation = Ldu m) xR"$(w) xG^, w)

[0094] the matrix Gx^ ( z^, to ) is the change-of-basis matrix from the basis (£) to the focused basis (x) to the depth and the pulse.

[0095] and a'+ are the lower and upper bounds of the bandwidth of the ultrasonic signals.

[0096] The integral over the pulsations is equivalent to a temporal windowing of the echoes from the object.

[0097]

[0098] Step e) of constructing an image of the object can be obtained by considering the diagonal of the reflection matrix

[0099] I(x,z M ) = I^^Z M )

[0100] with x the position vector in the plane of the object.

[0101] Note that the two preceding equations can be combined so as to obtain a confocal image I(X, Z^} of the object from R"^( m) without going through the focused reflection matrix R^Z^).

[0102] According to another embodiment, in step c), the matrix imaging algorithm can be an algorithm using a matrix distortion technique with a spatio-frequency correction basis.

[0103]

[0104] Advantageously, the distortion matrix technique with a spatio-frequency correction basis (£) can comprise the following steps:

[0105] - calculation of a dual reflection matrix between the focused basis (x) and the basis of spatio-frequency correction Q-):

[0106] Rfx(zM, u>) = G^(m) xR^Cw) x^x(zM, m)

[0107] the matrix G^C w) is the transition matrix describing the projection of the transducer basis (u) to the spatio-frequency correction basis (£) at the pulsation 0J,

[0108] the matrix ( tü) is the transition matrix describing the projection of the emission basis (i) to the focused basis (*) at the depth zm and the pulsation œ,

[0109] - deduction of a frequency distortion matrix w) by performing the term-by-term product of the dual reflection matrix with the phase conjugate matrix of the reference matrix that would be obtained without a diffusing screen, i.e. here G^(w):

[0110] Such that z^ = R(x, Zm, f)

[0111] - calculation of the correlation matrix,

[0112] - determination of the spatio-frequency correction law ¢(¾) by analysis of the Cgg correlation matrix.

[0113]

[0114] The coefficients of the correlation matrix Cgg can be given By:C( {?', / '},zM) = LxD(x,S,zM,f)D'(x,f'.zM,f)

[0115]

[0116] The correlation matrix C can be determined in the focused basis x, by the following calculation of the elements of the correction matrix C = Cxx: c ( x, x' ) = ( X, £ zM, / ) x D "(x\ zM, / )

[0117] * is the conjugation operator.

[0118]

[0119] The analysis of the correlation matrix (¾) can be carried out by an eigenvalue decomposition of the correlation matrix C^(zw), and the spatio-frequency correction law ¢(^ / ) is the first eigenvector U] of the correlation matrix C^(s«j in the correction basis (^).

[0120]

[0121]

[0122]

[0123] The analysis of the correlation matrix p / _j can also be performed by a singular value decomposition of the rearranged distortion matrix as follows: d(z„) = [»( The analysis of the Cgg correlation matrix can also be performed by solving from the following equation: e( j = exp( j {CJ x ¢(z„) ) ) iteratively by the following expression, which corresponds to an iterative phase-reversal calculation = exp ( j arg {C^zJ X ( zM )} )

[0125] where x is the matrix product,

[0126] with: O0 an arbitrary wavefront, for example — [ ] j ]T.

[0127]

[0128] The analysis of the correlation matrix C xx can also be carried out by solving the following equation: W(zM) = exp( J arg {C^(zM) XW(zM)} )

[0129] where x is the matrix product,

[0130] iteratively by the following expression: = exp(j arg(C M (z M ) x W n (z M )} )

[0131] where x is the matrix product,

[0132] with Wo an arbitrary wavefront, for example Wo = [ 1 l]r

[0133]

[0134] The invention also relates to the use of a predetermined spatio-frequency correction law on an image acquired of an object by means of a predefined network of transducers and a predefined diffusing screen and by carrying out steps d) and e) above.

[0135] This predetermined spatio-frequency correction law is determined by applying a matrix imaging algorithm following a preliminary phase in which steps a) to c) above were carried out using an assembly comprising the predefined array of transducers, the predefined diffusing screen and a phantom-type model object; a reflectivity statistic (ultrasonic speckle) and a speed of sound of said assembly being predefined.

[0136] Thus, several spatio-frequency correction or focusing laws for the transducer array-screen combination can be determined for a phantom-type (or other) model object in which a well-known reflectivity and speed of sound are present. Once determined, these focusing laws can be reused when the probe + diffusing screen are used to image biological or other tissues.

[0137] According to another aspect of the invention, an ultrasonic system for constructing a confocal image of an object contained in a medium is provided, the system comprising:

[0138] - an array of transducers adapted to generate a series of ultrasonic waves incident 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;

[0139] - a diffusing screen along the wave path between the transducer array and the environment to be imaged, and

[0140] - a computing unit connected to the transducer network and adapted to put into implements the process described above.

[0141]

[0142] A computer program product is also envisaged, comprising instructions which, when the program is executed by a computer, cause the computer to carry out the steps of the process described above.

[0143]

[0144] A computer-readable medium is also provided, comprising instructions which, when executed by a computer, cause the computer to carry out the steps of the process described above.

[0145] Brief description of the drawings

[0146] Other advantages and features of the invention will become apparent from the detailed description of implementations and embodiments, which are by no means limiting, and the following attached drawings.

[0147] Fig. 1 is a schematic overall view of an experiment to illustrate the estimation and correction of diffusion phenomena in a plane conjugate to the diffusing screen in a transmission configuration according to the invention;

[0148] Fig. 2 is a schematic overall view of an experiment illustrating the estimation and correction of diffusion phenomena in a plane conjugate to the diffusing screen in a reflection configuration according to the invention;

[0149]

[0150] Fig. 3 is a schematic view illustrating an example of an ultrasonic construction system for implementing the method according to the present invention;

[0151] The [Fig.4] is a diagram of the method for constructing an ultrasonic image according to the present invention;

[0152] Figure 5 is a two-dimensional graphical representation of the chromato-axial memory effect as observed from an intermediate plane.

[0153] Figure 6 comprises several images acquired after successive iterations of a SUPER-CLASS algorithm,

[0154] Figure 7 comprises acquired confocal images and graphical representations allowing comparison in the absence and presence of the scattering medium, with and without correction, and

[0155] Fig. 8 illustrates images allowing a comparison of the energy of the reflection matrices in the absence and in the presence of the diffusing medium in the plane of the diffusing screen. Detailed description of the figures

[0156] It is understood that the embodiments described below are by no means limiting. Variants of the invention may, in particular, be imagined comprising only a selection of features described hereafter, isolated from the other features described, if this selection of features is sufficient to confer a technical advantage or to differentiate the invention from the prior art. This selection includes at least one preferably functional feature without structural detail, or with only a portion of the structural details if this portion alone is sufficient to confer a technical advantage or to differentiate the invention from the prior art.

[0157] The various embodiments and aspects described in this disclosure can be combined or simplified in numerous ways. In particular, the steps of the various processes can be repeated, reversed, and / or carried out in parallel, unless otherwise specified.

[0158] This disclosure relates to methods and systems for the ultrasonic characterization of a medium, and is particularly applicable to medical imaging of living or non-living tissues. The medium may be, for example, a heterogeneous medium that one seeks to characterize in order to, for example, identify and / or characterize heterogeneities. These construction techniques are notoriously non-invasive to the medium, which is advantageously preserved, particularly in its nature and integrity.

[0159]

[0160] Figure 1 is a schematic view of a system 1 according to the invention comprising a matrix probe 2 controlled to emit and detect signals to and from an object 4 present in a medium. This medium may be the interior of a head. The matrix probe 2 may be disposed on the surface of this head, in the direction of the object.

[0161] Matrix probe 2 can be controlled to perform the following acquisition sequence: [Tables 1] Parameter Value Sampling Emitted signal Pulse of three half-periods of a 3 MHz sinusoidal signal Sampling frequency 6 MHz (IQ modulation) Recording time 180 ps

[0162]

[0163] Implementing the sequence allows the acquisition of the canonical reflection matrix of the medium. The latter comprises a flat object 4 to be imaged, contained in the plane z = zM = 110 mm. This pentagonal object 4 was made from a hard, abrasive disc. Between object 4 and the matrix probe 2, at a depth zp = 30 mm, a polyamide fiber mesh is stretched, onto which glass beads of diameter are arranged. 1.5 mm which constitutes a diffusing screen or diffusing medium 3. All these elements are immersed in water, speed of sound c0 = 1480m.s *.

[0164] A pyramid 5 is distinguished, with dotted lines, having a base constituted by the matrix probe 2 and a point constituted by the object 4. This pyramid 5 represents the set of insonification directions of the object in the absence of the diffusing medium 3.

[0165] A volume 6 is distinguished representing the set of insonification directions of the object in the presence of the diffusing medium 3.

[0166] The present invention aims to learn how to image object 4 via the diffusing screen without prior calibration and with a resolution much better than in free space by virtually increasing the angular aperture of the matrix probe. This diffusing medium 3, which could be considered an obstacle, advantageously becomes, according to the invention, a component enabling super-resolution.

[0167] The method according to the invention is based on the acquisition and projection of the reflection matrix onto a spatio-frequency basis whose coordinate —44 21 combines the spatial coordinate of the diffusing screen, the frequency, and zo, the distance between the diffusing screen and the object. This basis maximizes the input-output correlations of the field associated with the object (chromato-angular memory effect in reflection associated with the object) and can be used to estimate the transfer function of the diffusing screen.

[0168] Once this transfer function is known, the angular diversity offered by the diffusion paths induced by the diffusing screen can be exploited and the angle under which the object is seen can be enlarged to obtain a precise image of the latter, with a resolution much better than in free space.

[0169] The transducer array-diffusing screen combination can be implemented in transmission, i.e., with the diffusing screen placed between the transducer array and the object to be imaged ([Fig. 1]), or in reflection, i.e., with the transducer array and the object placed on the same side with respect to the diffusing screen ([Fig. 2]). In both cases, the surface area of ​​the diffusing screen is much larger than the physical aperture of the probe, which allows for a significant improvement in image resolution according to the invention.

[0170] The field of vision is limited by the range of the memory effect associated with the diffusing screen. If this diffusing screen is two-dimensional, the range of the memory effect is valid over the entire angular domain, and the field of vision is limited only by the geometric decay of the ultrasonic waves. If the diffusing screen is volumetric, the angular range of the memory effect is on the order of 2 / L in transmission and in reflection, where L is the thickness of the diffusing medium and K is the mean free path of the wave within the diffusing screen. This range of the memory effect denotes the size P of the patch on which the transfer function H(A ■'') of the diffusing screen can be considered spatially invariant: L in transmission and Thus, the estimation of a single transfer function will be necessary if the size of the area to be imaged is less than P. For a given field of view (FOV), the number of transfer functions to be determined is on the order of FOV / P. In this case, the entire process of estimating the transmittance H will have to be repeated for different areas of the field of view of size P.

[0171]

[0172] Ultrasonic construction system

[0173] Figure 3 illustrates an example of an ultrasonic imaging system 7 for implementing the ultrasonic imaging method of medium M according to the present invention. This system and the method allow the formation of an ultrasound image of at least a part (area of ​​interest or field of view) of the medium.

[0174] System 7 comprises:

[0175] - a sounding device 20 comprising the matrix probe 2,

[0176] - a computing unit 30 for calculating an image from the signals received from the survey device 20,

[0177] - a control panel 40 connected to the computing unit 30, this control panel including, for example, buttons 41 and a touchpad 42,

[0178] - a display device 50 for viewing an image and various elements or measures.

[0179] The sounding device 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 being the result of reflections of the ultrasonic waves emitted by the scattering medium 3 inside the medium M.

[0180] The sounding device 20 comprises the probe 2 equipped with a plurality of transducers. The probe 2 is matrix-shaped but can, for example, be a linear, curved, or two-dimensional array. The transducers are capable of converting an electrical signal into a vibration and vice versa. The transducers are, for example, piezoelectric ultrasonic transducers that can 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 transducer array of the probe 2 is then associated with the computing unit 30. The probe 2 can comprise one hundred or more transducers.

[0181] The computing unit 30 may include a housing 31 comprising receiving devices for amplifying and / or filtering the signals received from the sounding device 20, and converters (analog-to-digital converters and digital-to-analog converters) for transforming the signals into representative signal data. The data may be stored in a memory of the computing unit 30 and / or directly processed to calculate intermediate data (channel formation data or other data). The computing unit 30 may implement any known method for constructing an image from the signal data received from the sounding device 20, such as channel formation.

[0182] The calculated image can be:

[0183] - a middle image (B-mode image) usually in greyscale for visualize organs in the environment, and / or

[0184] - an image showing a velocity or flow in the medium (color image) by a useful example for visualizing blood vessels in the medium, and / or

[0185] - an image showing a mechanical characteristic of the medium (elasticity) by useful example for identifying tumors within the medium.

[0186] The term "connection" or "link" between the sounding device 20, the computing unit 30, and the display device 50 means any type of wired connection, whether electrical or optical, or any type of wireless connection using any protocol such as WiFi™, Bluetooth™, or others. These connections or links may be unidirectional or bidirectional. The associated display device 50 may be of any type, such as a touchscreen or non-touchscreen, connected or not.

[0187] The display device 50 is a screen for viewing the image calculated by the processing unit 30. The display device 50 can also display other information such as image scales, configuration information for 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 by the user.

[0188] The control panel 40 is, for example, a portion of a system enclosure, said portion comprising a panel enclosure having a substantially flat surface 40a inclined towards the user for one-handed operation. As shown in [Fig. 3], the control panel 40 may include a control screen 49 for displaying various configuration information.

[0189] The computing unit 30 is configured for the implementation of calculation and / or processing steps, including the implementation of process steps according to this disclosure. By convention, a spatial frame of reference of the medium M is defined, taking a The first X-axis and a second Z-axis perpendicular to it. For simplicity, the first X-axis corresponds to the transverse direction in which the transducers are aligned in the example of a linear array, and the second Z-axis corresponds to the depth of the medium M relative to this transducer array. This definition can be adapted to the context and thus extended, for example, to a three-axis spatial coordinate system in the case of a matrix array, or to a polar coordinate system in the case of a curved array, or to any other suitable coordinate system depending on the structure and shape of the ultrasonic transducer array. Therefore, in the remainder of this disclosure, we will use a Cartesian coordinate system XZ, corresponding to a linear probe, for the sake of simplicity in the explanations, but a specialist in the field could easily generalize and apply the results to any type of coordinate system.

[0190] In the remainder of this disclosure, reference is made to a transducer array for transmission and reception, it being understood that, more generally, several transducer arrays may be used simultaneously. The transducers may be both transmitters and receivers, or only transmitters for some and only receivers for others. Similarly, an array may consist of one (1) to N transducers, of the same type or of different types.

[0191] The probe 2, consisting of a transducer array, serves, for example, both as a transmitter and as a receiver, or is composed of several sub-arrays of transducers, some dedicated to the transmission, others to the reception of ultrasonic waves. A transducer array is understood to mean at least one transducer, an aligned or non-aligned sequence of transducers, a two-dimensional distribution of transducers (for example, a transducer matrix), or any spatial distribution of transducers.

[0192] Where reference is made in this disclosure to computational or processing steps for the implementation of process steps, it is understood that each computational or processing step may be implemented by software, hardware, firmware, microcode, or any suitable combination of these or related technologies. Where software is used, each computational or processing step may be implemented by computer program instructions or code that may, for example, be interpreted or executed. These instructions may be stored or transmitted to a computer-readable storage medium (or computing unit) and / or executed by a computer (or computing unit) to implement these computational or processing steps.

[0193]

[0194] Figure 4 shows a diagram of the main steps according to the invention. A step a) acquisition of a canonical reflection matrix R ui(t) is distinguished. In b), a focused reflection matrix R'^( w) is determined by projecting the canonical reflection matrix into a space-frequency basis:

[0195] £ = s ' 0 ^'0

[0196] In step c) a corrected reflection matrix R"^( w) is determined •

[0197] Step d) allows determining an object reflection matrix (zM) in projecting the corrected reflection matrix R"^ ( M) onto a plane of the object x at the depth

[0198] In step e), an image is constructed from the object reflection matrix Rxx ( z M ) •

[0199] These steps are described in more detail below.

[0200]

[0201] According to the invention, the ultrasonic construction method implemented by the computing unit 30 of the system 1 comprises at least one acquisition of a reflection matrix. This reflection matrix can be acquired in the following manner:

[0202] - a step of generating a series of incident ultrasonic waves USin in a zone of said medium, by means of probe 2, said series of incident ultrasonic waves being an emission basis i; and

[0203] - for each emitted wave i in, the field reflected by the medium is measured by each transducer and is denoted 7?(u out,im), where t is the echo time and the vector u out marks the position of each transducer. Each field is stored in the canonical reflection matrix R Ui(t)=[7?(u out,i in,t)] defined between the transmitting basis i at the input and a receiving basis u at the output.

[0204] One possible method for measuring this canonical reflection matrix is ​​to successively emit an ultrasonic pulse from each transducer of the array, whose position is located by the coordinate uin. This results in a diverging cylindrical (or spherical) incident wave. This wave is reflected by the scatterers of the medium, and the backscattered field is recorded by each transducer as a function of time. By repeating this operation with each transducer used successively as a source, the canonical reflection matrix Ruu(t) is determined, expressed in the basis of the transducers, and composed of all the impulse responses AYuout, uin, t) between each transducer. This matrix is ​​thus rich in information about the medium under study. However, the method assumes that the medium remains stationary throughout the measurement period.Furthermore, the recorded signals have a poor signal-to-noise ratio because the medium is insonified by a single transducer.

[0205] A second way of constructing this canonical reflection matrix consists of insonifling the medium with a plane wave series basis. This method avoids the previous problems. A delay law r' is applied to each signal at the emission for the formation of a wavefront inclined at an angle θin with respect to the transducer array. At reception, the field backscattered by the medium, Φ(u (oub 0 in, t), is measured by all the position sensors u out for each incident plane wave 0 ia. The set of these responses forms a canonical reflection matrix Ruü(t)=[ Æ(u out, 0 t)]. This method gave rise to ultrafast imaging and elastography, and is described, for example, in the document:

[0206] “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).

[0207] A third way to create this canonical reflection matrix is ​​to insoniflate the medium with a basis of diverging waves, which allows the acoustic field to be illuminated more broadly than by using plane waves. This basis is located by the position s in of the virtual source associated with each diverging wave. This technique, used particularly in super-resolution imaging, is explained in the document:

[0208] “Ultrafast imaging of the heart using Circular Wave Synthetic Imaging with Phased Arrays”, Couade et al., IEEE International Ultrasonics Symposium (2009).

[0209] The recorded canonical reflection matrix R ui(t) can be a "real" matrix, that is, composed of real coefficients in the time domain, the electrical signals recorded by each of the transducers being real numbers. Alternatively, this matrix can be a "complex" matrix, that is, composed of complex values, for example in the case of demodulation for in-phase and quadrature beamforming (known in English as "beamforming IQ").

[0210]

[0211] Projection of ultrasonic data into a new spatio-frequency basis.

[0212] The coordinates of this basis depend both on the position vector in the plane of the diffusing screen (^) and on the frequency œ

[0213] £ =

[0214] with zo the distance between the object and the diffusing screen.

[0215] This change of coordinates makes it possible to highlight a chromato-angular memory effect associated with the field reflected by the object.

[0216] Figure 4 is a two-dimensional graphical representation of the chromato-axial memory effect as observed in an intermediate plane (the plane of the diffusing screen). [A] A virtual emitter placed in the intermediate plane sends a wave, which is reflected by the object and then detected by a virtual receiver also placed in the intermediate plane. [B] At the same frequency, by applying the translation ôpep to the source, the inverse translation -5pep must be applied to the receiver in order for it to detect the same field, up to parabolic and deterministic phases, thanks to the memory effect. By changing the frequency and keeping the emitter in the same position, it is possible to move the receiver so that it measures the same field, up to parabolic and deterministic phases, while keeping λ constant.

[0217]

[0218] 1st step: Projection of R onto the basis (^) of the diffusing screen

[0219] Thus, a focused reflection matrix R / > / >(z0, w) of the medium can be obtained by focusing using the following matrix calculation:

[0220] gIXoOxR^uùxP^w)

[0221] in which

[0222] the matrix Rwt- ( tit, ) is the Fourier transform of each reflection matrix canonicalRwu). zxx ;rf R«i (w ) = z )e

[0223] The GB / 9(w) matrix is ​​the suitable receiving pass-through matrix for the pass-through from the receiving basis (u) to the focused basis (^) at the depth zp and the angular frequency

[0224] The Pip(to) matrix is ​​the emission transition matrix adapted for the transition from the emission basis (i) to the focused basis (^) at the angular frequency

[0225] The symbols * and f denote respectively the matrix operations of conjugation and transposition-conjugation.

[0226] The symbol x denotes a matrix product.

[0227] The coefficients of the transition matrix G correspond to the normal derivative of the Green's function relating each focal point of spatial position (^, ​​zp) and each transducer of spatial position (u, 0).

[0228] In the case of a linear transducer array for generating a two-dimensional image, the coefficients of the transition matrix G can be written as follows: G(u,p,Zp,j") ^VzG2I)(u,r,f )

[0229] where Vz is the gradient projected along the depth direction z, and

[0230] G2D(U, r) is the 2D Green's function that relates each transducer U - (y, 0) at each point f — ( p, Zp ) of the diffusing screen, with: G^vJ^Wolu-rQ

[0231] where kQ = 2 / rf / c0 is the wave number,

[0232] Ho is the first-order Hankel function whose asymptotic expression is the next: ^(2^ / lu-rl / Co)

[0233]

[0234] In the case of a matrix-type transducer array for generating a three-dimensional image, the coefficients of this transition matrix G can be written as: G(u, p, Zp, f) = (u, r, f ) where G3D(u, r) is the 3D Green's function that links each transducer U = (lit, ()) at each point F = (p, zp) of the midpoint M, with: CFqf) ( ^9 f ) — I-------

[0235] The coefficients of the change-of-basis matrix P are therefore written in this case as follows: jz G ( U, p, Zp, f) - -l cu

[0236] The coefficients of the change-of-basis matrix P / p are therefore written in this case as follows: G(u, p,Zp,f) = -i-...................

[0237] In the case of an illumination basis corresponding to a plane wave basis (i =k), the transition matrix P is the Fourier transform operator.

[0238] In the case of a linear transducer array for generating a two-dimensional image, the coefficients of this transition matrix P can be written as follows: P ( kin, p,Zp,f)=exp( iZp^Ÿ-kli ) expP ( - ikinP )

[0239] where kin, the transverse component of the wave vector k associated with each plane wave.

[0240] In the case of a matrix-type transducer network for generating a three-dimensional image, the coefficients of this transition matrix P can be written: P ( kiw p,Zp,f)~ exp ( iZp\ / (^)2-||^„|P ) exp p ( - ikiKp )

[0241] where

[0242] kin is the transverse component of the wave vector k associated with each plane wave, and

[0243] P, the transverse position vector.

[0244]

[0245] If the illumination basis is that of the transducers (i=u ), then the transition matrix Pjp will be taken as equal to the matrix GB / , expressed above.

[0246]

[0247] 2nd step: Compensation of the curvature of the wavefronts in the plane of the screen displaying

[0248] Rfp p. , o?) = I*(p ,cj\R(p , p. , (u)I*[p. , oD

[0249] with ^) = 'c parabolic phase term under the paraxial approximation

[0250]

[0251] Step 3: Change of variable^ =

[0252] gj

[0253]

[0254] The three preceding steps can be recombined in the form of the following equation: R'^(w) = o [^( w) xR^w) x P^(w) ]°lj(m)

[0255] With the ( œ ) = [ / (£«) ] [°256]

[0257] The symbol 0 represents the Hadamard product

[0258] the symbol x represents the matrix product.

[0259]

[0260] Aberration correction process

[0261] At least two matrix imaging algorithms can be used.

[0262] SUPER-CLASS Algorithm

[0263] The idea here is to develop an algorithm called SUPER-CLASS inspired by the CLASS algorithm but in the spatio-frequency basis ÙJ introduced above, whereas the CLASS algorithm was developed in the frequency domain only from the basis of plane waves, a basis from which no gain in resolution can be expected and which is not suitable for compensating aberrations by a screen.

[0264] The algorithm according to the invention is iterative. Each iteration is broken down into five steps, the result of which is a new estimate of the reflection matrix associated with the object R^m. At iteration 0, the initial reflection matrix corresponds to the measured one:

[0265] Step 1

[0266] The first step of the SUPER-CLASS algorithm consists of summing the hyperdiagonals of the reflection matrix defined such that £ — £ + £ — a constant so as to construct an estimator of the spectrum '+ 7 yes K angular reflectivity of the object: [02671 ' r / ~ OUt 1 v ~ UUt UUl /

[0268] In the original Class algorithm, there is no sum over the angular frequency

[0269] Step 2

[0270] The second step of the algorithm consists of applying the phase conjugate of this estimator to the reflection matrix so as to make the object virtually consistent: [02711 =«<"■”(

[0272] Step 3

[0273] The third step consists of a time windowing of the ultrasonic echoes which translates in the frequency domain by a convolution with a function whose bandwidth Au? is inversely proportional to the duration At of the time window applied to the ultrasonic signals in the time domain: 102741 «) «O*»-

[0275] with B(w, Au?) the frequency filter of characteristic width Au?, which can typically be a Gaussian function. As iterations progress, the width Aoj can be decreased to correct increasingly complex aberrations by manipulating a large number of frequency degrees of freedom.

[0276] Step 4

[0277] Two estimators, and £ / (t ..x , of the transfer function of The diffusing screen can be estimated by summing the rows and columns of the "coherent" and filtered reflection matrix R1"11 ■ 102781«>) =exp(, w)} ) 102791 «.) = exp(>w)} )

[0280] Step 5

[0281] The phase conjugates of these two estimators can be applied to the reflection matrix to obtain a reflection matrix R^t for which the phase shift induced by the diffusing screen has been compensated: 102821 = u!)

[0283]

[0284] After a few iterations, the algorithm converges and the reflection matrix in the plane of the aberrator can be obtained by reintroducing the parabolic phase terms that had previously been compensated:

[0285] R^f»!^) ° [lmR^\u;)pI^

[0286]

[0287] Final stage

[0288] An image of the object can be obtained by projecting the corrected reflection matrix onto the object plane (x) and summing the result over the pulsations: Rxx(2w ) — a) ) x ( w ) x ( z M , w )

[0289] The matrix (zw, m) is the change-of-basis matrix from the basis (£) to the focused basis (x) at depth zm and at the pulsation

[0290]

[0291] An image of the object is then obtained by considering the diagonal of the reflection matrix

[0292] 1(^2^)= / ^^^2^)

[0293] with x the position vector in the plane of the object

[0294]

[0295]

[0296] Figure 6 shows output images from successive iterations during the implementation of a SUPER-CLASS algorithm. The matrix Rxx(z^) can be used to initialize the SUPER-CLASS algorithm. Figure 6 depicts the different confocal images formed after correction of the reflection matrix with the estimates of the aberration laws obtained after iterations for Gf = 400 kHz, then Gf = 300 kHz and 200 kHz, and finally Gf = 100 kHz, 50 kHz, 20 kHz, 10 kHz, and 5 kHz, where is the characteristic width of the frequency filter. B(a / . Am) is considered here to be Gaussian. We can thus observe that, over the iterations and as we use an increasingly longer confocal filter time, the confocal image is progressively corrected, since the pentagonal shape of the object eventually appears. In the later iterations, we can also distinguish the hole drilled in the object, which confirms the proper functioning of the method and a gain in resolution. As the lateral resolution is improved, we simultaneously observe a reduction in the axial echo trail present beneath the object. The gain in lateral resolution can also be seen by observing the progressive thinning of the radial RPSF (Reflection Point Spread Function) formed in the plane of the object and also shown in Figure 6. The RPSF describes the spread function of the reflection imaging system.This quantity is estimated from the antidiagonals of the matrix RXx(^if) tc' 9ue described in the article: . F. Bureau et al., Three Dimensional Ultrasound Matrix Imaging, Nat. Common. 14, 6793, 2023.

[0297] The first line (#0) corresponds to uncorrected data.

[0298] [AB] : confocal images in the planes z=zM and y=0.

[0299] [CD] : Supplementary aberration law in output obtained at the end of the iterations, the total aberration law used to form the confocal images at this iteration corresponding to the summation of the supplementary laws.

[0300] [C] : in the plane. kc ~ U'J

[0301] [D] : In the plane f=3MHz.

[0302] [E] : Radial RPSF estimated in the plane z=zM.

[0303] With the invention, the corrected reflection matrices correspond to the acquired reflection matrices corrected with the final estimation of the aberration laws obtained after the succession of all the iterations of the SUPER-CLASS algorithm with the different .

[0304] Fig. 7 includes several images and graphical representations allowing a comparison of confocal images and resolution in the absence of the diffusing medium and in its presence, with and without correction.

[0305] [A] : Confocal images in the plane z=zM.

[0306] [B] : RPSF estimated in the plane z = zM.

[0307] [C] : RPSF radials in the same plane.

[0308] [D] : Normalized confocal intensity profile along segment 1 defined in line dotted line on the central confocal image.

[0309] Figure 7 thus shows confocal images formed from uncorrected reflection matrices without a scattering medium and corrected and uncorrected matrices with a scattering medium, as well as the associated RPSFs. The image without a scattering medium gives a poorly resolved image of the object, due to the limited angle (<9°) at which the object sees the probe. By adding the scattering medium, an equivalent image of the object is obtained, but with lower contrast, due to the energy loss of the ballistic wave and the blurring induced by scattering events.

[0310] These observations are confirmed by a study of the associated RPSF. Before correction and in the presence of the diffusing medium, the RPSF visible in [Fig. 7] has the following profile:

[0311] a confocal peak around A p = 0 related to ballistic background and an incoherent background induced by diffusion. We observe that the main lobe of the RPSF is drastically refined following the correction of aberrations, decreasing from a mean width at half maximum (MWHM) of 3.1 to 1.6 mm. Finally, the level of the incoherent background is lowered by approximately 20 dB.

[0312] Finally, in [Fig. 7], we plot the confocal intensity profile along a segment passing through the hole drilled in the object. These graphs allow us to verify that the intensity is attenuated by a factor close to 20 in the presence of the diffusing medium. Nevertheless, the aberration correction maximizes the confocal intensity and thus multiplies its maximum level by a factor of approximately 10. Even better, the Aberration correction makes it possible to reveal the hole drilled within the object, since a minimum intensity can be clearly identified at its level.

[0313] We thus observe that the uncorrected images with and without the diffusing medium have the same resolution. Moreover, the image obtained without the diffusing medium theoretically exhibits no aberrations and allows us to define the optimal resolution of the system at this depth. Consequently, the new resolution made possible by correcting the dispersive aberrations of the diffusing screen corresponds to super-resolution from the probe's point of view. This super-resolution is achieved by inserting the diffusing medium between the probe and the object. This diffusing medium virtually enlarges the probe's aperture by capturing echoes from the object that are too inclined relative to the ez axis and would not normally reach the probe.

[0314]

[0315] Fig. 8 allows a comparison of the energy of the reflection matrices in the absence and in the presence of the scattering medium in the plane of the aberrator, the energies being represented without normalization so that they are comparable to each other.

[0316] [A] : In the absence of the diffusing medium.

[0317] [B] : In his presence.

[0318] [C] : Difference of the two, positive values ​​representing gains related to the addition of the diffusing medium. The dotted box corresponds to the outline of the intersection of the aberrator plane with the rectangular-based pyramid whose base is the probe and which also includes among its vertices the origin of the object plane.

[0319] It can thus be seen that outside this dotted box and despite the attenuation, there is more energy in the presence of the scattering medium. It is the scattering medium which makes it possible to redirect waves from the periphery of the plane of the aberrator towards the object, that is to say from all directions included in volume 6 of [Fig.1].

[0320]

[0321] Variant through the Super-Distortion matrix

[0322] An alternative approach to SUPER-CLASS consists of a spatio-frequency approach to aberration compensation based on the concept of a distortion matrix with a spatio-frequency correction basis (f).

[0323] The first step consists of calculating a dual reflection matrix between the focused basis (x) and the spatio-frequency correction basis (£):

[0324] w (w) x (œ) x (zM,)

[0325] The matrix Gw^(w) is the transformation matrix describing the projection of the transducer basis (u) onto the spatio-frequency correction basis (£) at the pulsation

[0326] the matrix ( ü)) is the transformation matrix describing the projection from the emission basis (i) to the focused basis (x) at the depth and the angular frequency

[0327] A frequency distortion matrix D^x(z / W, w) is then deduced by performing the term-by-term product of the dual reflection matrix with the conjugate matrix in phase of the reference matrix that would be obtained without a diffusing screen, i.e. here w):

[0328] Such that f)=R(x.Ç, zM, fïG^X. z^f)

[0329] The next step is to calculate the correlation matrix Cgg whose coefficients are given by: c( (f,n, (f,

[0330] According to a second variant, the correlation matrix C is determined in the focused basis x, by the following calculation of the elements of the correction matrix C = CxX: C(x, x') = Ef / >(x, S, z„ f) *d\x', zM.f)

[0331] * is the conjugation operator

[0332]

[0333] According to a first variant, the analysis of the correlation matrix is carried out by an eigenvalue decomposition of the correlation matrix Cgg( and the spatio-frequency correction law ¢(¾) is the first eigenvector U! of the correlation matrix C^(zm) in the correction basis (2).

[0334] Since the correlation matrix is ​​Hermitian (_ çd), its eigenvalues ​​are real and positive.

[0335] The correlation matrix C^(^) can thus be written: j _ y UpUp

[0336]

[0337]

[0338]

[0339] or in terms of matrix coefficients: c ( (S, f I, ! ff ' ). x, z ) = (g, flUpd'-f) with Up corresponding to the eigenvectors of the correlation matrix C corresponding to the real and positive eigenvalues ​​of the correlation matrix Cgg(2.w) arranged in descending order We then have the spatio-frequency correction law ) which is equal to the first eigenvector, i.e. = U, ' or its normalized version, = exp( jarg {U}} ) '-c- a spatio-frequency correction line whose The coefficients have a unit amplitude but a phase equal to that of U] (the symbol arg {X} denotes the phase of the vector X); or to an inverse filter type correction, Z(J „ exp ( j} ) / | Uj j • The first option is preferable if there is a poor signal-to-noise ratio (matched filter). In general, however, the second option will be preferred so that the correction does not act as an amplitude filter but only corrects 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 the end.

[0340]

[0341] According to a second variant, the analysis of the correlation matrix p / _ f is carried out by a singular value decomposition of the distortion matrix rearranged as follows: = [d( {£ f} x zw l]

[0342] The eigenvalue decomposition of the correlation matrix j carried out in the first variant is indeed equivalent to the singular value decomposition (SVD) of each distortion matrix.

[0343] Singular value decomposition applies to rectangular matrices, and when applied to the distortion matrix, it is written as follows:

[0344] or in terms of matrix coefficients: D( {f}, x) = Y^pUp(c,f)Vp(x)

[0345] with Up = [ Up(£, f ) ] corresponding to the singular vectors of the distortion matrix jj^^j in the correction basis, or equivalently, to the eigenvectors of the matrix Cgg as defined in the first variant.

[0346] Vp-[Vp(x)] corresponding to the singular vectors of the distortion matrix in the focused basis (x),

[0347] ^p corresponding to the singular values ​​of the distortion matrix D^ which are, by definition, equal to the square root of the eigenvalues ​​of the correlation matrix C as defined in the first variant: (yp —

[0348] We then have the spatio-frequency correction law j which is equal to the first singular vector of the distortion matrix D^, i.e. ®(x, z) = ; or to its version normalized, O(zM) = exp(jarg{Uj}), i.e., a spatio-frequency correction law whose coefficients have unit amplitude but whose phase is equal to that of (the symbol arg{X] denotes the phase of the vector X); or to an inverse filter type correction, = exp({U]}) / |U(| •

[0349] The advantage of singular value decomposition of the dual reflection matrix Dfx, compared to eigenvalue decomposition of the correlation matrix Cgg, is the speed of computation of the numerical algorithms for singular value decomposition.

[0350] The advantage of the singular value decomposition of the distortion matrix D, compared to an eigenvalue decomposition of the correlation matrix Cgg is the speed of calculation of numerical algorithms for singular value decomposition.

[0351]

[0352] This search for the spatio-frequency correction law 0^ ) is also equivalent to solving the following equation: j ) X )

[0353] where x is the matrix product and a is a constant,

[0354] iteratively by the following expression, which corresponds to an iterative time-reversal calculation:

[0355] On+1(z JJX J'

[0356] with ®o an arbitrary wavefront, for example 0$ — [ | ] ]T

[0357]

[0358] Then, the spatio-frequency correction law 0^ ) is obtained by: 103591 ¢(¾)=

[0360] or its standardized version: [°361] J = eXp^ )'

[0362] or its inverse filter version:

[0363] rh / .

[0364] For ” *, the iterative time-reversal algorithm converges to the same first eigenvector of the matrix C^. In practice, there may be an advantage to using an iterative time-reversal algorithm rather than an SVD because it can converge after a few iterations, resulting in faster computation.

[0365]

[0366] According to a third variant, the analysis of the correlation matrix Cgg is carried out by solving the following equation:

[0367] iteratively by the following expression, which corresponds to an iterative phase-reversal calculation: ^(} = exp ( y arg ( x (}

[0368] where x is the matrix product,

[0369] with :Oo an arbitrary wavefront, for example 0 = [ 1 1 ]r.

[0370] Then, the spatio-frequency correction law 0^r is obtained by:

[0371] ®(zM)=Um®„(zM),

[0372] Or its inverse filter version:

[0373] fh / A '

[0374] The advantage of an iterative phase reversal algorithm compared to previous alternatives is that it is a more reliable estimator of the phase of the correction law and therefore ultimately provides better compensation for the phase distortions induced by the aberrator.

[0375]

[0376] According to a fourth variant, the analysis of the correlation matrix C xx is carried out by solving the following equation: = ex P(J arg{C xx (z M ) xW(z M )} )

[0377] where x is the matrix product,

[0378] iteratively by the following expression: ( z M ) = exp( j arg{C xx (z M ) x W„(z M ) ) )

[0379] where x is the matrix product,

[0380] with Wo an arbitrary wavefront, for example Wo = [ 1 1 ]r

[0381] which allows us to obtain the following vector W ( ZM ) : W(z„) =

[0382] This vector W(zw) = [ w(x zM)] defined in the focused basis (x) contains the phase of each incoherent guide star synthesized at the depth zm,

[0383] The phase conjugate of this vector W(zM) can then be used to rephase each incoherent virtual star so that they can be recombined coherently and thus obtain an estimator of the spatio-frequency correction law (zM) unbiased by the random reflectivity of the medium. Mathematically, this operation is written as follows: 0 ( £ f, x, zM ) = exp {jx arg {( x, t zM, f ) W^x, zM)} ]

[0384] The advantage of this approach compared to an SVD of the distortion matrix (second variant) or the iterative phase reversal algorithm (third variant) is to converge towards a correction law not biased by the larger amplitude of the ultrasonic signal on certain frame of the reflection matrix (large amplitude caused by the passage of a bright scatterer such as a bubble or an experimental problem).

[0385] The advantage of the distortion matrix compared to CLASS is that it can spatially filter the data by passing through the focused basis in the plane of the object at each iteration, thereby restricting the field of view and respecting the underlying isoplanetary assumption. The disadvantage lies in the multiple fundamental changes inherent in this approach that can be computationally costly in terms of computation time and memory.

[0386] Of course, the invention is not limited to the examples just described. Many modifications can be made to these examples without departing from the scope of the present invention as described.

Claims

Demands

1. Ultrasonic construction method of a confocal image of an object (4) contained in a medium, the method comprising the following steps: a) acquisition, by means of a transducer array (2) and a diffusing screen (3) disposed in the path of the wave between the transducer array and the object, of at least one canonical reflection matrix R ui(t)=[R(u out,i in,t)] defined between an ultrasonic wave emission basis i at the input and a reception basis 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 the object via the diffusing screen; t denoting the echo time;b) determination of a focused reflection matrix R'^ a?) by projecting the canonical reflection matrix into a space-frequency basis depending on both a position vector in a plane p of the diffusing screen and a pulsation co of the ultrasonic waves, this basis being defined by: £_ 01 P £ ” where Co is the speed of sound in the medium, a distance between the diffusing screen and the object, c) determination of a corrected reflection matrix R”^( w) in the space-frequency basis by application of a matrix imaging algorithm, d) determination of a reflection matrix associated with the object Rxx ( by projecting the corrected reflection matrix R"^( m) into a plane of the objectx located at a distance zM from the transducer array, e) construction of an image from the object reflection matrix;

2. A method according to claim 1, characterized in that the step of acquiring at least one canonical reflection matrix R ui (t) comprises the emission of an ultrasonic pulse from each transducer of the array whose position is located by the coordinate u in, this pulse gives rise to a divergent cylindrical or spherical incident wave which is reflected by diffusers of the medium, These reflected echoes form a backscattered field which is recorded by each of the transducers as a function of time; the canonical reflection matrix Ruu(t) expressed in the basis of the transducers being composed of a set of impulse responses R(u out,u in,t ) between transducers.

3. A method according to claim 1, characterized in that the step of acquiring at least one canonical reflection matrix R ui(t) comprises an insonification of the medium with a series of plane waves with a delay r'(u) applied to each signal at emission for the formation of a wavefront inclined at an angle 0 ia with respect to the array of transducers, a backscattered field by the medium, R(u out , 0 ia, t) is measured by all the position transducers u out for each incident plane wave 0 ia, the set of responses forming a canonical reflection matrix Ru 0(t)=[ R(u out, 0 ;n, t)].

4. A method according to claim 1, characterized in that the step of acquiring at least one canonical reflection matrix R ui (t) comprises an insonification of the medium with a series of diverging waves.

5. A method according to any one of the preceding claims, characterized in that the diffusing screen is an element endogenous to the medium.

6. A method according to any one of claims 1 to 4, characterized in that the diffusing screen is an exogenous element which is introduced into the medium before the canonical reflection matrix acquisition step.

7. A method according to any one of the preceding claims, characterized in that step a) further comprises a step of applying a time window to the canonical reflection matrix.

8. A method according to any one of the preceding claims, characterized in that step b) comprises the following steps: - a first step of determining a focused reflection matrix R / ^( w) by projecting the canonical reflection matrix R Ui(t) into the basis P of the diffusing screen according to the following equation: R / v O) = ( w ) x R^ ( w ) x Pp ( w ) in which the matrix ( o?, ) is the Fourier transform of each canonical reflection matrix ( t ), +? ; The matrix G' / ?(w) is the R'(MR'(') reception pass-through matrix adapted for the pass-through from the receiving basis (u) to the basis of the scattering screen at the pulsation w of the ultrasonic waves; the matrix P^(m) is the transmission pass-through matrix adapted for the pass-through from the transmission basis (i) to the basis of the scattering screen at the pulsation w of the ultrasonic waves; the symbols * and t denote respectively the matrix operations of conjugation and transposition-conjugation; the symbol x denotes a matrix product; - a second step of determining a compensated matrix Æpp, , CO j by compensating for the curvature of wavefronts in the plane of the scattering screen according to the following equation: R(P0Uf Pin' = ^{Po^ M)R(Po^ P^ ^(P^ W) with a parabolic phase term under the paraxial approximation; P0Ut being a first spatial position point corresponding to a virtual output transducer;Pjn being a second spatial position point corresponding to a virtual input transducer, - a third step of determining the focused reflection matrix R'^( w) by performing a change of variable defined by: £ — c0 ¾ from the compensated matrix so as to obtain the following relation between the coefficients of the matrices R'^( w) and co): R'(Ç w) = r(^ X ' ouf ■ ui ) X ' ouf ' in !;

9. 9. A method according to any one of the preceding claims, characterized in that, in step c), the matrix imaging algorithm is an iterative CLASS algorithm for "Closed-Loop Accumulation of Single Scattering," this CLASS algorithm comprising the following steps: - construction of an angular spectrum estimator j of the object's reflectivity by summing hyperdiagonals of the focused reflection matrix R'^( (f) -, these hyperdiagonals being defined such that £—£.+£ — constant, and the estimator is defined s+ ” in vout according to the following equation: w «>) n-1 being the number of iterations, - application of a phase conjugate of the estimator to the focused reflection matrix R'^( tn) so as to make the object virtually coherent: ( ■ %ouf ^ouf M ouf ^ouf 0J ) ^Oh> ( £+ ) ntn-t) is a consistent matrix, ^coh - application on a coherent matrix of a time window of ultrasonic echoes consisting, in the frequency domain, by a convolution with a function whose bandwidth Aa> is inversely proportional to the duration At of the time window applied to the ultrasonic signals in the time domain: with B((A, Au;) the frequency filter of characteristic width Aw - determination of two estimators, / / and / / / £ \, of the screen transfer function broadcasting in summing the rows and columns of the filtered coherent reflection matrix • H™ “ eX P ( * 31 § { ^ouf œ )} ) H on* ( ^ouf “ CXP ( * ar§ {itî ouf W )} ) - application of the in-phase conjugates of these two estimators to the reflection matrix to obtain a reflection matrix For which the phase shift induced by the diffusing screen has been compensated: - iteration of the steps of the CLASS type algorithm in order to converge towards a corrected reflection matrix in the plane of the diffusing screen, then reinjection of the parabolic phase terms that had been previously compensated: R%4 w) = E(a,) o [limR"W(oi (

10. 10. Method according to claim 9, characterized in that step d) of projecting the corrected reflection matrix into the plane of the object x further comprises a summation of the results on the frequencies according to the following equation: Rxx(zM) = J wda) GxS ( zM, (o ) x R"^ ( w ) x ( zM, œ ) the matrix Gr^ ( zM, co ) is the transformation matrix from the basis (£) to the focused basis (x) at the depth zm and at the angular frequency w and a'+ are the lower and upper bounds of the bandwidth of the ultrasonic signals.

11. 11. Method according to claim 10, characterized in that step e) of constructing an image of the object is obtained by considering the diagonal of the reflection matrix: I ( X, Z^ ) — R(X,X,Z^) with x the position vector in the plane of the object.

12. 12. A method according to any one of the preceding claims, characterized in that at step c), the matrix imaging algorithm is an algorithm using a matrix distortion technique with a spatio-frequency correction basis.

13. 13. Method according to claim 12, characterized in that the distortion matrix technique with a spatio-frequency correction basis (£) comprises the following steps: - calculation of a dual reflection matrix between the focused basis (x) and the spatio-frequency correction basis (£): Rfx ( ZM, (!) ) = ( œ) XR^.(w) x (ZM, (!) ) the matrix Gw^(0)) is the transition matrix describing the projection of the transducer basis (u) to the spatio-frequency correction basis (£) at the pulsation w, the matrix (w) is the transition matrix describing the projection of the emission basis (i) to the focused basis (x) at the depth zm and the pulsation w, - deduction of a frequency distortion matrix D|x(zM, w) by performing the term-by-term product of the dual reflection matrix with the phase conjugate matrix of the reference matrix that would be obtained without a diffusing screen, i.e. here G^(w) • Such that £ z„,f) = «1 -V- f, zM, - calculation of the correlation matrix Cgg ,. - determination of the spatio-frequency correction law ¢(¾) by analysis of the correlation matrix Cgg.

14. 14. A method according to claim 13, characterized in that the coefficients of the correlation matrix Cgg are given by: c( {£ n ri zM) = ç, Zm, f)D\x, zM, f) •

15. 15. Method according to claim 13, characterized in that the correlation matrix C is determined in the focused basis x, by the following calculation of the elements of the correction matrix C = CxX: C(x, x' ) = E^D(x £ zM, f) x Ç, zM, f) * is the conjugation operator.

16. 16. A method according to any one of claims 13 to 15, characterized in that the analysis of the correlation matrix Cgg (¾) is carried out by an eigenvalue decomposition of the correlation matrix Ccc(7w), and the spatio-frequency correction law ¢(¾) is the first eigenvector U, of the correlation matrix in the correction basis (£).

17. 17. A method according to any one of claims 13 to 15, characterized in that the analysis of the correlation matrix is ​​performed by a singular value decomposition of the distortion matrix rearranged as follows:

18. 18. A method according to any one of claims 13 to 15, characterized in that the analysis of the correlation matrix Cgg is carried out by solving the following equation: $ (zM) = exp( j arg{ iteratively by the following expression, which corresponds to an iterative phase-reversal calculation: ^+1(¾) = exP( J x 0«(sw)} ) where x is the matrix product, with: > an arbitrary wavefront, for example — [ ] ] ]T.

19. 19. A method according to any one of claims 13 to 15, characterized in that the analysis of the CM correlation matrix is ​​performed by solving the following equation: W(zM) = exp(jarg{Cxx(zM) xW(^)}) where x is the matrix product, iteratively by the following expression: Wn+1(zM) =exp(j xW„(z / U)} ) where x is the matrix product, with Wo an arbitrary wavefront, for example Wo = [ 1 1 ]T ■

20. Use of a predetermined spatio-frequency correction law linked to an image acquired of an object by means of a predefined array of transducers and a predefined diffusing screen and by carrying out steps d) and e) according to claim 1; this predetermined spatio-frequency correction law being determined by application of a matrix imaging algorithm following a preliminary phase during which steps a) to c) of claim 1 were carried out using an assembly comprising the predefined array of transducers, the predefined diffusing screen and a phantom-type model object; a reflectivity statistic and a speed of sound of said assembly being predefined.

21. 21. Ultrasonic construction system for a confocal image of an object contained in a medium, the system comprising: - an array (10) of transducers adapted to generate a series of ultrasonic waves incident in a region of interest of the medium, and to measure as a function of time the ultrasonic waves backscattered by said region of interest; - a diffusing screen on the path of the waves between the array of transducers and the medium to be imaged, and - a computing unit (30) connected to the array of transducers and adapted to implement the method according to any one of claims 1 to 19.

22. 22. Product computer program comprising instructions which, when the program is executed by a computer, cause the computer to carry out the steps of the process according to any one of claims 1 to 19.

23. 23. Computer-readable medium comprising instructions which, when executed by a computer, cause the computer to carry out the steps of the process according to any one of claims 1 to 19.

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