Method for achieving high-resolution probing by means of scattered waves

Abstract

The invention relates to a method for constructing ultrasonically a confocal image of an object contained in a medium, the method comprising the following steps: a) acquiring a canonical reflection matrix Rui(t) by insonifying the object via a scattering screen present in the medium; b) determining a focused reflection matrix R' ξξ (ω) by projecting the canonical reflection matrix into a spatio-frequential basis ξ: (I); c) determining a corrected reflection matrix R'' ξξ (ω); d) determining a reflection matrix R xx (zM) associated with the object by projecting the corrected reflection matrix R'' ξξ (ω) into a plane x of the object, e) constructing an image from the object reflection matrix R xx (zM). The spatio-frequential basis ξ ensures an independence between the spatial and sequential data and makes it possible to demonstrate a chromato-angular memory effect associated with the field reflected by the object. The scattering screen makes it possible to increase the base resolution of the acquisition probe.

Description

DESCRIPTION TITLE: HIGH-RESOLUTION PROBING METHOD USING BROADCAST WAVES. Technical field

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

[0002] The invention is advantageously applicable to the field of medical imaging, but can be applied to any field of ultrasound imaging, whether in air or via a coupling fluid. 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] The lateral resolution of an ultrasound image is limited by several phenomena. Firstly, it is limited by the size of the probe via the phenomenon of diffraction. The resolution is indeed dictated by the angle at which the point to be imaged sees the probe, such that θ = θ / (2 sin θ) ≈ θ / θ, with θ ^ the distance between the probe and the point to be imaged.

[0005] Furthermore, due to inhomogeneities in the speed of sound between different tissues in the human body, ultrasound images can also suffer from both transverse and axial aberrations that degrade their contrast and impair their resolution. Scattering events between the probe and the target point also induce multi-diffusion noise in the image, which limits its contrast.

[0006] To overcome these problems (aberration and scattering), a matrix approach to ultrasound imaging has been developed in recent years. It relies on the acquisition of the reflection matrix and consists of various post-processing algorithms to determine the laws of focusing to apply to overcome aberrations and obtain an image whose resolution is only limited by diffraction.

[0007] We are familiar with the document by Bureau, F., Robin, J., Le Ber, A. et al., “Three-dimensional Ultrasound Matrix Imaging.” Nat Commun 14, 6793 (2023), which describes a method for compensating aberrations using the concept of a distortion matrix in ultrasound imaging. This technique, based on a time-windowed reflection matrix, does not allow for a different correction law at each frequency and can therefore only correct low-order aberrations.

[0008] We are familiar with the document by Kwon, Y., Hong, JH, Kang, S. et al., “Computational conjugate adaptive optics microscopy for longitudinal through-skull imaging of cortical myelin.” Nat Commun 14, 105 (2023), which describes a method for compensating aberrations using the CLASS algorithm in the plane of an aberrant screen. CLASS stands for “Closed-Loop Accumulation of Single Scattering.” As with the previous method, this technique is also based on a time-windowed reflection matrix and does not allow access to a different correction law at each frequency. Therefore, it can only correct low-order aberrations.

[0009] We are familiar with the document YR Lee, et al., “Exploiting volumetric wavecorrelation for enhanced depth imaging in scattering medium.” Nat Commun 14, 1878 (2023), describing a CLASS matrix imaging algorithm in the frequency domain. However, this algorithm operates from the plane wave basis and therefore cannot correct aberrations induced by a scattering screen.

[0010] Par ailleurs, dans ces documents, les algorithmes développés ne do not allow the diffusion process to be exploited to enhance the resolution of the medium. However, it has been shown, through transmission experiments [A. Derode, P. Roux, and M. Fink, “Robust Acoustic Time Reversal with High-Order Multiple Scattering”, Phys. Rev. Lett. 75, 4206, 1995], that any diffusing medium could be transformed into a lens if the laws of focusing through the latter. In transmission, this process is relatively easy using methods such as time reversal or inverse filtering.

[0011] Néanmoins, en imagerie, nous n’avons pas accès à la matrice detransmission but to the reflection matrix. The object that we are trying to image is therefore hidden behind the diffusing screen.

[0012] La présente invention a pour but un nouveau procédé d’imagerie ultrasonic in which the diffusion processes induced by the diffusing screen will be compensated and, even better, exploited to improve the resolution of the ultrasound image and its contrast.

[0013] Un autre but de l’invention est de montrer comment l’association d’un A network of sensors and a diffusing screen (reflecting or transmitting) can constitute an intelligent probe with a small number of elements (which limits the cost and complexity of the associated electronics), potentially even a minimal one, while still allowing imaging of a large field of view at a resolution close to 1 / 2 without prior calibration. Description of the invention

[0014] On atteint au moins l’un des objectifs précités avec un procédé deultrasonic construction of a confocal image of an object contained in a medium, the process comprising the following steps: a) acquisition, by means of a network of transducers and a diffusing screen disposed on the path of the wave between the network of transducers and the object, of at least one canonical reflection matrix Rui(t)=[R(uout,iin,t)] defined between an ultrasonic wave emission basis i at the input and a reception basis u at the output; the coefficients of this canonical reflection matrix corresponding to the signals received by the transducers and induced by the ultrasonic waves reflected by the object via the diffusing screen; t denoting the echo time; b) determination of a focused reflection matrix ^′^^(^) by projection of the canonical reflection matrix into a space-frequency basis ^ depending on both a position vector in a plane ^ of the diffusing screen and a pulsation ^ of the ultrasonic waves, this basis being defined by: ^ = ^ ^ ^^ ^ ^ where C0 is the speed of sound in the medium, ^^ a distance between the diffusing screen and the object, c) determination of a corrected reflection matrix in the spatio-frequency basis ^ by applying a matrix imaging algorithm, d) determination of a reflection matrix associated with the object ^^^(^^) by projecting the corrected reflection matrix in a plane of the object ^ located at a distance zM from the transducer array, e) construction of an image from the object reflection matrix ^ ^^ (^ ^ ).

[0015] Dans le cadre de la présente divulgation, il sera indifféremment utilisé the term pulsation ^ or frequency f in the text and in the equations, the two parameters being proportional and well known to the person skilled in the art.

[0016] L’invention permet d’exploiter le milieu diffusant comme une lentilleIn order to obtain an image of the reflectivity of the medium of interest with a resolution much better than in free space, the angular aperture of the transducer array is virtually increased. This achieves super-resolution.

[0017] L’invention permet en outre l’utilisation de transducteurs de taille plus important and therefore more powerful in order to improve the signal-to-noise ratio.

[0018] Avec la présente invention, un objet peut être imagé via l’écran broadcasting without calibration experience.

[0019] Le procédé selon l’invention est basé sur l’acquisition et la projection of the reflection matrix in a spatio-frequency basis whose coordinate ^ = ^ ^ ^ ^ ^ ^ combines spatial coordinates ^ of the diffuser screen, ^, the pulse and^ ^ The distance between the diffusing screen and the object is the basis. This basis maximizes the input-output correlations of the field associated with the object, which can be used to estimate the transfer function of the diffusing screen. The present invention takes advantage of the chromatic-angular memory effect in reflection associated with the object.

[0020] Une fois la fonction de transfert de l’écran diffusant connue, on peutexploit the angular diversity offered by the diffusion paths induced by the screen diffuses and magnifies the angle from which the object is seen to obtain a precise image of the latter, with a resolution much better than in free space.

[0021] L’association réseau de transducteurs – écran diffusant peut être carried out in transmission, i.e. with the diffusing screen placed between the transducer array and the object to be imaged (Figure 1), or in reflection, i.e. with the transducer array and the object placed on the same side with respect to the diffusing screen (Figure 2).

[0022] De préférence, l’objet à imager selon l’invention est bidimensionnel with a thickness less than the depth of field.

[0023] Le champ de vision est limité par la portée de l’effet mémoire associéto the diffusing screen. If this diffusing screen is two-dimensional, the memory effect extends over the entire angular range, and the field of view is limited only by the geometric decay of the ultrasonic waves. If the diffusing screen is volumetric, the angular range of the memory effect is on the order of θ in transmission and θ in reflection, where θ is the thickness of the diffusing medium. The mean free path of the wave within the scattering screen. This range of the memory effect designates the size ^ of the patch on which the transfer function H(^, ^) of the scattering screen can be considered spatially invariant: ^~^^^ / ^ in transmission and ^~^^^ / ℓ^. Thus, the estimation of only one transfer function will be necessary if the size of the area to be imaged is less than P. For a given field of view ^^^, the number of transfer functions to be determined is on the order of ^^^ / ^.

[0024] Dans les méthodes de correction d’aberrations de l’art antérieur, onThe ultrasonic data is projected onto the plane of the aberrator, and the spatial and frequency dependencies of the aberrator are determined independently. In the present invention, the spatio-frequency basis ensures optimal exploitation of the chromato-angular memory effect associated with the field reflected by the object and allows for a much more reliable estimation of the transfer function of the diffusing screen.

[0025] Cette estimation non biaisée de la fonction de transfert améliore ainsiThe focusing quality and resolution gain are achieved for confocal images because inserting the diffusing screen between the probe and the object allows the imaging system's aperture to be enlarged, thus obtaining super-resolution. The resolution is given by: λ = λ / (2 sin λ') where λ' is the angle at which the object sees the diffusing screen and λ is the size of the diffusing screen. Since the size λ of the screen is much larger than the size of the probe, and the screen is closer to the object being imaged than the probe, the resolution of the final confocal image is much better than in free space.

[0026] L’étape d’acquisition comprend des mesures du champ réfléchi parThe object is reflected via the diffusing screen by a set of incident waves generated by the transducer array, also reflected via the diffusing screen. This set of reflected fields forms the reflection matrix R(t), stored in memory. The variable t represents the echo time associated with the signals recorded during the measurement. For each measurement, the amplitude and phase of the ultrasonic signal are acquired.

[0027] Selon une mise en œuvre avantageuse de l’invention, l’étapethe acquisition of at least one canonical reflection matrix Rui(t) may 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) expressed in the basis of the transducers being composed of a set of impulse responses R(uout,uin,t) between transducers.

[0028] On entend par matrice « canonique » une matrice obtenue suite à ultrasonic measurements and from which all post-processing is carried out.

[0029] Selon une variante, l’étape d’acquisition d’au moins une matrice de Canonical reflection Rui(t) can include an insonification of the medium with a series of plane waves with a delay τ'(u) applied to each signal at emission for the formation of a wavefront inclined at an angle θin with respect to to the network 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)=[ R(uout, θin, t)].

[0030]

[0031] Selon encore une variante, l’étape d’acquisition d’au moins une canonical reflection matrix Rui(t) can include an insonification of the medium with a series of diverging waves.

[0032]

[0033] Selon une caractéristique de l’invention, l’écran diffusant peut être un An endogenous element in the environment. This is, for example, an element naturally present, such as a skull in ultrasound imaging.

[0034]

[0035] L’écran diffusant peut par ailleurs être un élément exogène qui est introduced into the path between the probe and the object to be imaged before the canonical reflection matrix acquisition step. It can be a removable element.

[0036]

[0037] A titre d’exemple, l’étape a) peut comprendre en outre une étape application of a time window on the canonical reflection matrix.

[0038]

[0039] Selon une caractéristique avantageuse de l’invention, l’étape b) peutUnderstanding the following steps: - a first step of determining a focused reflection matrix by projecting the canonical reflection matrix Rui(t) onto the basis of the diffusing screen according to the following equation: ^^^ in which the matrix ^^^(^, ) is the Fourier transform of each canonical reflection matrix ^^^(^), ^^^(^) = ∫ ^^ ^^^^ ^^^(^)^^^^^; the matrix ^ ^^ ( ^ )is the reception transformation matrix adapted for the transition from the reception basis (u) to the basis ^ of the diffusing screen at the frequency ^ of the ultrasonic waves; the matrix ^^^(^) is the transmission transformation matrix adapted for the transition from the transmission basis (i) to the basis ^ of the diffusing screen and at the frequency ^ of the ultrasonic waves; the symbols ∗ and † respectively denote the matrix operations of conjugation and transposition-conjugation; the symbol × denotes a matrix product, - a second step of determining a compensated matrix ^^(^^^^, ^^^, ^) by compensating the curvature of wavefronts in the plane of the diffusing screen according to the following equation: avec = ^ ^ ^ ^^^, a parabolic phase term under the paraxial approximation; ^^^^ being a first spatial position point corresponding to a virtual output transducer; ^^^ being a second spatial position point corresponding to a virtual input transducer, - a third step of determining the focused reflection matrix^′^^(^) by performing a change of variable defined by: from the compensated matrix in order to obtain the following relationship between the matrix coefficients :

[0040]

[0041] Ces trois étapes inclues dans l’étape b) peuvent être recombinées in the form of the following equation:

[0045] le symbole ∘ représente le produit d’Hadamard

[0046] le symbole × représente le produit matriciel.

[0047]

[0048] Selon un mode de réalisation, à l’étape c), l’algorithme d’imageriematrix can be an iterative algorithm of type CLASS for "Closed-Loop Accumulation of Single Scattering" in English, or "accumulation en boucle fermé des contributions de diffusion simple" in French, this CLASS algorithm comprising the following steps:

[0049] - construction d’un estimateur angular spectrum of the object's reflectivity by summing hyperdiagonals of the focused reflection matrix these hyperdiagonals being defined such that = ^^^ + ^^^^ = ^^^^^^^^^ , and the estimator is defined according to the following equation:

[0050] Γ^^^(^^) = ∑^^^^ ∑ (^^^) ^ ^ (^^ − ^^^^, ^^^^, ^)

[0051] n-1 étant le nombre d’itérations, (à noter que dans l’algorithme Classic class, there is no sum over ^)

[0052] - application d’un conjugué en phase de l’estimateur à la matrice de focused reflection R′^^(^) so as to make the object virtually coherent (this corresponds to a spatial Fourier transform of the real and positive object):

[0054] ^ (^^^) ^ ^^ is a coherent matrix,

[0055] - application sur la une matrice cohérente d’une fenêtre temporelleultrasonic echoes consisting, in the frequency domain, of a convolution with a function whose bandwidth Δ^ is inversely proportional to the duration Δ^ of the time window applied to the ultrasonic signals in the time domain:

[0057] avec ℬ(^^, Δ^) le filtre fréquentiel de largeur caractéristique Δ^,

[0058] - détermination de deux estimateurs, ^^^^(^^^, ^) et ^^^^^(^^^^ , ^), de la transfer function of the diffusing screen by summing the rows and columns of the filtered coherent reflection matrix ^ ( ^ ^^^) :

[0059] ^^^^(^^^, ^) = exp ^^ arg ^∑ (^^^) ^^^^ ^^ (^^^, ^^^^, ^) ^^

[0061] - application des conjugués en phase de ces deux estimateurs sur la reflection matrix ^ (^^^) ^^ (^) to obtain a reflection matrix ^′′ ( ^ ^ ^ ^^) (^)for which the phase shift induced by the diffusing screen has been compensated:

[0063]

[0064] - itération des étapes de l’algorithme de type CLASS de façon à converge towards a corrected reflection matrix in the plane of the diffusing screen, then reinject the parabolic phase terms that had been previously compensated:

[0067] Le filtre fréquentiel peut être typiquement une fonction Gaussienne.As iterations progress, the width Δ^ can be decreased in order to correct increasingly complex aberrations by activating a large number of frequency degrees of freedom.

[0068]

[0069] L’algorithme de type CLASS, inspiré de l’algorithme CLASS classique, This applies here in the space-frequency basis (^), whereas the classical CLASS algorithm was developed in the frequency domain only from the plane wave basis, a basis from which no gain in resolution can be expected and which is not suitable for compensating aberrations with a scattering screen. Such a prior art technique is described in YR Lee, et al. Exploiting volumetric wave correlation for enhanced depth imaging in scattering medium. Nat Commun 14, 1878 (2023).

[0070] La compensation des aberrations par l’algorithme CLASS dans le planThe use of an aberrant screen is discussed in another article, but on a time-windowed reflection matrix, which does not allow frequency correction of aberrations: Kwon, Y., Hong, JH, Kang, S. et al. Computational conjugate adaptive optics microscopy for longitudinal through-skull imaging of cortical myelin. Nat Commun 14, 105 (2023).

[0071] L’algorithme développé selon l’invention est itératif. Chaque itération breaks down into several steps, the result of which is a new estimation of the reflection matrix associated with the object ^ ( ^ ^) ^ (^). At iteration 0, the initial reflection matrix corresponds to the measured one: ^(^)(^^ − ^^^^ , ^^^^, ^) =^^(^^ − ^^^^, ^^^^, ^).

[0072]

[0073] De préférence, l’étape d) de projection de la matrice de réflexion corrected in the plane of the object ^ can further include a sum of the results on the frequencies according to the following equation:

[0075] la matrice is the transformation matrix from the basis (^) to the focused basis (^) at the depth ^^ and the angular frequency ^.

[0076] ^^ et ^^ sont les bornes inférieure et supérieure de la bande passanteultrasonic signals.

[0077] L’intégrale sur les pulsations est équivalente à un fenêtrage temporel echoes emanating from the object.

[0078]

[0079] L’étape e) de construction d’une image de l’objet peut être obtenue considering the diagonal of the reflection matrix

[0080] ℐ(^, ^^) = ^(^, ^, ^^)

[0081] avec ^ le vecteur position dans le plan de l’objet.

[0082] A noter que les deux équations précédentes peuvent être combinées so as to obtain a confocal image ℐ(^, ^^) of the object from sans go through the focused reflection matrix ^ ^^ ( ^ ^ ) .

[0083] Selon un autre mode de réalisation, à l’étape c), l’algorithme Matrix imaging can be an algorithm using a matrix distortion technique with a spatio-frequency correction basis.

[0084]

[0085] Avantageusement, la technique de la matrice distorsion avec une The spatio-frequency correction base (^) may include the following steps:

[0086] - calcul d’une matrice de réflexion duale entre la base focalisée (x) et the spatio-frequency correction basis (^):

[0088] la matrice ^^^(^) est la matrice de passage décrivant la projection de the base of the transducers (u) to the base of the spatio-frequency correction (^) to the pulsation ^,

[0089] la matrice ^^^(^) est la matrice de passage décrivant la projection de the emission base (i) to the focused base (^) at the depth ^^ and at the pulsation ^,

[0090] - déduction d’une matrice distorsion fréquentielle en performing the term-by-term product of the dual reflection matrix with the phase conjugate matrix of the reference matrix that would be obtained without a diffusing screen, i.e. here ^ ^ ^ ^ ( ^ ) :

[0091] Tel que

[0092] - calcul de la matrice de corrélation ^^^ ,

[0093] - détermination de la loi de correction spatio-fréquentielle ^(^^) par correlation matrix analysis ^ ^^ .

[0094]

[0095] Les coefficients de la matrice de corrélation ^^^ peuvent être donnés par :

[0098] La matrice de corrélation C peut être déterminée dans la base focused ^, by the following calculation of the elements of the correction matrix C =^ ^^ :

[0100] * est l’opérateur de conjugaison.

[0101]

[0102] L’analyse de la matrice de corrélation ^^^ (^^) peut être effectuée par an eigenvalue decomposition of the correlation matrix ^ ^^ (^ ^ ), and the spatio-frequency correction law ^(^^) is the first eigenvector ^^ of the correlation matrix ^^^(^^) in the correction basis (^).

[0103]

[0104] L’analyse de la matrice de corrélation ^^^(^^) peut également êtreperformed by a singular value decomposition of the distortion matrix rearranged as follows:

[0105] ^(^^) = [^({^, ^}, x, ^^)]

[0106]

[0107] L’analyse de la matrice de corrélation can also be done by solving the following equation:

[0108] ^(^^) = exp^^ arg^^^^(^^) × ^(^^)^^

[0109] de manière itérative par l’expression suivante, qui correspond à un calculation by iterative phase reversal:

[0111] où × est le produit matriciel,

[0112] avec : ^^ un front d’onde arbitraire, par exemple ^^ = [1 ⋯ 1] ^ .

[0113]

[0114] L’analyse de la matrice de corrélation Cxx peut aussi être effectuée by solving the following equation:

[0115] ^(^^) = exp(^ arg{^^^(^^) × ^(^^)})

[0116] où × est le produit matriciel,

[0117] de manière itérative par l’expression suivante :

[0118] ^^^^(^^) = exp(^ arg{^^^(^^) × ^^(^^)})

[0119] où × est le produit matriciel,

[0120] avec ^^ un front d’onde arbitraire, par exemple ^^ = [1 ⋯ 1] ^

[0121]

[0122] L’invention concerne également l’utilisation d’une loi prédéterminée spatio-frequency correction on an image acquired of an object by means of a predefined network of transducers and a predefined screen diffusing and carrying out steps d) and e) above.

[0123] Cette loi prédéterminée de correction spatio-fréquentielle estdetermined by applying a matrix imaging algorithm following a preliminary phase in which steps a) to c) above were performed using a set comprising a predefined transducer array, a predefined diffusing screen, and a phantom-type model object; a reflectivity statistic (ultrasonic speckle) and a speed of sound of said set being predefined. Thus, several spatio-frequency correction or defocusing laws for the transducer array-screen combination on a model object can be determined. of the phantom type (or other) in which we have well-known reflectivity statistics and the speed of sound. Once determined, these focusing laws can be reused when the probe + diffusing screen are used to image biological or other tissues.

[0124] Selon un autre aspect de l’invention, il est prévu un système deultrasonic construction of a confocal image of an object contained in a medium, the system comprising: -a network of transducers adapted to generate a series of ultrasonic waves incident in a zone of interest of the medium, and to measure as a function of time the ultrasonic waves backscattered by said zone of interest; -a diffusing screen on the path of the waves between the network of transducers and the medium to be imaged, and -a computing unit connected to the network of transducers and adapted to implement the process described above.

[0125]

[0126] 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.

[0127]

[0128] On prévoit également un support lisible par ordinateur comprenant instructions which, when executed by a computer, lead the computer to implement the steps of the process described above.

[0129] Brief description of the drawings

[0130] D’autres avantages et particularités de l’invention apparaîtront à la reading the detailed description of implementations and methods of realization, which are in no way exhaustive, and the following attached drawings.

[0131] La figure 1 est une vue schématique globale d’une expérience allowing to illustrate the estimation and correction of diffusion phenomena in a plane conjugate to the diffusing screen in a transmission configuration according to the invention;

[0132] La figure 2 est une vue schématique globale d’une expérience allowing to illustrate the estimation and correction of diffusion phenomena in a plane conjugate to the diffusing screen in a reflection configuration according to the invention;

[0133]

[0134] La figure 3 est une vue schématique illustrant un exemple d’un ultrasonic construction system for implementing the process according to the present invention;

[0135] La figure 4 est un diagramme du procédé de construction d’une image ultrasonic according to the present invention;

[0136] La figure 5 est une représentation graphique à deux dimensions de the chromato-axial memory effect as observed from an intermediate plane,

[0137] La figure 6 comporte plusieurs images acquises après des itérations successive stages of a SUPER-CLASS algorithm,

[0138] La figure 7 comporte des images confocales acquises et desgraphical representations allowing comparison in the absence and presence of the diffusing medium, with and without correction, and

[0139] La figure 8 illustre des images permettant une comparaison de The energy of the reflection matrices in the absence and presence of the diffusing medium in the plane of the diffusing screen. Detailed description of the figures

[0140] Il est bien entendu que les modes de réalisation qui seront décrits The following are by no means limiting. In particular, variants of the invention may be imagined comprising only a selection of 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 functional preference feature without structural detail, or with only part of the structural details if that part alone is sufficient to confer a technical advantage or to differentiate the invention from the prior art.

[0141] 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.

[0142] 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.

[0143]

[0144] La figure 1 est une vue schématique d’un système 1 selon l’invention comprising a matrix probe 2 controlled to emit and detect signals to and from an object 4 present in a medium. This medium can be the inside of a head. The matrix probe 2 can be positioned on the surface of this head, facing the object.

[0145] La sonde matricielle 2 peut être pilotée pour la réalisation de la Next acquisition sequence: Table 1 P aramètre Valeur Sampling Emitted signal: Pulse of three half-periods of a 3 MHz sinusoidal signal. Sampling frequency: 6 MHz (IQ modulation). Recording duration: 180 µs.

[0146]

[0147] La mise en œuvre de la séquence permet d'acquérir la matrice deCanonical reflection of the medium. The latter comprises an object 4 to be imaged, flat and contained in the plane z = zM = 110 mm. This object 4, in the shape of a perforated pentagon, was made from a hard, abrasive disc. Between object 4 and the matrix probe 2, at a depth zp = 30 mm, a polyamide fiber mesh is stretched, onto which 1.5 mm diameter glass beads are arranged, forming a diffusing screen or diffusing medium 3. All these elements are immersed in water, at the speed of sound c0 = 1480 m / s -1 .

[0148] On distingue une pyramide 5, traits en pointillés, ayant une base consisting of the matrix probe 2 and a point consisting of the object 4. This pyramid 5 represents the set of insonification directions of the object in the absence of the diffusing medium 3.

[0149] On distingue un volume 6 représentant l’ensemble des directions 3. insonification of the object in the presence of the diffusing medium.

[0150] La présente invention a pour objet d’apprendre à imager l’objet 4 viaThe screen diffuses without prior calibration and with a resolution far superior to that of free space by virtually increasing the angular aperture of the matrix probe. This diffusing medium 3, which could be considered an obstacle, advantageously becomes, according to the invention, a component enabling super-resolution.

[0151] Le procédé selon l’invention est basée sur l’acquisition et la projection of the reflection matrix in a spatio-frequency basis whose coordinate ^ = ^ ^ ^ ^ ^ ^ combines the spatial coordinates of the screen diffuser, ^, the frequency and ^ ^ , the distance between the diffusing screen and the object. This basis maximizes the input-output correlations of the field associated with the object (chromato-angular memory effect in reflection associated with the object) and which can be used to estimate the transfer function of the diffusing screen.

[0152] Une fois cette fonction de transfert connue, on peut exploiter laangular diversity offered by the diffusion paths induced by the diffusing screen and enlarge the angle under which the object is seen to obtain a precise image of the latter, with a resolution much better than in free space.

[0153] L’association réseau de transducteurs – écran diffusant peut être The imaging can be performed in transmission, i.e., with the diffusing screen placed between the transducer array and the object to be imaged (Figure 1), or in reflection, i.e., with the transducer array and the object placed on the same side of the diffusing screen (Figure 2). In both cases, the surface area of ​​the diffusing screen is much larger than the physical aperture of the probe, which allows for a significant improvement in image resolution according to the invention.

[0154] Le champ de vision est limité par la portée de l’effet mémoire associéto the diffusing screen. If this diffusing screen is two-dimensional, the memory effect extends over the entire angular range, and the field of view is limited only by the geometric decay of the ultrasonic waves. If the diffusing screen is volumetric, the angular range of the memory effect is on the order of θ in transmission and θ in reflection, where θ is the thickness of the diffusing medium. The mean free path of the wave within the diffusing screen is denoted by . This range of the memory effect denotes the size ^ of the patch over which the transfer function H(^, ^) of the diffusing screen can be considered spatially invariant: ^~^^^ / ^ in transmission and ^~^^^ / ℓ^. Thus, the estimation of a single transfer function will be necessary if the size of the area to be imaged is less than P. For a given field of view ^^^, the number of transfer functions to be determined is on the order of ^^^ / ^. In this case, the entire process of estimating the transmittance H will have to be repeated for different areas of the field of view of size P.

[0155]

[0156] Système de construction ultrasonore

[0157] La figure 3 illustre un exemple d’un système 7 d’imagerie ultrasonore for the implementation of the ultrasonic imaging method of medium M, according to the present invention. This system and the method allow the formation of an ultrasound image of at least a part (area of ​​interest or field of view) of the medium.

[0158] Le système 7 comprend :- a sounding device 20 including the matrix probe 2, - a processing unit 30 for calculating an image from the signals received from the sounding device 20, - a control panel 40 connected to the processing unit 30, this control panel including for example buttons 41 and a touchpad 42, - a display device 50 for viewing an image and various elements or measurements.

[0159] Le dispositif de sondage 20 est relié à l’unité de calcul 30 via un câble 21 or via a wireless connection, and is capable of emitting ultrasonic waves W into the medium M and receiving ultrasonic waves W from the medium M, said ultrasonic waves being the result of reflections of the ultrasonic waves emitted by the diffusing medium 3 inside the medium M.

[0160] Le dispositif de sondage 20 comprend la sonde 2 doté d’une pluralitéof transducers. Probe 2 is a matrix array but can, for example, be a linear, curved, or two-dimensional array. The transducers are capable of converting an electrical signal into a vibration and vice versa. For example, the transducers are piezoelectric ultrasonic transducers that can take the form of a rigid bar placed in direct or indirect contact with an external surface of the medium M to be coupled to the medium and to vibrate and emit and receive ultrasonic waves W. The transducer array of probe 2 is then associated with the computing unit 30. Probe 2 can comprise one hundred or more transducers.

[0161] L’unité de calcul 30 peut comprendre un boitier 31 incluant desReceiving devices for amplifying and / or filtering the signals received from the sounding device 20, and converters (analog-to-digital converters and digital-to-analog converters) for transforming the signals into representative signal data. The data can be stored in the memory of the computing unit 30 and / or directly processed to calculate intermediate data (track formation data or other data). The computing unit 30 can implement any known method for constructing an image from the signal data received from the sounding device 20, such as track formation.

[0162] L’image calculée peut être :- an image of the medium (B-mode image) usually in greyscale to visualize organs in the medium, and / or- an image showing a velocity or flow in the medium (colour image) for example useful to visualize blood vessels in the medium, and / or- an image showing a mechanical characteristic of the medium (elasticity) for example useful to identify tumors within the medium.

[0163] Par "connexion" ou "liaison" entre le dispositif de sondage 20, l'unité calculation 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.

[0164] Le dispositif d’affichage 50 est un écran permettant de visualiserThe 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.

[0165] Le panneau de contrôle 40 est par exemple une portion d’un boitier system, said portion comprising a panel housing having a substantially flat surface 40a inclined towards the user for one-handed operation. As shown in Figure 3, the control panel 40 may include a control screen 49 for displaying various configuration information.

[0166] 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, a spatial coordinate system of the medium M is defined, taking a first axis X and a second axis Z perpendicular to it. For simplification, the first axis X corresponds to the The transverse direction in which the transducers are aligned, as in the example of a linear array, and the second axis Z corresponds to the depth of the medium M relative to this transducer array. This definition can be adapted to the context and thus, for example, extended to a three-axis spatial coordinate system in the case of a matrix array, or to a polar coordinate system in the case of a curved array, or to any other suitable coordinate system depending on the structure and shape of the ultrasonic transducer array. Therefore, in the remainder of this disclosure, we will use a Cartesian coordinate system XZ, corresponding to a linear probe 2, for the sake of simplicity in the explanations, but a specialist in the field could easily generalize and apply the results to any type of coordinate system.

[0167] Dans la suite de la divulgation, il est fait référence à un réseau deTransducers for transmission and reception, it being understood that, more generally, several transducer networks can be used simultaneously. The transducers can be both transmitters and receivers, or only transmitters for some and only receivers for others. Similarly, a network can consist of one (1) to N transducers, of the same type or of different types.

[0168] La sonde 2 constituée d’un réseau de transducteurs sert par exemple acting as both a transmitter and a receiver, or consisting of several sub-arrays of transducers, some dedicated to the transmission, others to the reception of ultrasonic waves. By transducer array, we mean at least one transducer, an aligned or non-aligned sequence of transducers, or a two-dimensional distribution of transducers (for example, a transducer matrix), or any spatial distribution of transducers.

[0169] Lorsque dans la présente divulgation, il est fait référence à des étapesFor calculation or processing purposes, particularly 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... example 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) in order to implement these calculation or processing steps.

[0170]

[0171] Sur la figure 4 est représenté un diagramme des principales étapesaccording to the invention. We distinguish a step a) acquisition of a canonical reflection matrix Rui(t). In b), we determine a focused reflection matrix ^′^^(^) by projecting the canonical reflection matrix onto a space-frequency basis ^:

[0172] ^ = ^ ^ ^ ^ ^ ^

[0173] A l’étape c) on détermine une matrice de réflexion corrigée (^).

[0174] L’étape d) permet de déterminer une matrice de réflexion objet ^^^(^^) by projecting the corrected reflection matrix in a plane of the object ^ at the depth ^^.

[0175] A l’étape e), on construit une image à partir de la matrice de réflexion object ^ ^^ (^ ^ ).

[0176] Ces étapes sont décrites plus en détails ci-après.

[0177]

[0178] Selon l’invention, le procédé de construction ultrasonore mis en œuvre The calculation unit 30 of system 1 includes at least one acquisition of a reflection matrix. This reflection matrix can be acquired in the following way:

[0179] - une étape de génération d’une série d’ondes ultrasonores incidentes USin in a zone of said medium, by means of probe 2, said series of incident ultrasonic waves being an emission basis i; and

[0180] - pour chaque onde émise iin, le champ réfléchi par le milieu estmeasured by each transducer and is denoted R(uout,iin,t,#m), where t is the echo time and the vector uout identifies the position of each transducer. Each field is stored in the canonical reflection matrix Rui(t)=[R(uout,iin,t)] defined between the transmitting basis i at the input and a receiving basis u at the output.

[0181] Une première possibilité pour mesurer cette matrice de réflexionThe canonical method involves successively emitting an ultrasonic pulse from each transducer in the array, whose position is identified by the coordinate uin. 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. By repeating this operation with each transducer used successively as a source, the canonical reflection matrix Ruu(t) is determined, expressed in the basis of the transducers. This matrix is ​​composed of all the impulse responses R(uout, uin, t) between each transducer. This matrix is ​​thus rich in information about the medium under study. However, the method assumes that the medium remains stationary throughout the measurements. Furthermore, the recorded signals have a poor signal-to-noise ratio because the medium is insonified by only one transducer.

[0182] Une deuxième manière de construire cette matrice de réflexionCanonical sonification involves insonifying the medium with a plane wave series basis. This method overcomes previous problems. A delay law τ' is applied to each signal at the source to form a wavefront inclined at an angle θin with respect to the transducer array. At the receiver, the backscattered field from the medium, R(uout, θin, t), 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) = [R(uout, θin, t)]. This method gave rise to ultrafast imaging and elastography, and is described, for example, in the document:

[0183] « 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).

[0184] Une troisième manière pour créer cette matrice de réflexionThe canonical method consists of insonizing the medium with a basis of divergent waves, which allows the acoustic field to be illuminated more broadly than with the use of 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 document:

[0185] « Ultrafast imaging of the heart using Circular Wave Synthetic Imaging with Phased Arrays”, Couade et al., IEEE International Ultrasonics Symposium (2009).

[0186] La matrice de réflexion canonique Rui(t) enregistrée peut être une A "real" matrix, meaning one composed of real coefficients in the time domain, where the electrical signals recorded by each transducer are real numbers. Alternatively, this matrix can be a "complex" matrix, meaning one composed of complex values, for example in the case of demodulation for beamforming in-phase and quadrature (known in English as "beamforming IQ").

[0187]

[0188] Projection des données ultrasonores dans une nouvelle base spatio-frequency.

[0189] Les coordonnées de cette base dépendent à la fois du vecteur position in the plane of the diffusing screen (^) and the frequency ^

[0191] avec ^^ la distance entre l’objet et l’écran diffusant.

[0192] Ce changement de coordonnées permet de mettre en évidence un chromato-angular memory effect associated with the field reflected by the object.

[0193] La figure 4 est une représentation graphique à deux dimensions de The chromato-axial memory effect as observed in an intermediate plane (the plane of the diffusing screen). [A] A virtual emitter placed in the intermediate plane sends a wave, which is reflected by the object and then detected by a virtual receiver also placed in the intermediate plane. [B] At the same frequency, applying the translation ^^^ ^ At the source, you need to apply the inverse translation -^^^ ^ to the receiver so that it detects the same field, within parabolic and deterministic phases, thanks to the memory effect. By changing the frequency and keeping the transmitter in the same position, it is possible to move the receiver so that it measures the same field, within parabolic and deterministic phases, while remaining at ^^^^ constant.

[0194]

[0195] 1ère étape : Projection de R dans la base (^) de l’écran diffusant

[0196] Ainsi, une matrice de réflexion focalisée ^^^(z0, ^) du milieu peut être obtained by focusing using the following matrix calculation:

[0198] dans lequel

[0199] la matrice ^^^(^, ) est la transformée de Fourier de chaque matrice de canonical reflection

[0200] la matrice ^^^(^) est la matrice de passage de réception adaptée pour the transition from the receiving base (u) to the focused base (^) at depth ^^ and at pulsation ^,

[0201] la matrice ^^^(^) est la matrice de passage d’émission adaptée pour the transition from the emission basis (i) to the focused basis (^) at the pulsation ^,

[0202] Les symboles ∗ et † désignent respectivement les opérations conjugation and transposition-conjugation matrices.

[0203] Le symbole × désigne un produit matriciel.

[0204] Les coefficients de la matrice de passage G correspondent à la dérivée normal of the Green's function relating each focal point of spatial position (^, ​​zP) and each transducer of spatial position (u, 0).

[0205] 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 G can be written as follows:

[0206] ^(^, ^, ^^ , ^) = ∇^^^^(^, ^, ^)

[0207] où ∇^ est le gradient projeté suivant la direction de profondeur z, et

[0208] ^^^(^, ^) est la fonction de Green 2D qui relie chaque transducteur ^ = (^, 0) at each point ^ = (^, ^^) of the displaying screen, with:

[0210] où ^^ = 2^^ / ^^ est le nombre d’onde,

[0211] is the Hankel function of 1 erorder whose asymptotic expression is as follows: ℋ^

[0212] Dans le cas d’un réseau de transducteurs de type matriciel pour To generate a three-dimensional image, the coefficients of this transition matrix G can be written as:

[0213] ^(^, ^, ^^ , ^) = ∇^^^^(^, ^, ^)

[0214] où ^^^(^, ^) est la fonction de Green 3D qui relie chaque transducteur ^ = (^^ , ^^ , 0) at each point ^ = (^, ^^) of the midpoint M, with:

[0216] Les coefficients de la matrice de passage P s’écrivent donc dans ce in the following way:

[0218] Les coefficients de la matrice de passage ^^^ s’écrivent donc dans ce in the following way:

[0220] Dans le cas d’une base d’illumination correspondant à une base des plane waves (i=k), the transition matrix P is the Fourier transform operator.

[0221] Dans le cas d’un réseau de transducteurs de type linéaire pour générer In a two-dimensional image, the coefficients of this change-of-basis matrix P can be written as follows:

[0223] où ^^^, la composante transverse du vecteur d’onde k associé à each plane wave.

[0224] 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:

[0225] ^^^^^, ^, ^^, ^^ = ^^^ ^^^^ ^ ^ ^ ^ ^ ^ ^− ‖^^^‖^^ ^^^(−^^^^. ^)

[0226] où

[0227] ^^^ est la composante transverse du vecteur d’onde k associé à each plane wave, and

[0228] ^, le vecteur position transverse.

[0229]

[0230] Si la base d’illumination est celle des transducteurs (i=u), alors laThe change-of-basis matrix ^^^ will be taken as equal to the matrix ^^^ expressed above.

[0231]

[0232] 2ème étape : Compensation de la courbure des fronts d’onde in the plane of the broadcasting screen ‖ ^ ^^ ^‖

[0234] avec = ^ ^ ^ ^^^ , the parabolic phase term under the paraxial approximation

[0235]

[0236] 3ème étape : Changement de variable ^ = ^ ^ ^ ^ ^ ^

[0238]

[0239] Les trois étapes précédentes peuvent être recombinées sous la forme from the following equation:

[0243] le symbole ∘ représente le produit d’Hadamard

[0244] le symbole × représente le produit matriciel.

[0245]

[0246] Processus de correction des aberrations

[0247] Au moins deux algorithmes d’imagerie matricielle peuvent être used.

[0248] Algorithme SUPER-CLASS

[0249] L’idée est ici de développer un algorithme nommé SUPER-CLASS inspired by the CLASS algorithm but in the spatio-frequency basis (^) introduced above, while the CLASS algorithm was developed in the frequency domain only from the basis of plane waves, a basis from which no gain in resolution can be expected and which is not suitable for compensating aberrations by a screen.

[0250] L’algorithme selon l’invention est itératif. Chaque itération se breaks down into five steps, the result of which is a new estimate of the reflection matrix associated with the object At iteration 0, the initial reflection matrix corresponds to the measured one: =

[0251] Etape 1

[0252] La première étape de l’algorithme SUPER-CLASS consiste à sommer the hyperdiagonals of the reflection matrix defined such as = ^^^ + ^^^^ =^^^ ^^^^^^^^^ so as to construct an estimator of the angular spectrum of the object's reflectivity:

[0254] Dans l’algorithme Class original, il n’y a pas de somme sur la pulsation ^.

[0255] Etape 2

[0256] La seconde étape de l’algorithme consiste à appliquer le conjugué en phase of this estimator to the reflection matrix so as to make the object virtually consistent:

[0258] Etape 3

[0259] La troisième étape consiste en un fenêtrage temporel des échos ultrasonic signals, which translates in the frequency domain into a convolution with a function whose bandwidth Δ^ is inversely proportional to the duration Δ^ of the time window applied to the ultrasonic signals in the time domain:

[0261] avec ℬ(^^ , Δ^) le filtre fréquentiel de largeur caractéristique Δ^, et qui can typically be a Gaussian function. As iterations progress, the width Δ^ can be decreased in order to correct increasingly complex aberrations by activating a large number of frequency degrees of freedom.

[0262] Etape 4

[0263] Deux estimateurs, and ^^^^^(^^^^, ^), of the transfer function of the diffusing screen can be estimated by summing the rows and columns of the "coherent" and filtered reflection matrix ^ ( ^ ^^^) :

[0266] Etape 5

[0267] Les conjugués en phase de ces deux estimateurs peuvent être applied to the reflection matrix ^ (^^^) ^^ (^) to obtain a reflection matrix ^ (^^^)^^ (^) for which the phase shift induced by the diffusing screen has been compensated:

[0268] ^(^)(^^^, ^^^^, ^) = ^^∗ ^^ (^^^, ^)^(^)(^^^, ^^^^ , ^)^^ ∗^^^ (^^^^ , ^)

[0269]

[0270] Au bout de quelques itérations, l’algorithme converge et la matrice de Reflection in the plane of the aberrator can be obtained by reintroducing the parabolic phase terms that had previously been compensated:

[0272]

[0273] Etape finale

[0274] Une image de l’objet peut être obtenu en projetant la matrice de corrected reflection in the plane of the object (^) and summing the result over the pulsations:

[0276] La matrice ^^^(^^, ^) est la matrice de passage de la base (^) à la base focused (^) on depth ^^ and pulsation ^.

[0277]

[0278] Une image de l’objet est alors obtenue en considérant la diagonale de the reflection matrix

[0279] ℐ(^, ^^) = ^(^, ^, ^^)

[0280] avec ^ le vecteur position dans le plan de l’objet

[0281]

[0282] La figure 6 comprend des images de sortie des itérations successives during the implementation of a SUPER-CLASS algorithm. The matrix ^ ^^ ( ^ ^ )can be used to initialize the SUPER-CLASS algorithm. Figure 6 shows the different confocal images formed after correction of the reflection matrix with the estimates of the aberration laws obtained at the end of the iterations for which ^ ^ = 400kHz, then ^ ^ = 300kHz and 200kHz, then finally étant la characteristic width of the frequency filter considered here as Gaussian. We can thus observe that, over the iterations and as we use an increasingly longer confocal filter time frame, the confocal image is progressively corrected, since the pentagonal shape of the object eventually appears. In the later iterations, we can also distinguish the hole drilled in the object, which confirms the proper functioning of the method and a gain in resolution. As the lateral resolution is improved, we simultaneously observe a reduction in the axial trail of echoes present beneath the object. The gain in lateral resolution can also be seen by observing the progressive thinning of the radial RPSF (Reflection Point Spread Function) formed in the plane of the object and also represented in Figure 6. The RPSF describes the spread function of the reflection imaging system.This quantity is estimated from the antidiagonals of the matrix ^^^(^^) as described in the article: F. Bureau et al., Three Dimensional Ultrasound Matrix Imaging, Nat. Commun. 14, 6793, 2023.

[0283] La première ligne (#0) correspond aux données non corrigées.

[0284] [AB] : images confocales dans les plans z=zM et y=0.

[0285] [CD] : Loi d'aberrations supplémentaire en sortie obtenue à l'issue of iterations, the total aberration law used to form the confocal images at this iteration corresponding to the summation of the additional laws.

[0286] [C] : dans le plan

[0287] [D] : Dans le plan f=3MHz.

[0288] [E] : RPSF radiales estimées dans le plan z=zM.

[0289] Avec l’invention, les matrices de réflexion corrigées correspondent to the acquired reflection matrices corrected with the final estimation of the aberration laws obtained after the succession of all iterations of the SUPER-CLASS algorithm with the different

[0290] La figure 7 comporte plusieurs images et représentations graphiques allowing a comparison of confocal images and resolution in the absence of the diffusing medium and in its presence, with and without correction.

[0291] [A] : Images confocales dans le plan z=zM.

[0292] [B] : RPSF estimées dans le plan z = zM.

[0293] [C] : RPSF radiales dans le même plan.

[0294] [D] : Profil de l'intensité confocale normalisée le long du segment l defined by a dotted line on the central confocal image.

[0295] La figure 7 montre ainsi des images confocales formées à partir desUncorrected reflection matrices without a scattering medium and corrected or uncorrected matrices with a scattering medium, as well as the associated RPSFs (Reflection-Sensitive Fields). The image without a scattering medium provides a poorly resolved image of the object due to the limited angle (<9°) at which the object sees the probe. Adding the scattering medium yields an equivalent image of the object, but with lower contrast due to energy loss from the ballistic wave and blurring caused by scattering events.

[0296] Ces observations sont confirmées par une étude des RPSF associées. Before correction and in the presence of the diffusing medium, the RPSF visible in figure 7 presents the following profile:

[0297] un pic confocal autour de ∆^ = ^ lié à l'onde balistique et un fond incoherent diffusion-induced pattern. We observe that the main lobe of the RPSF is drastically refined following the correction of aberrations, going from an average width at half-height of 3.1 to 1.6 mm. Finally, the level of the incoherent background is lowered by approximately 20 dB.

[0298] Sur la figure 7 enfin, nous traçons le profil des intensités confocalesalong a segment passing through the hole drilled in the object. These graphs allow us to verify that the intensity is attenuated by a factor close to 20 in the presence of the diffusing medium. Nevertheless, aberration correction maximizes the confocal intensity and thus multiplies its maximum level by a factor of approximately 10. Even better, aberration correction makes the hole drilled in the object visible, since we can clearly identify a minimum intensity at its level.

[0299] Nous observons ainsi que les images non corrigées avec et sans milieuDiffusing media have the same resolution. Furthermore, the image obtained without a diffusing medium theoretically exhibits no aberrations and allows us to define the optimal resolution of the system at this depth. Consequently, the new resolution achieved by correcting the dispersive aberrations of the diffusing screen corresponds to super-resolution from the probe's perspective. This super-resolution is obtained by inserting the diffusing medium between the probe and the object. This diffusing medium virtually enlarges the probe's aperture by capturing echoes from the object that are too inclined relative to the ez axis and would not normally reach the probe.

[0300]

[0301] La figure 8 permet une comparaison de l'énergie des matrices de reflection in the absence and in the presence of the diffusing medium in the plane of the aberrator, the energies being represented without normalization so that they are comparable to each other.

[0302] [A] : En l'absence du milieu diffusant.

[0303] [B] : En sa présence.

[0304] [C] : Différence des deux, les valeurs positives représentant les gainsrelated to the addition of the diffusing medium. The dotted box corresponds to the outline of the intersection of the aberrator plane with the rectangular-based pyramid having the probe as its base and also including among its vertices the origin of the object's plane.

[0305] On constate ainsi qu'en dehors de cet encadré pointillé et malgré Attenuation occurs when there is more energy in the presence of the scattering medium. It is the scattering medium that allows waves originating from the periphery of the aberrator plane, that is, from all directions included in volume 6 of figure 1, to be redirected towards the object.

[0306]

[0307] Variante en passant par la matrice Super-Distorsion

[0308] Une approche alternative à SUPER-CLASS consiste en une approche spatio-frequency aberration compensation based on the concept of distortion matrix with a spatio-frequency correction basis (^).

[0309] La première étape consiste à calculer une matrice de réflexion duale between the focused basis (x) and the spatio-frequency correction basis (^):

[0311] la matrice ^^^(^) est la matrice de passage décrivant la projection de the base of the transducers (u) to the base of the spatio-frequency correction (^) to the pulsation ^,

[0312] la matrice ^^^(^) est la matrice de passage décrivant la projection dethe emission base (i) to the focused base (^) at the depth ^^ and at the pulsation ^,

[0313] Une matrice distorsion fréquentielle is then deduced by performing the term-by-term product of the dual reflection matrix with the phase conjugate matrix of the reference matrix that would be obtained without a diffusing screen, i.e. here ^ ^ ^ ^ ( ^ ) :

[0314] Tel que

[0315] L’étape suivante est de calculer la matrice de corrélation ^^^ dont les The coefficients are given by:

[0317] Selon une deuxième variante, la matrice de corrélation C est determined in the focused basis ^, by the following calculation of the elements of the correction matrix C = ^^^:

[0319] * est l’opérateur de conjugaison

[0320]

[0321] Selon une première variante, l’analyse de la matrice de corrélation (^^) is performed by an eigenvalue decomposition of the decorrelation matrix ^^^(^^), and the spatio-frequency correction law ^(^^) is the first eigenvector ^^ of the correlation matrix ^^^(^^) in the correction basis (^).

[0322] La matrice de corrélation étant hermitienne (^ = ^^), ses valeurstheir properties are real and positive.

[0323] La matrice de corrélation ^^^(^^) peut ainsi s’écrire :

[0325] ou en termes de coefficients matriciels :

[0326]

[0327] avec ^^ correspondant aux vecteurs propres de la matrice de correlation C

[0328] ^^ correspondant aux valeurs propres réelles et positives de la Correlation matrix ^^^(^^) arranged in descending order: ^^ > ^^ > ⋯ > ^^

[0329] On a alors la loi de correction spatio-fréquentielle ^(^^) qui est égale to the first eigenvector, i.e., ^(^^) = ^^; or to its normalized version, ^(^^) = 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 distortions.) of phase. Finally, the third option is relevant when the aberrant medium inhomogeneously attenuates certain components and / or frequencies of the field that we wish to enhance in order to have a more faithful estimator of the reflectivity in the end.

[0330]

[0331] Selon une deuxième variante, l’analyse de la matrice de corrélation ^^^(^^) is performed by a singular value decomposition of the rearranged distortion matrix as follows:

[0332] ^(^^) = [^({^, ^}, x, ^^)]

[0333] La décomposition en valeurs propres de la matrice de corrélation ^^^(^^) carried out in the first variant is indeed equivalent to the singular value decomposition (SVD) of each distortion matrix.

[0334] La décomposition en valeurs singulières s’applique sur des matrices rectangular in shape, and applied to the distortion matrix ^(^ ^ ), it is written as follows:

[0336] ou en termes de coefficients matriciels :

[0337]

[0338] avec ^^ = ^^^(^, ^)^ correspondant aux vecteurs singuliers de la distortion matrix ^(^^) in the correction basis, or equivalently, to the eigenvectors of the matrix as defined in the first variant.

[0339] ^^ = ^^^(^)^ correspondant aux vecteurs singuliers de la matrice distortion ^^^ in the focused basis (x),

[0340] ^^ correspondant aux valeurs singulières de la matrice distorsion which are, by definition, equal to the square root of the eigenvalues ​​^ ^ of the correlation matrix C as defined in the first variant: ^^ = ^ ^ ^ .

[0341] On a alors la loi de correction spatio-fréquentielle ^(^^) qui est égale to the first singular vector of the distortion matrix ^^^, i.e. ^(^, ^) = ^^ ; or to its normalized version, ^(^^) = exp(^arg{^^}), i.e. a spatio-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{^^}) / |^^| .

[0342] L’intérêt de la décomposition en valeurs singulières de la matrice de dual reflection ^^^, compared to an eigenvalue decomposition of the correlation matrix ^ ^^ is the speed of computation of numerical algorithms for singular value decomposition

[0343] L’intérêt de la décomposition en valeurs singulières de la matricedistortion ^, compared to an eigenvalue decomposition of the correlation matrix is the speed of calculation of numerical algorithms for singular value decomposition.

[0344]

[0345] Cette recherche de la loi de correction spatio-fréquentielle ^(^^) est also equivalent to solving the following equation:

[0346] a^(^^) = ^^^(^^) × ^(^^)

[0347] où × est le produit matriciel et a est une constante,

[0348] de manière itérative par l’expression suivante, qui correspond à un calculation by iterative time reversal:

[0349] ^^^^(^^) = ^^^(^^) × ^^(^^),

[0350] avec ^^ un front d’onde arbitraire, par exemple ^^ = [1 ⋯ 1] ^

[0351]

[0352] Alors, la loi de correction spatio-fréquentielle ^(^^) est obtenue par :

[0354] ou sa version normalisée :

[0355] ^(^^) = exp ^^arg ^ ^ ^^ → ^ ^ ^ ^ (^ ^ )^^,

[0356] ou sa version filtre inverse :

[0358] 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 by an SVD because it can converge after a few iterations, hence a greater computation speed.

[0359]

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

[0362] de manière itérative par l’expression suivante, qui correspond à un calculation by iterative phase reversal:

[0364] où × est le produit matriciel,

[0365] avec : ^^ un front d’onde arbitraire, par exemple ^^ = [1 ⋯ 1] ^ .

[0366] Alors, la loi de correction spatio-fréquentielle ^(^^) est obtenue par :

[0367] ^(^^) = ^^^ ^ ^ (^ ), ^→^ ^

[0368] Ou sa version filtre inverse :

[0370] 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 ^(^^) and therefore ultimately provides better compensation for phase distortions induced by the aberrator.

[0371]

[0372] Selon une quatrième variante, l’analyse de la matrice de corrélation Cxx is calculated by solving the following equation:

[0373] ^(^^) = exp(^ arg{^^^(^^) × ^(^^)})

[0374] où × est le produit matriciel,

[0375] de manière itérative par l’expression suivante :

[0376] ^^^^(^^) = exp(^ arg{^^^(^^) × ^^(^^)})

[0377] où × est le produit matriciel,

[0378] avec ^^ un front d’onde arbitraire, par exemple ^^ = [1 ⋯ 1] ^

[0379] ce qui permet d’obtenir le vecteur W(^^) suivant :

[0380] ^(^^) = ^^^ ^ (^ ) ^→^ ^ ^

[0381] Ce vecteur ^(^^) = [^(^, ^^)] défini dans la base focalisée (x) contient the phase of each inconsistent guiding star synthesized at depth ^^.

[0382] Le conjugué en phase de ce vecteur ^(^^) peut alors être exploitéto rephase each incoherent virtual star so that they can be recombined coherently and thus obtain an estimator of the spatio-frequency correction law ^ ( ^ ^ ) unbiased by the random reflectivity of the medium. Mathematically, this operation is written as follows:

[0383] ^(^, ^, ^, ^^) = ^^^^^ × ^^^{∑^ ^(^, ^, ^^, ^)^∗(^, ^^)}^

[0384] L’intérêt de cette approche par rapport à une SVD de la matrice distortion (second variant) or the iterative phase reversal algorithm (third variant) aims to converge towards a correction law unbiased by the larger amplitude of the ultrasonic signal on certain frames of the reflection matrix (a large amplitude caused by the passage of a bright scatterer such as a bubble or an experimental problem). The advantage of the distortion matrix compared to CLASS is that it can spatially filter the data by passing through the focused basis in the plane of the object at each iteration, thus restricting the field of view and respecting the underlying isoplanetary assumption. The disadvantage lies in the multiple basis changes inherent in this approach, which can be computationally expensive in terms of processing time and memory.

[0385]

[0386] Bien entendu, l’invention n’est pas limitée aux exemples qui viennentto be described. Numerous modifications can be made to these examples without departing from the scope of the present invention as described.

Claims

CLAIMS 1.Ultrasonic construction method of a confocal image of an object (4) contained in a medium, the method comprising the following steps: a) acquisition, by means of a network of transducers (2) and a diffusing screen (3) disposed on the path of the wave between the network of transducers and the object, of at least one canonical reflection matrix Rui(t)=[R(uout,iin,t)] defined between an ultrasonic wave emission basis i at the input and a reception basis u at the output; the coefficients of this canonical reflection matrix corresponding to the signals received by the transducers and induced by the ultrasonic waves reflected by the object via the diffusing screen; t denoting the echo time; b) determination of a focused reflection matrix ^′^^(^) by projection of the canonical reflection matrix into a spatio-frequency basis ^ depending on both a position vector in a plane ^ of the diffusing screen and a pulsation ^ of the ultrasonic waves, this basis being defined by:.^ = ^ ^ ^ ^ ^ ^ where C0 is the speed of sound in the medium, ^ ^ a distance between the diffusing screen and the object, c) determination of a corrected reflection matrix in the spatio-frequency basis ^ by applying a matrix imaging algorithm, d) determination of a reflection matrix associated with the object ^^^(^^) by projecting the corrected reflection matrix in a plane of the object ^ located at a distance zM from the transducer array, e) construction of an image from the object reflection matrix ^ ^^ (^ ^2. A method according to claim 1, characterized in that the step of acquiring at least one canonical reflection matrix Rui(t) 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) expressed in the basis of the transducers being composed of a set of impulse responses R(uout,uin,t) between transducers. 3.A method according to claim 1, characterized in that the step of acquiring at least one canonical reflection matrix Rui(t) comprises insonification of the medium with a series of plane waves with a delay τ'(u) applied to each signal at emission for the formation of a wavefront inclined at an angle θin with respect to the transducer array, a backscattered field by the medium, R(uout, θin, t) is measured by all the transducers at position uout for each incident plane wave θin, the set of responses forming a canonical reflection matrix Ruθ(t)=[ R(uout, θin, t)].

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

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

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

8. A method according to any one of the preceding claims, characterized in that step b) comprises the following steps: - a first step of determining a focused reflection matrix^^^( by projecting the canonical reflection matrix Rui(t) onto the basis^ of the diffusing screen according to the following equation: in which the matrix ^^^(^, ) is the Fourier transform of each canonical reflection matrix ^^^(^), ^^^(^) = ∫ ^^ ^^^^ ^^^^ ^^^(^)^; the matrix ^ ^^ ( ^ )is the reception pass-through matrix adapted for the pass-through from the reception basis (u) to the basis ^ of the screen diffusing at the pulse ^ of the ultrasonic waves; the matrix is the emission transition matrix adapted for the transition from the emission basis (i) to the basis ^ of the diffusing screen and to the pulsation ^ of the ultrasonic waves; the symbols ∗ and † respectively denote the matrix operations of conjugation and transposition-conjugation; the symbol × denotes a matrix product, - a second step of determining a compensated matrix ^^(^^^^, ^^^, ^) by compensating the curvature of wavefronts in the plane of the diffusing screen according to the following equation: avec = ^ ^ ^ ^^^, a parabolic phase term under the paraxial approximation; ^^^^ being a first spatial position point corresponding to a virtual output transducer; ^^^ being a second spatial position point corresponding to a virtual input transducer, - a third step of determining the focused reflection matrix^′^^(^) by performing a change of variable defined by: from the compensated matrix in order to obtain the following relationship between the matrix coefficients 9. A method according to any one of the preceding claims, characterized in that, in step c), the matrix imaging algorithm is an iterative CLASS algorithm (Closed-Loop Accumulation of Single Scattering), this CLASS algorithm comprising the following steps: - construction of an estimator of the angular spectrum of the object's reflectivity by summing hyperdiagonals of the focused reflection matrix^′^^(^) , these hyperdiagonals being defined such that ^^ = ^^^ + ^^^^ = ^^^^^^^^^^, and the estimator is defined according to the following equation: n-1 being the number - application of a phase conjugate of the estimator to the focused reflection matrix ^′^^(^) so as to make the object virtually coherent: ^ (^^^) ^ ^^ is a coherent matrix, - application on a coherent matrix of a time window of ultrasonic echoes consisting, in the frequency domain, by a convolution with a function whose bandwidth Δ^ is inversely proportional to the duration Δ^ of the time window applied to the ultrasonic signals in the time domain: with ℬ(^^, Δ^) the frequency filter of characteristic width Δ^- determination of two estimators, ^^^^(^^^ , ^) and ^^^^^(^^^^, ^), of the transfer function of the diffusing screen by summing the rows and columns of the reflection matrix - application of the phase conjugates of these two estimators on the reflection matrix to obtain a reflection matrix pour in which the phase shift induced by the diffusing screen has been compensated: - iteration of the steps of the CLASS type algorithm in order to converge towards a corrected reflection matrix in the plane of the diffusing screen, then reinjection of the parabolic phase terms that had been previously compensated:

10. A method according to claim 9, characterized in that step d) of projecting the corrected reflection matrix onto the plane of the object ^ further comprises a summation of the results on the frequencies according to the following equation the matrix is the change-of-basis matrix (^) to the focused basis (^) at depth ^^ and angular frequency ^.et ^ ^ are the lower and upper bounds of the bandwidth of the ultrasonic signals.

11. A method according to claim 10, characterized in that step e) of constructing an image of the object is obtained by considering the diagonal of the reflection matrix: ℐ(^, ^^) = ^(^, ^, ^^) with ^ the position vector in the plane of the object.

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

13. Method according to claim 12, characterized in that the distortion matrix technique with a spatio-frequency correction basis (^) comprises the following steps: - calculation of a dual reflection matrix between the focused basis (x) and the spatio-frequency correction basis (^): The matrix ^^^(^) is the transition matrix describing the projection of the transducer basis (u) onto the spatio-frequency correction basis (^) at the angular frequency ^. The matrix ^^^(^) is the transition matrix describing the projection of the emission basis (i) onto the focused basis (^) at the depth ^^ and the angular frequency ^. A frequency distortion matrix ^^^(^^, ^) is deduced by performing the term-by-term product of the dual reflection matrix with the phase conjugate matrix of the reference matrix that would be obtained without a diffusing screen, i.e., here ^ ^^ ^ ( ^ ) : Tel que - Calculation of the correlation matrix ^^^ ,- Determination of the spatio-frequency correction law ^(^^) by analysis of the correlation matrix ^ ^^ 14. A method according to claim 13, characterized in that the correlation matrix coefficients are given by:

15. A method according to claim 13, characterized in that the decorrelation matrix C is determined in the focused basis ^, by the following calculation of the elements of the correction matrix C = ^^^: * is the conjugation operator.

16. A method according to any one of claims 13 to 15, characterized in that the analysis of the correlation matrix ^^^ (^^) is performed by an eigenvalue decomposition of the correlation matrix ^ ^^ (^ ^), and the spatio-frequency correction law ^(^^) is the first eigenvector ^^ of the correlation matrix ^^^(^^) in the correction basis (^).

17. A method according to any one of claims 13 to 15, characterized in that the analysis of the correlation matrix ^^^(^^) is performed by a singular value decomposition of the distortion matrix rearranged as follows: ^(^^) = [^({^, ^}, x, ^^)].

18. A method according to any one of claims 13 to 15, characterized in that the analysis of the correlation matrix is performed by solving the following equation: ^(^^) = exp^^ iteratively using the following expression, which corresponds to an iterative phase-reversal calculation: where × is the matrix product, with: ^^ an arbitrary wavefront, for example ^^ = [1 ⋯ 1] ^19. A method according to any one of claims 13 to 15, characterized in that the analysis of the correlation matrix Cxx is carried out by solving the following equation: ^(^^) = exp(^ arg{^^^(^^) × ^(^^)}) where × is the matrix product, iteratively by the following expression: ^^^^(^^) = exp(^ arg{^^^(^^) × ^^(^^)}) where × is the matrix product, with ^^ an arbitrary wavefront, for example ^^ = [1 ⋯ 1] ^20. Use of a predetermined spatio-frequency correction law on an image acquired of an object by means of a predefined array of transducers and a predefined diffusing screen, and by performing steps d) and e) according to claim 1; this predetermined spatio-frequency correction law being determined by applying a matrix imaging algorithm following a preliminary phase during which steps a) to c) of claim 1 were performed using an assembly comprising the predefined array of transducers, the predefined diffusing screen, and a phantom-type model object; a reflectivity statistic and a speed of sound of said assembly being predefined. 21.Ultrasonic construction system for a confocal image of an object contained in a medium, the system comprising: - an array (10) of transducers adapted to generate a series of ultrasonic waves incident in a region of interest of the medium, and to measure over time the ultrasonic waves backscattered by said region of interest; - a diffusing screen along the path of the waves between the array of transducers and the medium to be imaged; and - a computing unit (30) connected to the array of transducers and adapted to implement the method according to any one of claims 1 to 19.

22. Product: computer program comprising instructions which, when the program is executed by the computing unit of the ultrasonic construction system according to claim 21, cause the latter to implement the steps of the method according to any one of claims 1 to 19.

23. Computer-readable support comprising instructions which, when executed by the computing unit of the ultrasonic construction system according to claim 21, cause it to carry out the steps of the process according to any one of claims 1 to 19.

Images