Method for achieving local compensation of aberrations in a dynamic medium during ultrasound imaging

Abstract

The invention relates to a method for constructing ultrasonically a confocal image of a dynamic medium, the method comprising the following steps: a) acquisition of a series of canonical reflection matrices Rui(t, #m); b) focused reflection matrices Rxx(z, #m); c) dynamic focused reflection matrices (I); d) correction laws Φ(x,z); e) corrected focused reflection matrices (II); f) dynamic confocal signal S c (x, z, #m) at every point of spatial position (x, z); g) construction of an image from the dynamic confocal signals.

Description

DESCRIPTION TITLE: METHOD FOR LOCAL COMPENSATION OF ABERRATIONS IN A DYNAMIC MEDIUM IN ULTRASONIC IMAGING. Technical field

[0001] The present invention relates to a method and a system for constructing a confocal image of a dynamic medium with local compensation of aberrations.

[0002] The invention is advantageously applicable to the field of medical imaging, but can be applied to any field of ultrasound imaging. Prior 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] However, due to inhomogeneities in the speed of sound between different tissues of the human body, ultrasound images suffer from both transverse and axial aberrations which degrade their contrast and alter their resolution.

[0005] Furthermore, in ultrasonic localization microscopy, it is possible to image the vascular network of an organ with high resolution by detecting, locating, and tracking isolated bubbles. However, this bubble detection and tracking process relies on convolution with a Gaussian spreading function, which is only valid in an ideal case free of aberrations.

[0006] Figure 1 illustrates a conventional focusing process for producing an ultrasound image of a medium. Unfortunately, the medium here contains an aberrant layer with a different speed of sound than the speed of sound observed in the rest of the medium. This results in spatial distortion and temporal dispersion (reverberation) of the acoustic wavefront, leading to transverse and axial aberrations in the resulting ultrasound image. These phenomena lead to a degradation of its resolution and of its contrast as well as the appearance of reverberation artifacts, particularly annoying during a medical examination.

[0007] In the diagram on the left of Figure 1, the array of transducers, positioned opposite a medium, allows for the insonification and imaging of the medium. The conventional method consists of insonifying the medium using focused emissions via a technique called beamforming. A set of appropriate delays τ, 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 with spatial position rin. = (xin, z). Due to the physical limitations of diffraction, the ultrasound waves are emitted through the aperture of the ultrasound probe, concentrated in an area often called the "focal spot." Furthermore, the waves passing through the aberrant layer are distorted, causing distortion and broadening of the focal spot around the focal point.This undesirable effect is illustrated in the diagram on the left of Figure 1.

[0008] Waves reflected at the focal point are returned to the transducer array and pass through the aberrant layer again, further distorting the reflected wavefront measured by the transducer array. A path-forming process applied to this type of signal results in an ultrasound image with significant lateral distortions due to the presence of the aberrant layer. If this layer is reverberant, multiple reflection echoes can cause axial distortion of the ultrasound image. These various effects lead to a loss of resolution and contrast in the ultrasound image. A heterogeneous distribution of sound velocity in the tissues traversed therefore impacts the quality of the reconstructed image.

[0009] The diagram on the right of Figure 1 illustrates the object of the invention: to determine the wavefront to be emitted in order to optimally focus the ultrasonic waves both spatially and temporally towards each point in the medium. Adaptive focusing techniques, or more recently matrix imaging, have been developed for this purpose. However, they rely on the invariance of the focal spot over a sufficient area in order to be able to Intelligently combining waves reflected from different contiguous points allows us to overcome disorder and access the aberration law associated with the area under consideration, commonly called the isoplanetary zone. These adaptive focusing techniques are well-known but remain limited because they can only compensate for relatively low-order aberrations associated with sufficiently large isoplanetary patches. Higher-order aberrations and reverberations vary too rapidly to be addressed by these state-of-the-art techniques. This results in a spatiotemporal distortion of the acoustic wavefront, leading to significant aberrations in the ultrasound image, and therefore a degradation of its resolution and contrast. These aberrations can be so severe that they compromise the ultrasound characterization, particularly in the case of a medical examination.

[0010] La présente invention a pour but un nouveau procédé d’imagerieultrasound in which higher-order aberrations and reverberations are optimally compensated for each focal point. The objective is to obtain an ultrasound image with the finest possible resolution and optimal contrast. Description of the invention

[0011] On atteint au moins l’un des objectifs précités avec un procédé de Ultrasonic construction of a confocal image of a dynamic medium, the process comprising the following steps: a) acquisition, by means of a transducer array, of a series of canonical reflection matrices Rui(t, #m)=[R(uout,iin,t,#m)] at different times, each canonical reflection matrix being 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 in the medium; t denoting the echo time and #m denoting the m ièmecanonical reflection matrix; b) determination of a focused reflection matrix Rxx(z, #m) for each canonical reflection matrix by input-output focusing for any point of at least one region of the medium, the coefficients of this focused reflection matrix are obtained by calculating an acoustic pressure field between all points of the region with lateral positions xin and xout, located at an expected depth z for an assumed speed of sound c0; c) determination of a dynamic component for each coefficient of each focused reflection matrix so as to constitute dynamic focused reflection matrices ^ ^ ^^ (^, #^)d) determination of a correction law ^(x, z) for each point x and depth z of the medium from the dynamic focused reflection matrices,e) determination of corrected focused reflection matrices ^ ^^^ (^, #^) by applying the correction law ^(x, z) at every point in the medium, f) determination of a dynamic confocal signal Sc(x,z, #^) of every spatial deposition point (x, z) from the diagonal coefficients of the corrected focused reflection matrix ^ ^ ^^ (z, #^),g) construction of an image from dynamic confocal signals.

[0012] Avec la présente invention, le procédé permet avantageusement de The medium is probed locally to obtain a local estimate of an aberration correction law adapted to correct the ultrasonic path formation process. This correction makes it possible to reduce or eliminate aberrations, for example, due to variations in the speed of sound in the medium or to multiple reflections of waves generated by one or more aberration zones in the medium.

[0013] L’étape d’acquisition peut consister en la réalisation des mesuresallowing the processing of reflection matrices or a posteriori processing of matrices from data stored in a memory space. The variable t represents the echo time associated with the signals recorded during the measurement, and f the ultrasonic wave frequency during the measurement. For each measurement, an amplitude and a phase are acquired for each pixel.

[0014] Ainsi les différents calculs de l’invention peuvent ainsi être réalisés independent of the measurement acquisition phase, in particular by modifying various calculation parameters, this allows for various ultrasonic construction analyses to be carried out either in real time or a posteriori.

[0015] Ces calculs de correction bénéficient d’informations locales extraites thanks to the dynamic part of the echoes reflected by the tissues.

[0016] Alors que les méthodes de correction d’aberrations existantesAdaptive focusing and matrix imaging rely on the assumption of local isoplanetism (spatial invariance of the focal spot) to average the correlations between ultrasonic signals from several contiguous focal points. The method according to the invention uses signal dynamics to obtain an independent focusing law for each pixel. Spatial averaging is not required, thus allowing access to very high-order aberrations exhibiting little or no isoplanetism.

[0017] L’invention est notamment remarquable par le fait qu’on acquière une A series therefore consists of several canonical reflection matrices at different times. Each acquisition can include several measurements with the application of several different plane waves to constitute a matrix. An acquisition can be called a frame, symbolized by #m.

[0018] Le fait d’avoir plusieurs matrices de réflexion canoniques d’un mêmeAcquiring data at different times allows us to account for the dynamic nature of the environment. This dynamic aspect, which could be considered a drawback, is used to improve the accuracy in determining correction laws.

[0019]

[0020] Selon une mise en œuvre avantageuse de l’invention, l’étape The acquisition of a series of canonical reflection matrices Rui(t, #m) can include the emission of an ultrasonic pulse from each transducer of the network whose position is located by the coordinate uin; 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,#m) expressed in the basis of the transducers being composed of a set of impulse responses R(uout,uin,t,#m) between transducers.

[0021]

[0022] Selon une variante, l’étape d’acquisition d’une série de matrices decanonical reflections Rui(t, #m) can include an insonification of the medium with a series of plane waves with a delay τ' applied to each signal at emission for the formation of a wavefront inclined at an angle θin with respect to the array of transducers, a backscattered field by the medium, R(uout, θin, t, is measured by all the position transducers uout for each incident plane wave θin, the set of responses forming a canonical reflection matrix Ruθ(t, #m)=[ R(uout, θin, t, #m)].

[0023]

[0024] Selon encore une variante, l’étape d’acquisition d’une série de canonical reflection matrices Rui(t, #m) can include an insonification of the medium with a series of diverging waves.

[0025]

[0026] Selon l’invention, l’étape de détermination de la matrice de réflexion focused Rxx(z,#m) can include:

[0027] - un processus de focalisation en entrée à partir de chaque matricecanonical reflection Rui(t,#m) which uses a forward time of flight of the waves between the ultrasonic wave emission base i and a virtual input transducer TVin and which creates a focal spot called the input spot around a first point P1 of spatial position rin=(xin,z), said input focal spot corresponding to the virtual input transducer TVin, and

[0028] - un processus de focalisation en sortie à partir de la matrice de canonical reflection Rui(t,#m) which uses a time-of-flight return of waves between a virtual TV output transducer out and the receiving base transducers u and which creates a focal spot called output around a second point P2 of spatial position rout=(xout,z), said focal spot output corresponding to the virtual output transducer TVout.

[0029]

[0030] A titre d’exemple, la coordonnée xout du deuxième point P2 est situéat a distance from the coordinate xin of the first point P1 which is less than or equal to a maximum distance Δxmax which is a function of a number of ultrasonic waves generated during the acquisition of the reflection matrix.

[0031]

[0032] En particulier, la matrice de réflexion focalisée peut être déterminée in the time domain or in the frequency domain.

[0033] Si on traite d’aberrations s’apparentant à de simples décalages temporal amplitudes of relatively small amplitude (typically lower than the temporal resolution of ultrasonic signals), then it will be advantageous to directly calculate the reflection matrix in the time domain and only at ballistic time.

[0034] Si on traite d’aberrations d’amplitude plus importantes et / ou de reverberations and / or frequency dispersion, then it is preferable to adopt a polychromatic approach and calculate the focused reflection matrix in the frequency domain.

[0035] Selon une caractéristique avantageuse de l’invention, la composante dynamics can be determined by subtracting from each coefficient of each focused reflection matrix a moving average over N focused reflection matrices.

[0036] De plus, la composante dynamique peut être déterminée enapplying a high-pass or band-pass filter according to a dimension of the numbers # ^ reflection matrices.

[0037] On utilise ici avantageusement le fait d’avoir acquis plusieurs trames of canonical reflection matrices.

[0038]

[0039] La composante dynamique peut encore être déterminée en réalisant a singular value decomposition of the focused reflection matrices rearranged in a two-dimensional matrix, one dimension of which is that of numbers # ^ reflection matrices. In other words, we concatenate all the reflection matrices into a global two-dimensional matrix, which we then use as a SVD.

[0040]

[0041] Selon l’invention, l’étape de détermination d’une loi de correction ^(^, ^) can include, for each dynamic focused reflection matrix^ ^ ^^ (^, #^), the following steps:

[0042] - détermination d’une matrice de réflexion duale Rcx(z, #^) par projection directly or indirectly from the dynamic focused reflection matrix ^^^^ (^, #^) to a correction basis (c),

[0043] - calcul de la loi de correction ^(^, ^) à partir de la matrice de réflexion dual Rcx(z, #^), said correction law being a correction law, ^ = [^(^, ^)]on correction basis (c),

[0044] - détermination des matrices de réflexion focalisées corrigées by back projection of the corrected dual reflection matrices^ ^ ^^ (z, #^) towards the focused basis (x), that is to say the set of points x at the considered depth z.

[0045]

[0046]

[0047] De préférence, les coefficients ^^ ^^ (^, #^) = [^^^ (^, ^, ^, #^)] of the corrected dual reflection matrix ^ ^ ^^ can be determined by performing a term-by-term product between the dual reflection matrix Rcx(z, #^) and the phase conjugate of the correction law ^(^, ^), i.e.:

[0048] ^ ^ ^^ = ^^^ ∘ ^∗

[0049] où le symbole * désigne une opération de conjugaison de phase, le symbol ∘ is the Hadamard product, such that:

[0051] L’étape de calcul de la loi de correction ^(x, z) peut comprendre lesNext steps: - Construction of a correlation matrix C(x,z) from the dual reflection matrices Rcx(z, , #^) for each point (x,z) in a field of view, - Determination of the focusing law ^(x,z) for each point in the field of view by performing one of the following operations: - Eigenvalue decomposition of the correlation matrix C(x,z), the correction law ^(x,z) being the first eigenvector ^^ of the correlation matrix C(x,z) in the correction basis (c), - Singular value decomposition of the dual reflection matrix rearranged as follows: ^^#(x, z) = [^(^, #^ , x, z)] the correction law ^(x, z) being equal to the first singular vector of the dual reflection matrix ^^#, i.e.^(^, ^) = ^^- solving the following equation: ^(x, z) = exp(^ arg{^^^(x, z) × ^(x, z)}) iteratively by the following expression, which corresponds to an iterative phase-reversal calculation: ^^^^(x, z) = exp(^ arg{^^^ × ^^(x, z)}) Where × is the matrix product, with ^^ an arbitrary wavefront, the correction law ^(x, z) being obtained by:. ^(x, z) = ^ ^^ → ^ ^^^ (x, z) - Solving the following equation: ^(x, z) = exp(^ arg{^##(x, z) × ^(x, z)}) where × is the matrix product, iteratively using the following expression: ^^^^(x, z) = exp(^ arg{^##(x, z) × ^^(x, z)}) where × is the matrix product, with ^^ an arbitrary wavefront, which allows us to obtain the following vector W(x, z): ^ (x, z) = ^ ^^ → ^ ^ ^^(x, z) the correction law ^(x, z) being obtained by:

[0052] Avantageusement, la matrice de corrélation C(x,z) peut êtredetermined in the correction basis c and in the frequency domain, by the following calculation of the elements of the correlation matrix C = Ccc: where * is the conjugation operator. c and c' being points of the correction base c

[0053] Cette opération permet de corréler les champs réfléchis dans la base correction for each virtual source in (x,z). This correlation is averaged over the different frames # ^ that is to say, the different realizations of speckle, in order to overcome the random reflectivity of the medium and thus synthesize a coherent guiding star from the various achievements # ^ speckle.

[0054] Autrement, la matrice de corrélation C(x,z) peut être déterminée in the number base # ^ , by the following calculation of the elements of the correction matrix C = ^ ## : * is the conjugation operator. c and c' are points in the correction base, c#m and #l denoting the m ièmes and ièmes frames of the recorded reflection matrix sequence.

[0055] De préférence, l’étape de calcul de la loi de correction ^(^, ^) peut be iterated at least twice, with at each iteration the projection going uses the corrected focused reflection matrix ^ ^ ^^ (^, #^) obtained during the return projection of the previous iteration in place of the focused reflection matrix Rxx(z,# ^ ).

[0056] L’étape de détermination d’une matrice de réflexion duale Rcx(z, #^) can also be iterated at least twice with, at each iteration, the use of a different correction basis c.

[0057]

[0058] L’étape de détermination d’une matrice de réflexion duale Rcx(z, #^) can otherwise be iterated at least twice with, at each iteration, the use of a projection either towards an input correction basis, or towards an output correction basis of the dynamic focused reflection matrix.

[0059]

[0060] Selon une caractéristique avantageuse de l’invention, la base de The correction could be one of the following bases:

[0061] - une base des ondes planes ou base de Fourier spatiale,

[0062] - une base des transducteurs u,

[0063] - une base correspondant au lieu supposé d’aberrateurs dans le medium,

[0064] - une base correspondant à un plan déterminé par optimisation.

[0065] Cela permet de réaliser des projections au niveau des transducteurs, aberrants or something similar.

[0066]

[0067] L’étape de détermination d’une matrice de réflexion duale Rcx(z, #^)can be achieved by forward projection of the focused dynamic reflection matrix ^^^^ (^, #^) to the correction basis (c) by considering a model propagator describing the propagation of waves from the focused basis (x) to the correction basis (c).

[0068] Selon une caractéristique de l’invention, la matrice de réflexion The initial consideration of the process can be the broadband focused reflection matrix, which can be obtained by digital channel formation in the time domain or in the Fourier domain from frequency matrices:

[0069] Cette matrice de réflexion large bande correspond à une matrice de focused, windowed reflection around ballistic time.

[0070] L’étape de détermination d’une matrice de réflexion duale largeThe Rcx(z, #^) band can be obtained by forward projection of the broadband focused reflection matrix derived from the dynamic focused reflection matrix ^^^^ (^, ^ = 0, #^) onto the correction basis (c), considering a propagator at the single center frequency ^^ = (^^ + ^^) / 2. The resulting aberration law then exhibits no frequency dependence, ^(^, ^, ^, ^) =^(^, ^, ^). This variant should be considered, for example, if the aberrations are similar to simple time shifts with an amplitude smaller than the temporal resolution of the ultrasonic measurement, the latter varying inversely with the bandwidth. Beyond this, a multi-frequency approach is preferable.

[0071]

[0072] Si les aberrations sont seulement axiales (variation de la Vitesse du(since it only depends on the depth), the step of determining a dual reflection matrix Rcx(z, #^) is not necessary. The correction law we are looking for is indeed only frequency-dependent: ^(^, ^, ^, ^) = ^(^, ^, ^). In this case, the matrix considered at the start of the process is the confocal signal of the dynamic focused reflection matrix ^ ^ ^^ (^, #^), this confocal signal being such that:

[0073] ^(^, ^, ^, #^) = ^(^, ^, ^, ^, #^)

[0074] Dans ce cas, la matrice de corrélation pour l’obtention de la loi de The frequency correction, ^(x, z) = [Φ(f, x, z)], can be given by:

[0075] ^(^, ^′, ^, ^) = ∑#^ ^(^, ^, ^, #^) ^∗(^, ^, ^^ , #^) where the symbol * denotes a phase conjugation operation, f and f' denote frequencies in the bandwidth of the ultrasonic signal, the correction basis being directly named here (f), i.e. , ^(^, ^, ^, #^) being the confocal signal of the focused dynamic reflection matrix ^^^^ (^, #^).

[0076] L’étape de calcul de la loi de correction ^(x, z), peut être réalisée :

[0077] - en définissant une matrice de corrélation pour l’obtention de la loi correction, ^(x, z) = [Φ(f, x, z)], by:

[0078] ^(^, ^′, ^, ^) = ∑#^ ^(^, ^, ^, #^) ^∗(^, ^, ^^ , #^)

[0079] - et en moyennant la matrice de corrélation sur les nombres #m maisalso on adjacent pixels belonging to the same patch

[0081] f et f’ désignent une fréquence du signal confocal dans la bande probe passage

[0082] xp est la coordonnée transverse du point central du patch of isoplanetism for which we seek to estimate the law of aberration ^

[0083] zp est la coordonnée axiale du point central du patch d’isoplanétisme for which we seek to estimate the law of aberration ^

[0084] Ω^: étant un patch d’isoplanétisme centré sur le point ^^^, ^^^.

[0085]

[0086] Selon l’invention, l’étape de détermination de matrices de réflexion focused corrected ^ ^ ^^ (^, #^) can be iterated at least twice, with each iteration using the corrected focused reflection matrix. ^ ^ ^^ (^, #^) obtained during the return projection of the previous iteration in place of the focused reflection matrix Rxx(z,#^).

[0087] De préférence, l’étape g) de construction d’une image à partir desDynamic confocal signals can include a step of: - determining an intensity of each dynamic confocal signal to construct a confocal image of the medium, or - determining an intensity of each dynamic confocal signal to construct a power Doppler image by summing, for each point of spatial position (x, z), the intensities of several confocal signals, or - determining a Fourier transform of the dynamic confocal signal^^(^, ^, #) along the time dimension #^: where the frequency ^ is the variable conjugate to the acquisition time #, to construct a directional Doppler image of the medium, - determination of the local dynamics for each ultrasound image point of spatial position (x, z), by measuring the average frequency ^D(x,z) of the Fourier transform ^^(^, ^, ^) of the complex confocal signal: to construct a map of the axial velocity of the diffusers at each point in the image.

[0088] Selon une caractéristique avantageuse de l’invention, la matrice de focused reflection Rxx(z,#m) can depend on a frequency f of the ultrasonic signals, the correction law being determined as a function of this frequency f and the coordinates of the correction plane.

[0089]

[0090] Selon une caractéristique avantageuse de l’invention, la matrice de Focused reflection Rxx(z,#m) can be integrated over the entire bandwidth, the correction law being determined solely as a function of the coordinates of the correction plane (c). The focused reflection matrix, as well as the dynamics, is considered only at the ballistic time.

[0091]

[0092] Selon un autre aspect de l’invention, il est prévu un système de Ultrasonic construction of a confocal image of a dynamic medium, the system comprising:

[0093] - un réseau de transducteurs adaptés pour générer une série of ultrasonic waves incident in a zone of interest of the medium, and to measure over time the ultrasonic waves backscattered by said zone of interest; and

[0094] - une unité de calcul reliée au réseau de transducteurs et adaptée to implement the process described above.

[0095]

[0096] On prévoit également un produit programme d'ordinateur including instructions which, when the program is executed by a computer, lead the computer to carry out the steps of the process described above.

[0097]

[0098] On prévoit également un support lisible par ordinateur comprenant Instructions which, when executed by a computer, lead the computer to carry out the steps of the process described above. Brief description of the drawings

[0099] D’autres avantages et particularités de l’invention apparaîtront à la Reading the detailed description of implementations and embodiments, which are by no means limiting, and the following accompanying drawings. Figure 1 is a schematic view illustrating the problem of aberrations in the acquisition of ultrasound images according to the prior art; Figure 2 is a schematic view illustrating an example of an ultrasonic construction system for implementing the method according to the present invention; Figure 3 is a diagram of the method for constructing an ultrasound image according to the present invention; Figure 4 illustrates several schematic views 2a to 2f showing emission / reception sequences used for ultrasonic imaging and characterization of a medium; Figure 5 is a schematic view showing the focusing principle in the method according to the invention; Figure 6 is a schematic view illustrating the operation of extracting the dynamic component of ultrasonic signals for a transcranial imaging experiment of a sleeping sheep brain; Figure 7 is a schematic view illustrating the operation of extracting aberration laws by iterative phase reversal in the dynamic speckle; Figure 8 shows several images illustrating the effect of applying different local transverse aberration laws in the sheep brain; Figure 9 shows several confocal images before and after correction of a part of the sheep brain;Figure 10 contains two power Doppler visualizations showing the gain in contrast and resolution achieved by ultra-local aberration correction; Figure 11 contains two images of local dynamic frequency maps in the sheep brain, before and after correction of transverse aberrations. Detailed description of the figures;

[0100] Il est bien entendu que les modes de réalisation qui seront décrits The following are by no means exhaustive. In particular, variants of the invention may be conceived comprising only a selection of the features described below, 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 details, or with only some structural details if this part alone is sufficient to confer an advantage. technical or to differentiate the invention from the prior art.

[0101] Les différents modes de réalisation et aspects décrits dans la présente Disclosure procedures can be combined or simplified in many ways. In particular, the steps of the different processes can be repeated, reversed, and / or performed in parallel, unless otherwise specified.

[0102] La présente divulgation concerne des procédés et systèmes de Ultrasonic characterization of a medium is particularly applicable to medical imaging of living and non-living tissues. The medium may be, for example, a heterogeneous one that we seek to characterize in order to identify and / or characterize heterogeneities. These construction techniques are notably non-invasive to the medium, which is advantageously preserved, particularly in terms of its nature and integrity.

[0103]

[0104] Approche usuelle de l’imagerie ultrasonore

[0105] Dans le domaine de l’imagerie par ultrasons, on cherche souvent àConstructing an image of a medium's reflectivity from echoes backscattered by heterogeneities within the medium is the principle behind ultrasound imaging, which allows visualization of the internal anatomy of an individual or animal. For the sake of simplicity, to enable the construction of an ultrasound image, the medium is considered homogeneous, with a constant sound propagation speed c0.

[0106] La dynamique du milieu peut être naturelle (par exemple liée au passage of blood in the blood vessels and to the cardiac cycle) or can be induced by a vibration of the medium induced by radiation pressure ("acoustic push") or by vibration of a probe.

[0107] Les méthodes d’échographie conventionnelle utilisent généralement an array of piezoelectric transducers that can emit and / or receive ultrasonic signals independently or almost independently, each transducer being at a position u in the strip supporting said array. The array of transducers, placed opposite a The medium allows for insonification and the construction of a representative image of the medium in various ways. A conventional method consists of insonifying the medium using focused emissions via a technique called beamforming. This method involves applying a set of appropriate delays τ(uin, xin, z, c0) to the signals emitted by each transducer, based on a homogeneous velocity model c0, in order to constructively interfere the wavelets produced by each transducer at the targeted focal point with spatial position (xin, z). Due to the physical limitations of diffraction, the ultrasound waves are emitted through the aperture of the ultrasound probe, concentrated in an area often called the "focal spot," with a lateral width δx.

[0108] Afin de permettre de construire ensuite éventuellement une imageIn the ultrasound imaging phase, illustrating the characteristics of the medium under study, a digital focusing step is also performed at the receiver. The echoes captured by the array transducers are phase-adjusted by temporally shifting them. The time delays τ(uout, xout, z, c0) are identical to those applied at the transmission phase, with the variable uout representing the position of each transducer. During the transmission phase, all signals interfere at the position point (xin, z) at the ballistic time t = z / c0 if the velocity model c0 used corresponds to the reality of the medium under study. At the receiver, the signals from this same point (xout = xin) interfere by summation at the echo time t = 2z / c0. This summation yields the final focusing result at the receiver. This confocal method with dual focusing at both the transmission and reception phases allows for direct imaging of the medium's reflectivity with a lateral resolution δx and good contrast.However, this method is time-consuming because it requires physically focusing the emission at each point of the medium, or at least at a given depth, on each of the lines of the constructed image representing the medium.

[0109]

[0110] La présente invention a pour objet de perfectionner les procédés de ultrasound surveys are known, particularly for correcting aberrations.

[0111]

[0112]

[0113] Système de construction ultrasonore

[0114] La figure 2 illustre un exemple d’un système 1 d’imagerie ultrasonore for implementing the ultrasonic imaging method of a medium such as a heterogeneous 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.

[0115] Le système 1 comprend :

[0116] - un dispositif de sondage 20 ou sonde 20,

[0117] - une unité de calcul 30 pour calculer une image à partir des signaux received from probe 20,

[0118] - un panneau de contrôle 40 relié à l’unité de calcul 30, ce panneau control panel including, for example, buttons 41 and a touchpad 42,

[0119] - un dispositif d’affichage 50 pour visualiser une image et divers elements or measures.

[0120] La sonde 20 est reliée à l’unité de calcul 30 via un câble 21 ou via unewireless 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 emitted ultrasonic waves on diffusing or diffusing particles inside the medium.

[0121] La sonde 20 peut comprendre un réseau 10 comprenant une pluralitéof transducers 11. The array 10 is, for example, a linear, curved, 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, 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 array 10 of transducers 11 of the probe 20 is then associated with the computing unit 30. The array 10 of transducers 11 can comprise one hundred or more transducers 11.

[0122] L’unité de calcul 30 peut comprendre un boitier 31 incluant desReceiving 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 representative signal data. The data can be stored in the memory of the processing unit 30 and / or directly processed to calculate intermediate data (track formation data or other). The processing unit 30 can implement any known method for constructing an image from the signal data received from the probe 20, such as track formation.

[0123] L’image calculée peut être :

[0124] - une image du milieu (image B-mode) habituellement en niveau de grey to visualize organs in the medium, and / or

[0125] - une image montrant une vitesse ou un flux dans le milieu (image color) for example useful for visualizing blood vessels in the medium, and / or

[0126] - une image montrant une caractéristique mécanique du milieu (elasticity) for example useful for identifying tumors within the medium.

[0127] Par "connexion" ou "liaison" entre le dispositif de sondage 20, l'unitécalculation device 30 and display device 50, we mean any type of wired connection, electrical or optical, or any type of wireless connection using any protocol such as WiFi TM Bluetooth TM or others. These connections or links are single-direction or two-way. The associated display device 50 can be of any type, such as a touchscreen or non-touchscreen, connected or not.

[0128] Le dispositif d’affichage 50 est un écran permettant de visualiser The image is 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 for the user.

[0129] Le panneau de contrôle 40 est par exemple une portion d’un boitiersystem, said portion comprising a panel housing having a substantially flat surface 40a inclined towards the user for one-handed operation. As shown in Figure 2, the control panel 40 may include a control screen 49 for displaying various configuration information.

[0130] L’unité de calcul 30 est configurée pour la mise en œuvre d’étapes decalculations and / or processing, particularly for the implementation of process steps according to this disclosure. By convention, as shown in Figure 5 depicting an array 10 of transducers 11 on a surface of a medium M, a spatial frame of reference for the medium M is defined by taking a first axis X and a second axis Z perpendicular to it. 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 frame of reference in the case of a two-dimensional array 10, or to a polar frame of reference in the case of a curved array 10, or to any other frame of reference adapted and / or dependent on the structure and shape of the array 10 of ultrasonic transducers.Thus, in the remainder of this disclosure, we will use a Cartesian XZ frame, corresponding to a linear probe 20, for simplicity in explanations, but a specialist in the field would easily generalize and apply the results to any type of frame.

[0131] Dans la suite de la divulgation, il est fait référence à un réseau 10 de transducers 11 for transmission and reception, it being understood that, in a more general case, several transducer arrays 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 transducers 11, of the same type or of different types.

[0132] Le réseau 10 de transducteurs 11 sert par exemple à la fois comme transmitter and receiver, or is made up of several subnetworks of transducers, some dedicated to the emission, others to the reception of ultrasonic waves. By transducer network, we mean at least one transducer, an aligned or non-aligned sequence of transducers, or a two-dimensional distribution of transducers (for example a transducer matrix), or any spatial distribution of transducers.

[0133] Lorsque dans la présente divulgation, il est fait référence à des étapesRegarding calculation or processing for the implementation of process steps, it is understood that each calculation or processing step can be implemented by software, hardware, firmware, microcode, or any appropriate combination of these or related technologies. When software is used, each calculation or processing step can be implemented by computer program instructions or code that can be interpreted or executed. These instructions can be stored or transmitted to a storage medium readable by a computer (or computing unit) and / or executed by a computer (or computing unit) to implement these calculation or processing steps.

[0134]

[0135] Sur la figure 3 est représenté un diagramme des principales étapesaccording to the invention. A step a) of acquiring a series of canonical reflection matrices Rui(t, #m) is distinguished. In b), a set of focused reflection matrices Rxx(z, #m) of the medium is determined by a focusing process for several points of transverse spatial position (x, y) of a region and axial position z=c0t / 2 from the canonical reflection matrix R ui (t, # m ) for a model of the speed of sound c0,

[0136] A l’étape c) on construit des matrices de réflexion focalisées dynamics ^^^^ (^, #^) by removing the static component.

[0137] L’étape d) permet de calculer des lois de correction ^(x, z) pour chaque pixel of the image from the dual reflection matrices, the latter being obtained by projection of the output of the dynamically focused reflection matrices ^^^^ (^, #^) into a correction basis c for aberrations,

[0138] A l’étape e), on détermine des matrices de réflexion focalisées corrected ^ ^ ^^ (^, #^).

[0139] A l’étape f), on détermine un signal confocal dynamique Sc(x,z, #^) for any point with spatial position (x, z).

[0140] Puis construction à l’étape g) d’une image à partir des signaux dynamic confocal.

[0141] Ces étapes sont décrites plus en détails ci-après.

[0142]

[0143] Selon l’invention, le procédé de construction ultrasonore mis en œuvreThe calculation unit 30 of system 1 comprises a series of reflection matrix acquisitions at different times. Each realization of the reflection matrix will be called a frame hereafter, and the m ième frame will be denoted #m. Each reflection matrix can be acquired in the following way:

[0144] - une étape de génération d’une série d’ondes ultrasonores incidentes USin in a zone of said medium, by means of a network 10 of transducers 11, said series of incident ultrasonic waves being an emission basis i; and

[0145] - pour chaque onde émise iin, le champ réfléchi par le milieu est measured by each transducer and is denoted R(uout,iin,t,#m), where t is the echo time and the vector uout marks the position of each transducer. Each field is stored in a series of canonical reflection matrices Rui(t,#m)=[R(uout,iin,t,#m)] defined between the transmitting basis i at the input and a receiving basis u at the output.

[0146] Une première possibilité pour mesurer cette matrice de réflexion The canonical method is to successively emit an ultrasonic pulse from each transducer of the array, whose position is located by the coordinate uin as shown schematically in Figure 4(a). This results in a diverging cylindrical (or spherical) incident wave. This wave is reflected by the scatterers in the medium, and the backscattered field is recorded by each transducer as a function of time, as shown in Figure 4(b). By repeating this operation with each transducer used successively as a source, the canonical reflection matrix Ruu(t,#m) expressed in the basis of the transducers is determined. This matrix is ​​composed of all the impulse responses R(uout,uin,t,#m) between each transducer. This matrix is ​​then rich in information about the medium under study. However, the method assumes that the medium remains stationary throughout the measurements. Furthermore, the recorded signals have a poor signal-to-noise ratio because the medium is insonified by a single transducer.

[0147] Une deuxième manière de construire cette matrice de réflexionCanonical illumination consists of insonifying the medium with a plane wave series basis. This method overcomes the previous problems. Figure 4(c) illustrates the principle of this plane wave illumination. A delay law τ' is applied to each signal at the emission stage to form a wavefront inclined at an angle θin with respect to the transducer array. At the reception stage, illustrated in Figure 4(d), the field backscattered by the medium, R(uout, θin, t, μm), is measured by all the position sensors uout for each incident plane wave θin. The set of these responses forms a canonical reflection matrix Ruθ(t, μm) = [R(uout, θin, t, μm)]. This method gave rise to ultrafast imaging and elastography, and is described, for example, in the document:

[0148] « Coherent plane-wave compounding for very high frame rate ultrasonography and transient elastography”, G. Montaldo et al. (IEEE Trans.Ultrason., Ferroelect. Freq. Control 56 489-506, 2009).

[0149] Une troisième manière pour créer cette matrice de réflexionCanonical sonification involves insonifying the medium with a basis for diverging waves, as shown in Figure 4(e) and Figure 4(f), which allows the acoustic field to be illuminated more broadly than with plane waves. This basis is located by the sin position of the virtual source associated with each diverging wave. This technique, used particularly in super-resolution imaging, is explained in the following document:

[0150] « Ultrafast imaging of the heart using Circular Wave Synthetic Imaging with Phased Arrays”, Couade et al., IEEE International Ultrasonics Symposium (2009).

[0151] Chaque matrice de réflexion canonique Rui(t,#m) enregistrée peut être a "real" matrix, that is, one composed of real coefficients in the time domain, since the electrical signals recorded by each of the transducers are real numbers. Alternatively, this matrix can be a "Complex" matrix, that is to say composed of complex values, for example in the case of demodulation for the formation of in-phase and quadrature channels (known in English as "beamforming IQ").

[0152]

[0153] Focalisation de la matrice de réflexion

[0154] Après la séquence d’acquisition ou en parallèle de celle-ci, un The channel formation process is applied independently at the input and output of the measured reflection matrices. The result is a series of focused reflection matrices Rxx(z,#m) which includes responses R(xout, xin,z,#m) of the midpoint between a virtual input transducer TVin of spatial position (xin,z) and a virtual output transducer TVout of spatial position (xout,z).

[0155] Les réponses de la matrice de réflexion focalisée Rxx(z,#m) correspond to an acoustic pressure field calculated between all points in the middle of lateral positions xin and xout, located at the expected depth z=c0t / 2 and at an echo time t, and for a speed of sound assumed to be c0.

[0156] Dans l’étape de détermination de la matrice de réflexion focalisée Rxx(z,#m), we apply with reference to figure 5:

[0157] - un processus de focalisation en entrée à partir de chaque matrice decanonical reflection Rui(t,#m) which uses a time of flight on the outward journey of the waves between the emitting base i and the virtual input transducer TVin and which creates a focal spot called the input spot around the first point P1 with spatial position rin = (x in ,z), said input focal spot corresponding to the virtual input transducer TVin,

[0158] - un processus de focalisation en sortie à partir de la matrice de canonical reflection Rui(t,#m) which uses a return time of the waves between the virtual output transducer TVout and the receiving base transducers u and which creates a focal spot called output around the second point P2 of spatial position rout=(xout,z), said focal spot output corresponding to the virtual output transducer TVout.

[0159] Ces processus de focalisation en entrée et en sortie forment un input-output focusing process, referred to in the remainder of this disclosure as focusing process or simply focusing.

[0160] Autrement dit, dans ce procédé de construction ultrasonore, leThe virtual input transducer TVin corresponds to an ultrasonic "virtual source" located at spatial position rin in the medium, and the virtual output transducer TVout corresponds to an ultrasonic "virtual sensor" located at spatial position rout. This virtual source and sensor are spatially separated by the difference in their spatial positions Δx = xout - xin.

[0161] La distance maximale Δxmax entre xout et xin est dictée par le nombre The illuminations used to acquire the reflection matrix are varied. In the plane wave basis, for example, the angular sampling of the illumination sequence imposes Δxmax ~^ / (2^^) to prevent the focused reflection matrix from being polluted by grating lobes. Ideally, Δxmax is chosen based on the level of aberrations to limit the amount of data to be acquired and stored in memory. It is typically on the order of a few millimeters in ultrasound imaging.

[0162] La profondeur attendue de transducteurs virtuels est le paramètre zused in the focusing law for a sound velocity model c0. Their actual depth is dictated by the axial (depth) position of the volume isochrone, that is, by the echo time t and by the sound velocity distribution c(r) in the medium. The lateral dimension of the virtual transducers is dictated by the focal spot produced by focusing at this actual depth.

[0163] Chaque matrice de réflexion focalisée Rxx(z,#m), peut être déterminée or calculated:

[0164] - soit dans le domaine temporel, auquel cas elle peut être notée explicitly with the time parameter t, that is, denoted Rxx(z,t,#m), and

[0165] en pratique les données des matrice de réflexion focalisée Rxx(z,t,#m) are calculated between two predetermined times; and

[0166] en pratique, elle peut être seulement considérée au temps balistique expected (i.e., at t=0 in the focused basis)

[0167] - soit dans le domaine fréquentiel, auquel cas elle peut être notée explicitly with the angular frequency parameter ^ which corresponds to a frequency f by ^ = 2^^, that is to say denoted Rxx(z, ^,#m), and

[0168] en pratique les données de la matrice de réflexion focalisée Rxx(z, ^,#m) are calculated between two pulsations ^, of a frequency bandwidth, for example between a lower pulsation ^ ^ and a higher pulse ^ ^, for a central pulse ^ ^ .

[0169] Ainsi, la suite des calculs du procédé peut être effectué dans le time domain or in the frequency domain.

[0170]

[0171] Dans le premier cas de calcul dans le domaine temporel, chaque Rxx focused reflection matrix The midpoint between the virtual input transducer TVin and the virtual output transducer TVout is obtained by focusing using a pathforming calculation at the input and output. The coefficients of this focused reflection matrix Rxx(z,t,#m) can be determined by:

[0173] dans laquelle :

[0174] Nin est un premier coefficient de normalisation,

[0175] Nout est un deuxième coefficient de normalisation,

[0176] Rui(t, #^) est la matrice de réflexion, dont chaque coefficient R(uout, iin, t, #^) is the field recorded by the spatial position transducer uouconsecutive to the emission of index iin in the emission basis (i) and at time t, to which the delay times τin and τout have been applied;

[0177] ^^^(^^^, ^^^^) et ^^^^(^^^^ , ^^^^ , ^) sont des coefficients d’apodisation qui are predefined, for example to maintain a constant digital aperture for both transmission and reception;

[0178] Le premier coefficient de normalisation Nin peut par exemple êtredefined by: ^^^(^^^, ^) = ∑^^^ ^^^(^^^, ^^^, ^) Similarly, the second denormalization coefficient Nout can be defined by: ^^^^(^^^^ , ^) = ∑^^^^ ^^^^(^^^^ , ^^^^ , ^)

[0179] ^^^(^^^, ^^^, ^) est le temps de vol attendu pour chaque onde incidente ^^^ to reach the first focal point of spatial position (^^^ , ^) in a sound speed model medium c0

[0180] ^^^^(^^^^ , ^^^^ , ^) est le temps de vol attendu pour une onde réfléchie from the second focal point of spatial position (^^^^ , ^) to the deposition transducer ^ ^^^ .

[0181] Ces temps de retard ^^^ et ^^^^ sont habituellement calculés par un A person skilled in the art can calculate the time of flight based on an established model of the speed of sound. A relatively simplifying assumption is to assume a homogeneous medium with a constant speed of sound c0. In this case, the time-of-flights are directly derived from the distances between the probe's transducers and the virtual transducers. Thus, these time-of-flight calculations depend on the type of wave, the assumed speed of sound, and the geometry of the transducer array.

[0182] Par exemple, dans le cas particulier d’une onde plane avec un angle of emission ^ in:

[0183] - le temps de retard à l’émission ^ in peut être obtenu par :

[0185] - le temps de retard à la réception ^ out peut être obtenu par :

[0187] Ainsi, ces exemples de calculs de temps de retard montrent bien qu’ils are a function of the type of wave and the speed of sound, assumed here to be constant in the medium.

[0188]

[0189] Le nombre d'éléments de la base d'émission Nin est par exemple greater than or equal to one (1), and advantageously greater than or equal to two (2). The number of elements of the Nout reception base is for example greater than or equal to two (2).

[0190]

[0191] Enfin, chaque matrice de réflexion focalisée Rxx(z,t,#m) exprimée in the time domain, can be transformed in the frequency domain into a focused reflection matrix Rxx(z, ^, #m) by a Fourier transform, that is to say by:

[0193] Cette transformée de Fourier peut être implémentée par tout type de Discrete Fourier transform, normalized or not.

[0194]

[0195] Dans le deuxième cas de calcul dans le domaine fréquentiel, chaque The canonical reflection matrix Rui(t, #m), expressed in the time domain, since it consists of the signals received by the transducers, can be transformed in the frequency domain into a canonical reflection matrix #^)) by a Fourier transform, that is to say by

[0197]

[0198] Cette transformée de Fourier peut être implémentée par tout type de Discrete Fourier transform, normalized or not.

[0199]

[0200] Ainsi, la matrice de réflexion focalisée Rxx(z, ^, #m) du milieu peut can be obtained by focusing using the matrix calculation below, substantially equivalent to focusing by temporal path formation explained previously, i.e. by the following matrix product:

[0202] dans lequel :

[0203] la matrice ^^^(^, #^) est la transformée de Fourier de chaque matrice canonical reflection ^^^(^, #^),

[0204] la matrice ^^^(^, ^) est la matrice de passage de réception adaptée for the transition from the receiving basis (u) to the focused basis (x) at depth z and angular frequency ^,

[0205] la matrice ^^^(^, ^) est la matrice de passage d’émission adaptée pour the transition from the emission basis (i) to the focused basis (x) at depth z and angular frequency ^,

[0206] Les symboles ∗ et † désignent respectivement les opérations conjugation and transposition-conjugation matrices.

[0207] Le symbole × désigne un produit matriciel.

[0208]

[0209] Extraction de la composante dynamique

[0210] Afin d’extraire les signaux des diffuseurs en mouvement, une étape Filtering of the static component of the reflection matrix is ​​performed. The separation of the dynamic and static components can be achieved in various ways.

[0211] Suivant un premier mode de réalisation, la composante dynamiqueis isolated by subtracting a moving average over N frames (typically N=5) from the signal. The coefficients of the dynamic focused reflection matrix R are thus obtained:

[0212] ^^(^, ^, ^, ^, #^) = ^(^, ^, ^, ^, #^) − 〈^(^, ^, ^, ^, #^)〉^^^^^^^^^

[0213] où ^^ ^^ (^, ^, #^) = [^^(^, ^, ^, ^, #^)] is the dynamic component of the reflection matrix. Note that the same filter can be applied upstream to the measured matrix Rui(t, #m), which would be computationally more advantageous. However, the benefit of applying it to the focused reflection matrix is ​​the ability to adjust the number N of frames over which the moving average is performed.

[0214] Suivant un deuxième mode de réalisation, un filtre passe haut (ou bandpass) more sophisticated is applied according to dimension # ^ of the reflection matrix in order to filter the static component of the reflection matrix.

[0215] Suivant un troisième mode de réalisation, la composante dynamiqueis isolated by performing a singular value decomposition of the focused reflection matrix rearranged in a two-dimensional form as follows, ^# = [^({^, ^, ^, ^}, #^)]. The singular value decomposition of this matrix is ​​written:

[0216] ^ = ∑ ^ ^ # ^ ^^^ ^^

[0217] avec ^^ = ^^^({^, ^, ^, ^}, ^)^ correspondant aux vecteurs singuliers of the reflection matrix in the associated space {^, ^, ^, ^}.

[0218] ^^ = ^^^(#^)^ correspondant aux vecteurs singuliers de la matrice de focused reflection ^ # in the basic frames,

[0219] ^^ correspondant aux valeurs singulières réelles et positives de la Focused reflection matrix ^# arranged in descending order: ^^ > ^^ > ⋯ > ^^

[0220] Les P premiers espaces propres associés aux valeurs singulières les higher (^ ^^ ^ ^^^ ) are associated with the static component. The last Q eigenspaces associated with the smallest singular values ​​(^^ < ^^^^) are associated with noise. The eigenspaces associated with intermediate singular values ​​(^^^^< ^^ < ^^^^) are associated with the dynamic signal of interest:

[0222]

[0223] Les seuils ^^^^ et ^^^^ peuvent être déterminés comme étant des inflection points of the distribution of singular values.

[0224]

[0225] A des fins d’allégement des notations, la composante dynamique de The reflection matrix will be denoted R and not ^^ in the following.

[0226] La figure 6 illustre l’extraction de la composante dynamique des Signals from data acquired on a sheep brain. The different representations in Figure 6 allow us to compare the evolution of the reflectivity of a point in a speckle zone of the medium over time before filtering, in image A, and that of the same point after filtering, image B. The temporal evolution of the complex reflectivity associated with the pixel designated by the white cross [A and B] is represented using a point cloud in the complex plane [C] before and after filtering the dynamic part of the signals, respectively at the periphery and the center. Image [D] is an enlargement of the central part of the complex plane, highlighting the quasi-random nature of the complex reflectivity after filtering.

[0227]

[0228] Procédé de correction des aberrations

[0229] Le procédé a pour but la correction des aberrations, ces aberrationsbeing for example due to variations in structures in the medium which induce variations in speed of sound and variations in reflectivity.

[0230] Le procédé comprend un traitement de correction comprenant des steps of:

[0231] - détermination d’un ensemble de lois de focalisation ^ à partir des responses from the environment obtained for the different realizations of speckle measured at times # ^ .

[0232] - détermination de matrices de réflexion corrigées ^′^^(^, ^, #^) du middle by application of the correction law ^ to the measured reflection matrices ^^^(^, ^, #^).

[0233] Grâce à ces dispositions, le procédé permet avantageusement de probe locally the medium and correct the focused reflection matrix with respect to aberrations, in particular by determining a correction law for each point of the medium and, optionally, for each frequency f of the ultrasonic wave.

[0234] En outre, le procédé peut comprendre une étape de :

[0235] - détermination d’une intensité ^^ d’un point d’image échographique corresponding to a point of spatial position r = (x, z) from the diagonals of the corrected reflection matrices ^′^^(^, ^, #^)

[0236] - détermination d’une intensité d’un point d’une image power Doppler by summing the intensity of the ultrasound image at the same point over all or part of the frames #^

[0237] - détermination d’une image Doppler colorée permettant d’accéder àthe directionality of movement in tissues by performing a Fourier transform along the temporal dimension #^ of the complex amplitude of the ultrasound image as described in the article:

[0238] E. Mace, G. Montaldo, B. -F. Osmanski, I. Cohen, M. Fink and M. Tanter, "Functional ultrasound imaging of the brain: theory and basics principles," in IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, vol. 60, no. 3, pp. 492-506, March 2013,

[0239]

[0240]

[0241] Détermination de la loi de focalisation

[0242] L’étape de détermination d’une loi de correction ^, comprend alors sub-steps performed at each depth z and each frequency f, of:

[0243] - détermination d’un ensemble de matrices de réflexion duale Rcx(z,f, #^) by forward projection of the focused reflection matrix Rxx(z,f,#^) towards a correction basis (c),

[0244] - calcul de la loi de correction ^(x, z) à partir de la matrice de réflexion dual Rcx(z,f, #^), said correction law being determined on the basis of correction (c), ^ = [^(^, ^, ^)], so that said correction law ^(x, z) is a spatio-frequency correction law,

[0245] - détermination d’une matrice de réflexion duale corrigée ^ ^ ^^around the reference point and whose coefficients are written according to ^ ^ ^^ (^, ^, #^) = [ ^^ ^ (^, ^, ^, ^, #^)], determined by performing the term-by-term product between the dual reflection matrix Rcx(z, f, #^) and the phase conjugate of the correction law ^(x, z), that is, by:

[0246] ^ ^ ^^ = ^^^ ∘ ^ ∗

[0247] où

[0248] le symbole * désigne une opération de conjugaison de phase

[0249] le symbole ∘ est le produit d’Hadamard, tel que :

[0250] ^^^ ^ (^, ^, ^, ^, #^) = ^^^(^, ^, ^, ^, #^)^∗(^, ^, ^, ^).

[0251] L’étape finale du procédé comprend la détermination d’un ensemble of corrected focused reflection matrices ^ ^ ^^ (^, #^) by back projection of corrected dual reflection matrices ^ ^ ^^ (z,f, #^) towards the focused basis (x).

[0252] Grâce à ces dispositions, le procédé permet avantageusement de probe locally the medium and correct the focused reflection matrix with respect to aberrations, in particular by determining a focusing law for each point of the medium, and for each frequency f of the ultrasonic wave.

[0253] Cette correction est effectuée dans une base de correction c adaptéeto correct the aberrations. The correction basis is an input correction basis or an output correction basis.

[0254] Des exemples de base de correction sont :

[0255] - une base des ondes planes ou base de Fourier spatiale,

[0256] - une base des transducteurs u,

[0257] - une base correspondant au lieu supposé des aberrateurs dans le middle, that is to say for example a plane between the plane of the transducers (transducer base u) and the focal plane (focal base x),

[0258] - une base correspondant à un plan déterminé par optimisation, par example by a correlation matrix whose first eigenvalue is maximal.

[0259]

[0260] Matrice de réflexion duale Rcx(z,f, #^)

[0261] Selon un mode de réalisation du procédé de la présente divulgation, The forward projection allows us to determine a dual reflection matrix Rc(z,f, #^). This forward projection can be performed by:

[0262] un produit matriciel entre une matrice de passage P et la matrice de focused reflection Rxx(z, f, #^), that is:

[0263] ^^^(^, ^, #^) = ^(^, ^) × ^^^(^, ^, #^)

[0264] où : ^(^, ^) = [^(c, x, ^, ^)] est la matrice de passage à chaque frequency f between the focused basis (x) at depth z and the correction basis (c).

[0265]

[0266] La matrice de passage P dépend de la base de correction c utilisée.

[0267]

[0268] Dans le cas d’une base de correction correspondant à une base des plane waves (c=k), the transition matrix P is the Fourier transform operator.

[0269] Dans le cas d’un réseau 10 de transducteurs 11 de type linéaire pourTo generate a two-dimensional image, the coefficients of this transition matrix P can be written as follows:

[0270] ^(^^ , ^, ^, ^) = ^(^^ , ^) = ^^^(−^^^^)

[0271] où ^^, la composante transverse du vecteur d’onde k associé à chaque plane wave.

[0272] Dans le cas d’un réseau 10 de transducteurs 11 de type matriciel pour To generate a three-dimensional image, the coefficients of this transition matrix P can be written as:

[0275] ^|| est la composante transverse du vecteur d’onde k associé à chaque plane wave, and

[0276] ^ = (^, ^), le vecteur position transverse.

[0277]

[0278] Dans le cas d’une base de correction correspondant à une base des transducers (c=u), the coefficients of the transition matrix P correspond to the normal derivative of the Green's function linking each focal point of spatial position (x, z) and each transducer of spatial position (u, 0).

[0279] Dans le cas d’un réseau de transducteurs de type linéaire pour générer In a two-dimensional image, the coefficients of the change-of-basis matrix P can be written as follows:

[0280] ^(^, ^, ^, ^) = ∇^^^^(^, ^, ^)

[0281] où ∇^ est le gradient projeté suivant la direction de profondeur z, et

[0282] ^^^(^, ^) est la fonction de Green 2D qui relie chaque transducteur ^ = (^, 0) at each point ^ of the midpoint M, with:

[0284] où ^^ = 2^^ / ^^ est le nombre d’onde,

[0285] is the Hankel function of 1 er order whose asymptotic expression is the following: ℋ^(2^^|^ − ^| / ^^) =

[0286] Dans le cas d’un réseau de transducteurs de type matriciel pour To generate a three-dimensional image, the coefficients of this transition matrix P can be written as:

[0287] ^(^, ^, ^, ^) = ∇^^^^(^, ^, ^)

[0288] où ^^^(^, ^) est la fonction de Green 2D qui relie chaque transducteur ^ = (^^ , ^^ , 0) at each point ^ = (^, ^) of the midpoint M, with:

[0290] Les coefficients de la matrice de passage P s’écrivent donc dans ce in the following way:

[0291]

[0292]

[0293] Matrice de corrélation

[0294] Selon un premier mode de réalisation, cette étape de calcul comprend :

[0295] - la construction d’une matrice de corrélation C(x,z) à partir des dual reflection matrix Rcx(z,f, , #^) for each point (x,z) of the field of vision

[0296] - l’analyse de cette matrice de corrélation C(x,z) pour déterminer la spatio-frequency focusing law ^(x,z) for each point of the field of vision.

[0297]

[0298] Selon une première variante, la matrice de corrélation C(x,z) est determined in the correction basis c and in the frequency domain, by the following calculation of the elements of the correlation matrix C = Ccc:

[0299] ^({^, ^}, {^’, ^’}, ^, ^) = ∑#^ ^(^, ^, ^, ^, #^) ^∗(^, ^^, ^, ^^ , #^)

[0300] Où * est l’opérateur de conjugaison.

[0301] Cette opération permet de corréler les champs réfléchis dans la base correction for each virtual source in (x,z). This correlation is averaged over the different frames. ^(i.e., different realizations of speckle) in order to overcome the random reflectivity of the medium and thus synthesize a coherent guide star from the different realizations # ^ speckle.

[0302]

[0303] Selon une deuxième variante, la matrice de corrélation C est determined in the base of frames # ^ , by the following calculation of the elements of the correction matrix C = ^ ## :

[0305] * est l’opérateur de conjugaison

[0306]

[0307] Estimation de la loi de focalisation

[0308] Selon une première variante, l’analyse de la matrice de corrélation C(x,z) is performed by an eigenvalue decomposition of the decorrelation matrix C(x,z), and the spatio-frequency correction law ^(x,z) is the first eigenvector ^ ^ of the correlation matrix C(x,z) in the correction basis (c), that is, C = Ccc.

[0309] La matrice de corrélation étant hermitienne (^ = ^^), ses valeurs their properties are real and positive.

[0310] La matrice de corrélation Ccc(x,z) peut ainsi s’écrire :

[0312] ou en termes de coefficients matriciels :

[0313] ^({^, ^}, {^’, ^’}, ^, ^) = ∑^ ^^^^(^, ^)^^∗(^′, ^′)

[0314] avec ^^ correspondant aux vecteurs propres de la matrice de correlation C

[0315] ^^ correspondant aux valeurs propres réelles et positives de la Correlation matrix Ccc(x,z) arranged in descending order: > ^^ > ⋯ > ^^

[0316] On a alors la loi de correction spatio-fréquentielle ^(x, z) qui est égale to the first eigenvector, i.e., ^(x, z) = ^^; or to its normalized version, ^(x, z) = exp(^arg{^^}), i.e., a spatio-frequency correction law whose coefficients have unit amplitude but whose phase is equal to that of ^ ^ (The symbol arg{^} denotes the phase of the vector X; or to an inverse filter type correction, ^(x, z) = exp(^arg{^^}) / |^^|. 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 accurate estimator of the reflectivity in fine.

[0317]

[0318] Selon une deuxième variante, l’analyse de la matrice de corrélationCcc(x,z) is performed by a singular value decomposition of the dual reflection matrix rearranged as follows:

[0319] ^^#(x, z) = [^({^, ^}, #^ , x, z)]

[0320] La décomposition en valeurs propres de la matrice de corrélation Ccc(x,z) performed in the first variant is indeed equivalent to the singular value decomposition (SVD) of each dual reflection matrix ^ ^#

[0321] La décomposition en valeurs singulières s’applique sur des matrices rectangular in shape, and applied to the dual reflection matrix ^ ^# at each point (x,z), it can be written as follows:

[0323] ou en termes de coefficients matriciels :

[0325] avec ^^ = ^^^(^, ^)^ correspondant aux vecteurs singuliers de la dual reflection matrix ^^#(^, ^) in the correction basis, or equivalently, to the eigenvectors of the matrix Ccc as defined in the first variant.

[0326] ^^ = ^^^(#^)^ correspondant aux vecteurs singuliers de la matrice de dual reflection ^ ^# in the basic frames,

[0327]

[0328] ^^ correspondant aux valeurs singulières de la matrice de réflexion dual ^ ^# which are, by definition, equal to the square root of the eigenvalues ​​of the correlation matrix C as defined in the first variant:^^ = ^ ^ ^ .

[0329]

[0330] On a alors la loi de correction spatio-fréquentielle ^(x, z) qui est égale to the first singular vector of the dual distortion matrix ^^#, i.e. ^(^, ^) =^^ ; or to its normalized version, ^(^, ^) = exp(^arg{^^}), i.e. a spatial-frequency correction law whose coefficients are of unit amplitude but whose phase is equal to that of ^^ (the symbol arg{^} denotes the phase of the vector X); or to an inverse filter type correction, ^(^, ^) = exp(^arg{^^}) / |^^| .

[0331] L’intérêt de la décomposition en valeurs singulières de la matrice de dual reflection^ ^# Compared to an eigenvalue decomposition of the correlation matrix Ccc, the speed of computation of numerical algorithms for singular value decomposition is

[0332]

[0333] Cette recherche de la loi de correction spatio-fréquentielle ^(x, z) est also equivalent to solving the following equation:

[0334] a^(x, z, ) = ^^^(x, z) × ^(x, z)

[0335] où × est le produit matriciel et a est une constante

[0336] de manière itérative par l’expression suivante, qui correspond à un calculation by iterative time reversal:

[0337] ^^^^(x, z) = ^^^(x, z) × ^^(x, z),

[0338] avec ^^ un front d’onde arbitraire, par exemple ^^ = [1 ⋯ 1] ^

[0339]

[0340] Alors, la loi de correction spatio-fréquentielle ^(x, z) est obtenue par :

[0341] ^(x, z) = ^ ^^ → ^ ^^^ (x, z),

[0342] ou sa version normalisée :

[0344] ou sa version filtre inverse :

[0346] Pour ^ → ∞, l’algorithme de retournement temporel itératif converge towards the same first eigenvector ^ ^ of the matrix ^ ^^ 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.

[0347]

[0348] Selon une troisième variante, l’analyse de la matrice de corrélation Ccc is performed by solving the following equation:

[0349] ^(x, z) = exp(^ arg{^^^(x, z) × ^(x, z)})

[0350] de manière itérative par l’expression suivante, qui correspond à un calculation by iterative phase reversal:

[0351] ^^^^(x, z) = exp(^ arg{^^^(x, z) × ^^(x, z)})

[0352] où × est le produit matriciel,

[0353] avec : ^^ un front d’onde arbitraire, par exemple ^^ = [1 ⋯ 1] ^ .

[0354] Alors, la loi de correction spatio-fréquentielle ^(x, z) est obtenue par :

[0358] L’intérêt d’un algorithme de retournement de phase itératif par Compared to previous alternatives, it is a more reliable estimator of the phase of the correction law ^(x, z) and therefore ultimately provides better compensation for phase distortions induced by the aberrator.

[0359]

[0360] Selon une quatrième variante, l’analyse de la matrice de corrélation C## is performed by solving the following equation:

[0361] ^(x, z) = exp(^ arg{^##(x, z) × ^(x, z)})

[0362] où × est le produit matriciel,

[0363] de manière itérative par l’expression suivante :

[0364] ^^^^(x, z) = exp(^ arg{^##(x, z) × ^^(x, z)})

[0365] où × est le produit matriciel,

[0366] avec ^^ un front d’onde arbitraire, par exemple ^^ = [1 ⋯ 1] ^

[0367] ce qui permet d’obtenir le vecteur W(x, z) suivant :

[0368] ^(x, z) = ^ ^^ → ^ ^ ^^(x, z)

[0369] Ce vecteur ^(x, z) = [^(#^ , ^, ^)] défini dans la base des frames contains the phase of each incoherent guide star synthesized by focusing at point (x,z) for each frame # ^ .

[0370] Le conjugué en phase de ce vecteur ^(x, z) peut alors être exploité to rephase each incoherent virtual star so that they can be recombined coherently and thus obtain an estimator of the spatio-frequency correction law ^(x, z) unbiased by the random reflectivity of the medium. Mathematically, this operation is written as follows:

[0372] L’intérêt de cette approche par rapport à une SVD de la matricedistortion Rc# (second variant) or the iterative phase reversal algorithm (third variant) is to converge towards a correction law unbiased by the larger amplitude of the ultrasonic signal on a certain frame of the reflection matrix (large amplitude caused by the passage of a bright scatterer such as a bubble or an experimental problem).

[0373] La figure 7 illustre un exemple d’extraction des lois d'aberrations parIterative phase reversal in the dynamic speckle. [A] The aberrated focused reflection matrix ^^^(^, #) [B] is projected at the output into a correction basis (c), here illustrated by the transducer basis (u). ^ = (^, ^) is the transverse position vector. Each frame of the dual matrix ^^^(^, #) constitutes a dynamic realization of the disorder. [C] This matrix is ​​rearranged along dimensions (c) and (#) to construct a matrix ^^#(^^^ , ^) at each point (^^^, ^) and calculate [D] the associated correlation matrix ^^^(^^^, ^). An analysis by RPI (iterative phase reversal) of the matrix ^^^(^^^, ^) allows us to extract from these wavefronts an estimate ^(^^^, ^) of the aberration laws at each point of the field of view. The phase conjugate of the aberration laws ^*(^^^, ^) is used as an adaptive focusing law in reception for each frame allowing to recover a corrected output focal spot.Although illustrated here in basis (c) = (u), the reasoning can be extended to another correction basis, in particular that of plane waves (k). This approach can be described by constructing a distortion matrix or represented schematically as in Figure 7 using the dual reflection matrix. The two approaches are equivalent: in the first case, an aberration law is extracted, while in the second, a defocusing law (aberration and geometric curvature) is extracted.

[0374] La figure 8 illustres des exemples de lois d'aberrations transversesLocal aberrations extracted from the dynamic speckle. [A] Several regions of the field of view chosen for illustrative purposes and their [B] corresponding transverse aberration laws. The association is made in pairs by color code. The outline of each transparent area on image [A] defines the area on which the law is estimated, while the opaque area at the center of image [A] delimits the area on which this law will be applied during correction. These areas also have an extension along the y-axis, which is not shown here. The Strehl ratio "S" associated with each of the aberration laws on images [B] is indicated.

[0375]

[0376] Correction des aberrations dans les matrices de réflexion

[0377] A partir de la loi de focalisation obtenue, on va compenser en post- aberrations are addressed by recalculating dual and focused reflection matrices from the estimated focusing law.

[0378] Matrice de réflexion duale corrigée

[0379] La matrice de réflexion duale corrigée ^^^^ (^, ^, #^) = [^′(^, ^, ^, ^, #^)] is determined by performing the term-by-term product between the dual reflection matrix Rc(z, f) and the phase conjugate of the focusing law ^, that is, by:

[0380] ^^ ^^ = ^^^ ∘ ^∗

[0381] où l’exposant * représente l’opération de conjugaison de phase

[0382] le symbole ∘ est le produit d’Hadamard, c’est-à-dire le produit matrix term by term of matrix coefficients, such that

[0383] ^′(^, ^, ^, ^, , #^) = ^(^, ^, ^, ^, #^)^∗(^, ^, ^, ^).

[0384]

[0385] Matrice de réflexion focalisée corrigée

[0386]

[0387] Une matrice de réflexion focalisée corrigée ^ ^ ^^ (^, ^) is then determined by back projection of the corrected dual reflection matrix ^ ^ ^^ (z,f) towards the focused basis (x).

[0388] La projection retour est effectuée par un produit matriciel entre la the transition matrix P defined above and the focused reflection matrix ^ ^ ^^ (z, f), that is to say:

[0389] ^ ^ ^^ (^, ^, #^) = ^^(^, ^) × ^^^^ (^, ^, #^)

[0390] Où l’exposant † désigne l’opération matricielle de trans-conjugaison.

[0391]

[0392] Itérations du traitement de correction

[0393] Selon le mode de réalisation du procédé, les étapes du traitement de correction, that is to say the steps of:

[0394] - de détermination de la loi de correction ^(x, z) ladite étapepossibly including the steps of determining the dual reflection matrix Rcx(z, f, #^), S160 of calculating the correction law ^(x, z) and determining the corrected dual reflection matrix ^ ^ ^^ (^, ^, #^), and

[0395] - de détermination de la matrice de réflexion focalisée corrigée

[0396] sont itérées plusieurs fois (deux fois ou plus de deux fois).

[0397] A chaque itération, la projection aller utilise la matrice de réflexion focused corrected ^ ^^^ (^, #^) obtained during the return projection of the previous iteration instead of the focused reflection matrix Rxx(z, #^).

[0398] Ainsi, à chaque itération, la loi de correction de spatio-fréquentielle is improved to take into account one or more anomalies in the environment more and more effectively.

[0399]

[0400] Selon une première variante de ce processus itératif, à chaque iteration of the step of determining the dual reflection matrix Rcx(z, we use a different correction basis c, for example to correct different aberrations located in different places in the medium.

[0401] Par exemple, le milieu peut être discrétisé ou modélisé par uneThe layers are a succession along the depth direction 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 in the medium are applied during the iterations.

[0402]

[0403] Selon une deuxième variante de ce processus itératif, à chaque During the iteration of the dual reflection matrix determination step, 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,f, #^) towards the correction basis is performed as follows:

[0404] ^^^(^, ^, #^) = ^(^, ^) × ^⊺ ^^ (^, ^, #^)

[0405] où le symbole ⊺ désigne l’opération matricielle de transposition.

[0406] Dans la succession des itérations, on peut alterner entre l’utilisation of an input correction basis and an output correction basis. Thus, the spatio-temporal correction law ^ is improved at each iteration, and the correction of aberrations is improved.

[0407]

[0408] Variantes du processus de correction des aberrations

[0409] Suivant les conditions expérimentales, le processus d’aberrationscan be simplified or made more complex according to several variants described below.

[0410]

[0411] Compensation spatiale des aberrations

[0412] Si le milieu en amont du plan focal n’induit pas de dispersion Given the temporal nature of the echoes (absence of reverberations, negligible multiple scattering), there is not necessarily any benefit in independently considering the frequency components of the confocal signals. In this case, one can consider the broadband focused reflection matrix,

[0414] comme point de départ du processus de correction des aberrations. The projection of the reflection matrix onto the correction basis is then done by considering the propagator at the center frequency. Everything else of the The process is identical to what has been described above. Only the frequency dependence of the different quantities expressed is no longer relevant.

[0415]

[0416] Compensation temporelle des aberrations

[0417] Si, au contraire, le milieu induit une dispersion principalement Given the temporal nature of the ultrasonic echoes and the minimal spatial aberrations, there is no point in considering the focused reflection matrix, only its confocal signal:

[0418] ^(^, ^, ^, #^) = ^(^, ^, ^, ^, #^)

[0419] La matrice de corrélation à considérer dans ce cas pour l’obtention de The correction law, ^(x, z) = [Φ(f, x, z)], is given by:

[0421]

[0422] Exploitation de l’effet mémoire spatial

[0423] Le nombre de frames peut être insuffisant pour une estimation correct for the focusing law. In this case, instead of the dual reflection matrix, we can consider the associated distortion matrix, ^^^(^, ^, #^) =[ ^^^(^, ^, ^, ^, #^)], and average the correlation matrix not only over the different frames but also over adjacent pixels resembling

[0426] et ^^^^ = ^^^^^(^, ^, ^, ^)^, une matrice de référence d’un milieu modèle in which the speed of sound is c0, the expected speed of sound for the medium, and in which a plane reflector is positioned at depth z. Averaging the correlation matrix over several speckle grains can accelerate the convergence of the correlation matrix to the associated covariance matrix. This results in a more accurate estimation towards the focusing law.

[0427]

[0428] Construction d’images du milieu

[0429] Image confocale dynamique

[0430] Selon un mode de réalisation du procédé de construction ultrasonoreIn addition to this disclosure, the process includes a further step of:

[0431] - détermination du signal confocal dynamique Sc(x,z, #^) d’un point spatial position (x, z), from the diagonal coefficients of the corrected focused reflection matrix ^ ^ ^^ (z,# ^ ) integrated over the bandwidth of the ultrasonic signals, that is, by combining the confocal responses of the point at several frequencies f. For example, we thus have the following calculation:

[0432] ^^(^, ^, #^) = ∑^ ^^^ ^ (^, ^, ^, ^, #^)

[0433] L’intensité de cette quantité,

[0434] ^^(^, ^, #^) = |^^(^, ^, #^)| ^ ,

[0435] déterminée en une pluralité de points (x,z) permet de construire une corrected confocal image of the medium, 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.

[0436] Sur la figure 9 est illustrée une comparaison des images confocalesDynamics before and after correction. Several examples of original confocal images (left) and their corrected equivalents (right) are shown for different frames, with or without microbubbles [AC] and without [D]. The benefits of the method are particularly noticeable in the image of the microbubbles (bright dots), which appear better resolved and more contrasted after correction.

[0437]

[0438] Image Doppler de puissance (« Power Doppler » en English)

[0439] Selon un mode de réalisation du procédé de construction ultrasonore In addition to this disclosure, the process includes a further step of:

[0440] - détermination d’une image Power Doppler IP(x,z) d’un point de spatial position (x, z), from the sum over the different frames of the dynamic confocal intensity ^^(^, ^, #^) measured at each point (x,z). For example, we thus have the following calculation:

[0442] L’intensité précédente déterminée en une pluralité de points permet to construct a corrected power Doppler image of the medium, which quantifies tissue movement during the acquisition sequence.

[0443] La figure 10 illustre deux images de type Doppler de puissance. Ondistinguishes the contrast gain provided by the correction. [A] is a PWD display of the 400 frames of the application block before and [B] after correction.

[0444]

[0445] Image Doppler Directionnelle

[0446] Selon un mode de réalisation du procédé de construction ultrasonore In addition to this disclosure, the process includes a further step of:

[0447] - détermination d’une image Doppler directionnelle ID(x,z) d’un point of spatial position ultrasound image (x, z), from the Fourier transform of the complex confocal signal ^^(^, ^, #) along the temporal dimension# ^ frames:

[0449] Où la fréquence ^ est la variable conjuguée au temps d’acquisition #.

[0450] L’image power doppler initiale peut ainsi être séparée en une positive component and a negative component of the displacement:

[0453]

[0454] Ces deux images peuvent ensuite être combinées pour former une Colored Doppler image ID(x,z) where blue encodes the negative component and road the positive component of tissue movement at each point (x,z).

[0455]

[0456] Carte de la dynamique locale

[0457] Selon un mode de réalisation du procédé de construction ultrasonore In addition to this disclosure, the process includes a further step of:

[0458] - détermination d’une carte de dynamique locale d’un point d’imagespatial position ultrasound (x, z), from the average frequency^D(x,z) of the Fourier transform ^^(^, ^, ^) of the complex confocal signal: This average frequency is related to the average velocity of the scatterers at each point in the medium. Figure 11 shows these local dynamics maps, allowing a comparison before [A] and after [B] correction of transverse aberrations. Aberration correction allows for a more precise estimation of the scatterer movement velocity within the medium.

[0460]

[0461] Image confocale statique

[0462] Au-delà de la composante dynamique des données acquises, les lois The focusing values ​​obtained can also be used to correct the raw reflection matrix, i.e. the reflection matrix considered before filtering the static component of the data.

[0463]

[0464] Le domaine d'application préférentiel est l'imagerie ultrasonore dansThe invention, in particular its Doppler and ULM (Ultrasound Localization Microscopy) modes, can be used to image the human brain through a skull, as well as the vascular network of the liver for medical imaging. It can also be used to image dynamic processes using non-destructive testing. Furthermore, the invention has potential applications in various fields of wave physics, such as optical coherence tomography for light and seismology for seismic waves.

[0465]

[0466] Bien entendu, l’invention n’est pas limitée aux exemples qui viennent to be described. Numerous modifications can be made to these examples without departing from the scope of the present invention as described.

Claims

CLAIMS 1. A method for constructing an ultrasonic confocal image of a dynamic medium, the method comprising the following steps: a) acquiring, by means of a transducer array, a series of canonical reflection matrices Rui(t, #m)=[R(uout,iin,t,#m)] at different times, each canonical reflection matrix being 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 in the medium; t denoting the echo time and #m denoting the m ièmecanonical reflection matrix; b) determination of a focused reflection matrix Rxx(z, #m) for each canonical reflection matrix by input-output focusing for any point in at least one region of the medium, the coefficients of this focused reflection matrix are obtained by calculating an acoustic pressure field between all points in the region with lateral positions xin and xout, located at an expected depth z for an assumed speed of sound c0; c) determination of a dynamic component for each coefficient of each focused reflection matrix so as to constitute dynamic focused reflection matrices ^ ^ ^^ (^, #^)d) determination of a correction law ^(x, z) for each point x and depth z of the medium from the dynamic focused reflection matrices,e) determination of corrected focused reflection matrices ^ ^^^ (^, #^) by applying the correction law ^(x, z) at every point in the medium, f) determination of a dynamic confocal signal Sc(x,z, #^) of every spatial deposition point (x, z) from the diagonal coefficients of the corrected focused reflection matrix ^ ^ ^^ (z, #^),g) construction of an image from dynamic confocal signals.

2. A method according to claim 1, characterized in that the step of acquiring a series of canonical reflection matrices Rui(t, #m) comprises the emission of an ultrasonic pulse from each transducer of the array whose position is located by the coordinate uin; this pulse gives rise to a diverging cylindrical or spherical incident wave which is reflected by scatterers in 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,#m) expressed in the basis of the transducers being composed of a set of impulse responses R(uout,uin,t,#m) between transducers. 3.A method according to claim 1, characterized in that the step of acquiring a series of canonical reflection matrices Rui(t, #m) comprises insonifying the medium with a series of plane waves with a delay τ' applied to each signal at emission to form a wavefront inclined at an angle θin with respect to the transducer array. A backscattered field by the medium, R(uout, θin, t, #m), is measured by all transducers at position uout for each incident plane wave θin. The set of responses forms a canonical reflection matrix Ruθ(t, #m) = [R(uout, θin, t, #m)].

4. A method according to claim 1, characterized in that the step of acquiring a series of canonical reflection matrices Rui(t, #m) comprises insonifying the medium with a series of diverging waves. 5.A method according to any one of the preceding claims, characterized in that the step of determining the focused reflection matrix Rxx(z,#m) comprises: - an input focusing process from each canonical reflection matrix Rui(t,#m) which uses a forward time of flight of the waves between the ultrasonic wave emission base i and a virtual input transducer TVin and which creates a so-called input focal spot around a first position point P1. spatial deposition rin=(xin,z), said input focal spot corresponding to the virtual input transducer TVin, and an output focusing process from the canonical reflection matrix Rui(t,#m) which uses a return time of flight of the waves between a virtual output transducer TVout and the receiving base transducers u and which creates a focal spot called the output spot around a second point P2 spatial deposition rout=(xout,z), said output focal spot corresponding to the virtual output transducer TVout.

6. Method according to claim 5, characterized in that xout is located at a distance from xin less than or equal to a maximum distance Δxmax which is a function of a number of ultrasonic waves generated during the acquisition of the reflection matrix.

7. Method according to any one of the preceding claims, characterized in that the focused reflection matrix is ​​determined in the time domain or in the frequency domain. 8.A method according to any one of the preceding claims, characterized in that the dynamic component is determined by subtracting from each coefficient of each focused reflection matrix a moving average over N focused reflection matrices. A method according to any one of claims 1 to 7, characterized in that the dynamic component is determined by applying a high-pass or band-pass filter along a dimension of the numbers #. ^ reflection matrices.

10. A method according to any one of claims 1 to 7, characterized in that the dynamic component is determined by performing a singular value decomposition of the focused reflection matrices rearranged in a two-dimensional matrix, one dimension of which is that of numbers# ^reflection matrices.

11. A method according to any one of the preceding claims, characterized in that the step of determining a correction law comprises, for each dynamic focused reflection matrix ^^^^ (^, #^) , the following steps: - determination of a dual reflection matrix Rcx(z, #^) by forward or backward projection of the dynamic focused reflection matrix ^ ^ ^^ (^, #^) to a correction basis (c), - calculation of the correction law ^(x, z) from the dual reflection matrix Rcx(z, #^), said correction law being a correction law, ^(^, ^) = [^(^, ^)] on the correction basis (c), - determination of the corrected focused reflection matrices ^ ^^^ (^, #^) by projection back of the corrected dual reflection matrices ^ ^ ^^ (z, #^) towards the focused basis (x).

12. Method according to claim 11, characterized in that the coefficients ^ ^ ^^ (^, #^) = ^, #^)] of the corrected dual reflection matrix ^ ^ ^^ are determined by performing a term-by-term product between the dual reflection matrix Rcx(z, #^) and the phase conjugate of the correction law ^(x, z), i.e.:^ ^ ^^ = ^^^ ∘ ^∗ where the symbol * denotes a phase conjugation operation, the symbol ∘ is the Hadamard product, such that: ^ ^^^ (^, ^, ^, #^) = ^^^(^, ^, ^, #^)^∗(^, ^, ^).

13. A method according to claim 11 or 12, characterized in that the step of calculating the correction law ^(x, z) comprises the following steps: - construction of a correlation matrix C(x,z) from the dual reflection matrices Rcx(z, , #^) for each point (x,z) of a field of vision, - determination of the focusing law ^(x,z) for each point of the field of vision by performing one of the following operations: - eigenvalue decomposition of the correlation matrix C(x,z), the correction law ^(x,z) being the first eigenvector ^^ of the correlation matrix C(x,z) in the correction basis (c), - singular value decomposition of the dual reflection matrix rearranged as follows: ^^#(x, z) = [^(^, #^ , x, z)] the correction law ^(x, z) being equal to the first singular vector of the dual reflection matrix ^^#, ie^(^, ^) = ^^- solving the following equation: ^(x, z) = exp(^ arg{^^^(x, z) × ^(x, z)}) iteratively by the following expression, which corresponds to an iterative phase-reversal calculation: ^^^^(x, z) = exp(^ arg{^^^ × ^^(x, z)}) Where × is the matrix product, with ^^ an arbitrary wavefront, the correction law ^(x, z) being obtained by:. ^(x, z) = ^ ^^ → ^ ^^^ (x, z) - Solving the following equation: ^(x, z) = exp(^ arg{^##(x, z) × ^(x, z)}) where × is the matrix product, iteratively using the following expression: ^^^^(x, z) = exp(^ arg{^##(x, z) × ^^(x, z)}) where × is the matrix product, with ^^ an arbitrary wavefront, which allows us to obtain the following vector W(x, z): ^ (x, z) = ^ ^^ → ^ ^ ^^(x, z) the correction law ^(x, z) being obtained by:

14. A method according to claim 13, characterized in that the decorrelation matrix C(x,z) is determined in the correction basis c and in the frequency domain, by the following calculation of the elements of the decorrelation matrix C = Ccc: where * is the conjugation operator. c and c' being points of the correction basis c15. Method according to claim 13, characterized in that the correlation matrix C(x,z) is determined in the number basis # ^ , by the following calculation of the elements of the correction matrix C = ^ ## : ^(#^ , #^ , ^, ^) = ∑^ ^(^, ^, ^, #^) × ^∗(^, ^, ^, #^)* is the conjugation operator. c and c' are points of the correction basis, c#m and #l denoting the m ièmes and ièmesframes of the recorded reflection matrix sequence 16. Method according to any one of claims 11 to 15, characterized in that the step of calculating the correction law ^(x, z) is iterated at least twice with, at each iteration, the projection uses the corrected focused reflection matrix ^ ^^^ (^, #^) obtained during the back projection of the previous iteration in place of the focused reflection matrix Rxx(z,#^).

17. A method according to any one of claims 11 to 16, characterized in that the step of determining a dual reflection matrix Rcx(z, #^) is iterated at least twice with, at each iteration, the use of a different correction basis c.

18. A method according to any one of claims 11 to 16, characterized in that the step of determining a dual reflection matrix Rcx(z, #^) is iterated at least twice with, at each iteration, the use of a forward projection either towards an input correction basis or towards an output correction basis of the dynamic focused reflection matrix.

19. A method according to any one of claims 11 to 18, characterized in that the correction basis is one of the following: - a plane wave basis or spatial Fourier basis, - a transducer basis, - a basis corresponding to the assumed locus of aberrators in the medium, - a basis corresponding to a plane determined by optimization.

20. A method according to any one of claims 11 to 19, characterized in that the step of determining a dual reflection matrix Rcx(z, z) is carried out by forward projection of the dynamic focused reflection matrix z. ^^^ (^, #^) towards the correction basis (c) considering a model propagator describing the propagation of waves from the focused basis (x) to the correction basis (c).

21. A method according to any one of the preceding claims, characterized in that the step of determining corrected focused reflection matrices is iterated at least twice, with at each iteration, the projection uses the corrected focused reflection matrix ^ ^ ^^ (^, #^) obtained during the return projection of the previous iteration in place of the focused reflection matrix Rxx(z,# ^22. A method according to any one of the preceding claims, characterized in that step g) of constructing an image from the dynamic confocal signals comprises a step of: - determining an intensity of each dynamic confocal signal to construct a confocal image of the medium, or - determining an intensity of each dynamic confocal signal to construct a power Doppler image by summing, for each point of spatial position (x, z), the intensities of several confocal signals, or - determining a Fourier transform of the dynamic confocal signal^^(^, ^, #) along the time dimension #^: where the frequency ^ is the variable conjugate to the acquisition time #to construct a directional Doppler image of the medium,- determination of the local dynamics for each ultrasound image point of spatial position (x, z), by measuring the average frequency^D(x,z) of the Fourier transform ^^(^, ^, ^) of the complex confocal signal: to construct a map of the axial velocity of the scatterers at each point of the image.

23. A method according to any one of the preceding claims, characterized in that the focused reflection matrix Rxx(z,#m) depends on a frequency f of the ultrasonic signals, the correction law being determined as a function of this frequency f and the coordinates of the correction plane.

24. A method according to any one of the preceding claims, characterized in that the focused reflection matrix Rxx(z,#m) is integrated over the entire bandwidth (considered only at the ballistic time), the correction law being determined solely as a function of the coordinates of the correction plane (c).

25. A method according to claim 13 and any one of claims 14 to 23, characterized in that the correlation matrix for obtaining the correction law, ^(x, z) = [Φ(f, x, z)], is given by: f and f' being frequencies in the bandwidth of the ultrasonic signal, the correction base being directly named here (f), i.e. ^(^, ^, ^, #^) being the confocal signal of the dynamic focused reflection matrix ^^^^ (^, #^).

26. Method according to claim 11 or 12, characterized in that the step of calculating the correction law ^(x, z) can be carried out: - by defining a correlation matrix for obtaining the correction law, ^(x, z) = [Φ(f, x, z)], by: - and by averaging the correlation matrix over the numbers #m but also over adjacent pixels belonging to the same isoplanetary patch f and f' denote a frequency of the confocal signal in the bandwidth of the probe. xp is the transverse coordinate of the central point of the isoplanetism patch for which we seek to estimate the aberration law. zp is the axial coordinate of the central point of the isoplanetism patch for which we seek to estimate the aberration law, where is an isoplanetism patch centered on the point .

27. Ultrasonic construction system for a confocal image of a dynamic 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; 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 26.

28. A computer program comprising instructions which, when executed by the computing unit of the system according to claim 27, cause the system to carry out the steps of the process according to any one of claims 1 to 26.

29. A computer-readable medium comprising instructions which, when executed by the computing unit of the system according to claim 27, cause the system to carry out the steps of the process according to any one of claims 1 to 26.

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