METHOD AND SYSTEM FOR ULTRASONIC CHARACTERIZATION OF A MEDIUM

Abstract

Method and system for ultrasonic characterization of a medium Method for ultrasonic characterization of a medium comprising a step of generating a series of incident ultrasonic waves, a step of generating an experimental reflection matrix R ui (t) defined between the emission base (i) at the input and a reception base (u) at the output, a step of determining a focused reflection matrix RFoc(r in , r out , δt) of the medium between a virtual input transducer (TVin) calculated from an input focus of the experimental reflection matrix and a virtual output transducer (TVout) calculated from an output focus of the experimental reflection matrix, the responses of the virtual output transducer (TVout) being taken at a time instant shifted by an additional delay δt relative to a time instant of the responses of the virtual input transducer (TVin). Figure for abstract: FIGURE 4

Description

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

[0001] The present description relates to methods and systems for ultrasonic characterization of a medium, and applies in particular to medical imaging or non-destructive testing and more generally to all fields in which ultrasonic imaging can be used. STATE OF THE ART

[0002] In the field of acoustic imaging, we seek to characterize a totally or partially unknown environment by actively probing it using ultrasonic waves. This is notably the principle of the ultrasound scanner used in medical imaging.

[0003] The resolution of an acoustic imaging system can be defined as the ability to discern small details of an object. In principle, an acoustic imaging system is diffraction limited and the theoretical resolution is given by X / 2 (where / is the wavelength of sound in the medium), or by the finite angular aperture of the detector. In practice, however, the resolution is often degraded by variations in sound speeds when the propagation medium is heterogeneous.

[0004] Indeed, most of the time in acoustic imaging, the medium is considered homogeneous, with a constant speed of sound c 0. However, the hypothesis of a homogeneous medium is not always respected. For example, in the case of liver ultrasound, the probe is placed between the patient's ribs. The acoustic waves pass through a succession of layers of fat and muscle before reaching the targeted organ. Soft tissues each have different mechanical properties. The speed of sound is therefore far from homogeneous, and it can vary for example between 1450 m / s for adipose tissue and 1600 m / s for the liver. Variations in the speed of sound cause a different phase shift of the waves depending on the locations through which they propagate. This results in an aberration of the acoustic wavefront which leads to a distortion of the resulting ultrasound image, and therefore to a degradation of its resolution and contrast.These aberrations can be such that they do not allow a reliable image to be reconstructed, compromising the results, for example during a medical examination.

[0005] As illustrated in Figures 1A to 1C, conventional ultrasound methods use an array 10 of piezoelectric transducers 11 that can emit and / or receive ultrasonic pulses independently. The position of each of the transducers by the vector u. When such a network is placed opposite a medium 20 that one seeks to study, the latter can be insonified and imaged in different ways.

[0006] A first way to generate an ultrasound image of the medium to be studied is to emit an ultrasound pulse from one of the transducers of the network whose position is identified by the vector uî« (figure 1A, left diagram). This gives rise to a divergent cylindrical (or spherical) incident wave for a 1D (or 2D) network of transducers. This wave is reflected by the diffusers 21 of the medium 20 and the backscattered field is recorded by each of the transducers 11 as a function of time (figure 1A, right diagram). By repeating this operation with each transducer used successively as a source, the set of impulse responses R (uout, uin, t) between each transducer is measured, where the vector u««t designates the position of the detector. These responses form the reflection matrix Ruu(z) expressed in the base of the transducers.The advantage of such a measurement lies in the fact that this matrix contains all the information on the medium studied, a set of matrix operations can then be applied to it for imaging purposes of the medium, for example. On the other hand, such an acquisition assumes that the medium remains fixed for the entire duration of the measurements, which can be very difficult in the case of in-vivo use. In addition, the energy emitted by a single piezoelectric element is low, which can induce a poor signal-to-noise ratio.

[0007] Other methods are known for generating an image of the medium to be studied in which focused emissions are carried out using a beamforming technique. As shown in Figure 1B, left diagram, these methods consist of applying to the transducers 11 a set of appropriate delays, based on a homogeneous speed model, in order to correct the wave travel times so that all the pulses arrive together at the targeted focal point, of position rin. The sound speed hypothesis retained will be noted c 0 ■ Due to the physical limits of diffraction, the emitted ultrasounds are concentrated in an area delimited by the opening of the ultrasound probe. In order to construct an ultrasound image, a focusing step is also carried out on reception.All the echoes captured by the elements 11 of the network 10 are then processed to simulate the effect of a lens in reception, as described in Figure 1B, right diagram. The signals received by the transducers are put back into phase by shifting them in time. These delays are identical to those applied to transmission. In the transmission phase, all the signals interfere at the position point ri«. In reception, the signals coming from this same point rout = rin interfere electronically by summing the signals at the ballistic time . t = ( Il Uout - rin II + Il Uin - rin II ) / CQ. This summation gives the result final focusing in reception. The method illustrated in Figure 1B, called the confocal method with double focusing in emission and reception, allows direct imaging of the reflectivity of the medium with a lateral resolution limited by diffraction, an excellent axial resolution only limited by the duration of the initial pulse and an excellent contrast. However, this method is time-consuming because it requires physical focusing in emission at each of the points of the medium or at least at a given depth, on each of the lines of the image.

[0008] Another imaging technique, developed more recently, consists of generating an image of the medium by insonifying the medium with a series of plane waves. Figure IC illustrates the principle of this so-called plane wave ultrasound, described for example in the article by G. Montaldo et al. “Coherent plane-wave compounding for very high frame rate ultrasonography and transient elastography” (IEEE Trans. Ultrason., Ferroelect. Freq. Control 56 489-506, 2009). Delays are applied to each signal at the transmission (Figure IC, left diagram) to form a wavefront inclined at an angle relative to the transducer array 10. At the reception (Figure IC, right diagram), the backscattered field from the medium, R ( uout, 0in. t ) is measured by all position sensors u»«t for a series of incident plane waves whose incidence angle Gin is varied.All of these responses form a reflection matrix RU0Ù) defined between the spatial Fourier basis (or plane wave basis) at the input and the basis of the transducers at the output. Once this matrix is recorded, the signals are time-shifted before being summed coherently in order to digitally focus the data at transmission and reception for each position point rm. The number of acquisitions required to form an ultrasound image is thus advantageously reduced compared to standard ultrasound (focused emissions), and this for the same level of contrast and resolution of the ultrasound image.

[0009] Figure 2 illustrates the influence of aberrations of the medium on conventional ultrasound imaging methods (Figures 1A to 1C). These aberrations appear when the speed of sound of the medium c(r) does not correspond to the hypothesis of a homogeneous medium with a constant speed of sound c 0 ■ The delays initially determined from this hypothesis and to be applied to each of the transducers of the network at transmission and reception are then not optimal for the evaluation of an image of the medium. In Figure 2, an aberrator layer 22 induces a distortion of the incident wavefront. At transmission or excitation, step 25, the delay laws used do not allow the acoustic energy to be concentrated in an area delimited by the limits of diffraction, areas usually called focal spot.At reception, in step 26, the delay laws used do not allow the ultrasonic signals coming from the focal point of the medium to be correctly selected, and mix the signals. coming from a focal spot that is also aberrated. This results in a double aberration in the image construction process, which significantly degrades its resolution. New delay laws can then be recalculated to compensate for the effect of the aberrant layer by adding, for example, an additional delay law to the delays generally used in channel formation.

[0010] However, these aberration corrections do not completely correct either these aberrations or the degradation in resolution. There is a need to better estimate the quality of the focusing in the medium.

[0011] The paper “The van Cittert-Zemike theorem in puise écho measurements”, (Raoul Mallart and Mathias Fink, J. Acoust. Soc. Am. 90(5), November 1991) studied the statistical properties of the field reflected by a random medium in a simple scattering regime. In particular, it is shown that, for a focused incident wave, the spatial covariance of the reflected field is proportional, from the far field, to the Fourier transform of the aperture function in transmission. In other words, this theorem explains that the study of the statistical properties of the reflected field in the far field makes it possible to determine the quality of focusing of the incident wave in the medium.

[0012] However, this approach only provides a global and average estimate of the resolution of an ultrasound image because it requires statistically averaging the correlations of the reflected field over a large number of realizations of the disorder, i.e. over a large number of focal points of the incident wave. It does not allow for a precise and local evaluation of the focusing quality at each point of the image. Furthermore, this approach is only valid in the simple diffusion regime.

[0013] It is therefore necessary to propose a method which overcomes each of the aforementioned drawbacks. SUMMARY

[0014] The present description relates, according to a first aspect, to a method for ultrasonic characterization of a medium, for carrying out a local spectral analysis in the medium, the method comprising:

[0015] - a step of generating a series of incident ultrasonic waves (USin) in a area of said medium, by means of an array (10) of transducers (11), said series of incident ultrasonic waves being an emission base i; and

[0016] - a step of generating an experimental reflection matrix R ui (t) defined between the transmission base i at the input and a reception base u at the output;

[0017] - a step of determining a focused reflection matrix RFoc(r, ôt) which comprises responses of the medium between a virtual input transducer (TVin) of spatial position r in and a virtual output transducer (TVout) of spatial position r out , the virtual input and output transducers being superimposed at the same position spatial r, with r in = r out = r, and the responses of the output virtual transducer (TV out) being taken at a time instant shifted by an additional delay ö relative to a time instant of the responses of the input virtual transducer (TVin), and

[0018] - a step of determining a frequency matrix RFreqt(r, œ) which is a time Fourier transform of each cell of the focused reflection matrix RFoc(r, ôt), this time Fourier transform being:

[0019] RFreq t {r, w) -TF^RFoc^ v, (¾)]

[0020] in which

[0021] TFt is the time Fourier transform, and

[0022] co is a pulsation with co = 2irf, f being the frequency corresponding to said pulsation.

[0023] Thanks to these provisions, the method advantageously makes it possible to locally probe the medium at any point and in any direction and with any time shift relative to a ballistic time of propagation of the ultrasound background in the medium.

[0024] This method applied to virtual confocal input and output transducers makes it possible to determine a frequency matrix after focusing which characterizes the frequency response of the medium at this confocal point of spatial position r. This frequency response is a function of the nature of the medium at this point or in this focal spot. This frequency response can make it possible to identify and characterize in real time scatterers, such as bubbles in the medium or to extract their behavior to improve the ultrasound image.

[0025] In various embodiments of the method according to the present disclosure, one and / or the other of the following provisions may optionally be further used.

[0026] According to a variant, the method further comprises a filtering step during which a frequency filtering of the cells of said frequency matrix is carried out.

[0027] According to a variant, the filtering extracts harmonic components of a fundamental frequency of the incident ultrasonic waves (USin).

[0028] According to a variant, the method further comprises a step of determining an average spectrum at a depth S(z, co) determined by an average of at least part of the spectra of the frequency matrix at a predetermined depth z in the medium.

[0029] According to a variant, a first average spectrum is determined at a first depth of the medium, a second average spectrum is determined at a second depth of the medium, and the first average spectrum and the second average spectrum are compared to deduce an attenuation value of the medium.

[0030] According to a variant, the method further comprises a step of determining the spectral correlation width ôco(r) for the point of spatial position r, by calculating the width at half-height of the autocorrelation of each spectrum of the fre- quantity RFreqt(r, œ), that is to say by the following formula: remove (r) - FWMHy-^ J RFreq^r, œ)RFreqt (r, œ + d(e) dw

[0032] in which

[0033] FWMH is the full width half maximum calculation function

[0034] ()* is the complex conjugation function,

[0035] a' and o?+ which are limit pulsations, Aco is the interval of the limit pulsations.

[0036] According to a variant, the method further comprises a step of determining at least at least one spectral correlation image, said at least one spectral correlation image being obtained by determining the spectral correlation widths ôco(r) for a plurality of points of the medium each corresponding to a point of the medium of spatial position r.

[0037] According to a variant, at the step of determining the focused reflection matrix:

[0038] the calculation of the responses of the virtual input transducer (TVin) corresponds to a input focusing process from the experimental reflection matrix R ui (t) which uses a forward time of flight of the waves between the transmitting base and the virtual input transducer (TVin) to create an input focal spot at the spatial position r in,

[0039] the calculation of the responses of the virtual output transducer (TVout) corresponds to an output focusing process from the experimental reflection matrix R ui (t) which uses a return flight time of the waves between the virtual output transducer (TVout) and the transducers of the reception base u, to create an output focal spot at the spatial position r out,

[0040] the additional delay ö being a time delay added to the outward and return flight times during the focusing processes.

[0041] According to a variant, the focused reflection matrix is calculated by the following formula:

[0042] RFoC (Fjn, Fout, Ôt) — VT. xt. ZL ^ui(«out' hn' ^*out> ^out' hn' ) 'in «out

[0043] in which

[0044] Nin is the number of elements of the emission base (i),

[0045] Nout is the number of elements of the receiving base (u) at output,

[0046] R ui (t) is the experimental reflection matrix, of which Rut(-, ijn, ( rin- rouo h™ àt Y) is the element of the experimental reflection matrix R ui (t) recorded by the spatial position transducer u out following the emission of index i in in the emission base and at time r,

[0047] r is a time which is the sum of the outward flight time rin of the ultrasonic wave between the transducers of the emission base (i) and the virtual input transducer (TVin ) of spatial position r in, and of the return flight time rout of the ultrasonic wave between the output transducer (TVout) of spatial position r out and the transducers of the receiving base u, and of the additional delay ôt, as explained by the following formula:

[0048] T(rin, rout, uOHt, iin, ôt) = Tin (rin, iin) + rout(ront, uout)+ôt

[0049] The present description relates, according to a second aspect, to a system for ultrasonic characterization of a medium for carrying out a local spectral analysis in the medium, and configured for the implementation of ultrasonic characterization methods as described previously. The ultrasonic characterization system according to the second aspect comprises:

[0050] - an array of transducers adapted to generate a series of ultrasonic waves in incident in an area of the medium, and to record as a function of time the ultrasonic waves backscattered by said area; and

[0051] - a computing unit associated with the transducer network and adapted to implement implements the method according to the first aspect. BRIEF DESCRIPTION OF THE FIGURES

[0052] Other advantages and characteristics of the technique presented above will appear on reading the detailed description below, presented in a non-limiting manner for the purposes of illustration, made with reference to the figures in which:

[0053] Figures 1A to 1C (already described) illustrate known transmission / reception mechanisms for ultrasound imaging and quantification;

[0054] Figure 2 (already described) illustrates the impact of aberrations in ultrasound imaging, according to the prior art;

[0055] Figure 3 illustrates an example of an ultrasonic characterization system for implementing the ultrasonic characterization methods according to the present description;

[0056] Figure 4 illustrates the definitions used in the ultrasonic characterization method according to the present description;

[0057] Figure 5 shows an ultrasound image in which a position associated with an echogenic element is selected and propagation images around this position are determined for several additional delays;

[0058] Figure 6 shows an ultrasound image in which a position associated with a set of underresolved scatterers of comparable reflectivity is selected and propagation images around this position are determined for several additional delays;

[0059] Figure 7 shows an ultrasound image in which a set of positions associated with under-resolved scatterers of comparable reflectivity are selected and coherent wave propagation images resulting from a combination of the images propagation times associated with each selected position are determined for several additional time frames;

[0060] Figure 8A shows curves of temporal variations of the intensity of the central point of a propagation image associated with a position corresponding to under-resolved scatterers and of comparable reflectivity and of the coherent wave propagation image;

[0061] Figure 8B shows frequency spectra of the curves of Figure 8A;

[0062] Figure 9A shows the image amplitude of the wavefront associated with the same position than that of figure 5;

[0063] Figure 9B shows the real part of the same wavefront image as used in Figure 9A;

[0064] Figure 10 shows the amplitude of several wavefront images associated with the same position as that selected for Figure 5 and obtained for 3 assumed sound speeds, and intensity curves on the ordinate axis Az of these wavefront images;

[0065] Figure 11 shows ultrasound images and corresponding integrated sound velocity images;

[0066] Figure 12 shows ultrasound images obtained without aberration correction (image A), with usual lateral aberration correction (image B) and with axial aberration correction using measurements in wavefront images according to the present disclosure;

[0067] Figure 13 shows an ultrasound image (A) comprising several areas with muscle fibers inclined in various directions, and wavefront images (B, C, D, E) corresponding to these different areas of the medium;

[0068] Figure 14 shows a curve for calculating the angle of a preferred direction of muscle fiber inclination in the medium;

[0069] Figure 15 shows a matrix of determined preferred directions superimposed on an ultrasound image of a medium with muscle fibers;

[0070] Figure 16 shows an ultrasound image (A), an enlargement of an area of this ultrasound image (B) around a particular point, the local time signal in real part (C) and amplitude (D) estimated for this particular point and the spectral analysis of this local time signal of the medium;

[0071] Figure 17 shows an ultrasound image (A) and an estimate of the average spectrum as a function of depth Z for the corresponding ultrasound image of this figure;

[0072] Figure 18 shows an ultrasound image (A) and the spectral correlation image determined for the corresponding ultrasound image of this figure.

[0073] In the various embodiments which will be described with reference to the figures, similar or identical elements bear the same references unless otherwise stipulated. DETAILED DESCRIPTION

[0074] In the following detailed description, only certain embodiments are described in detail to ensure clarity of the disclosure, but these examples are not intended to limit the general scope of the principles emerging from the present description.

[0075] The various embodiments and aspects described in the present description may be combined or simplified in multiple ways. In particular, the steps of the different methods may be repeated, interchanged, and / or executed in parallel, unless otherwise specified.

[0076] The present description relates to methods and systems for ultrasonic characterization of a medium, and applies in particular to medical imaging of living or non-living tissues. The medium is for example a heterogeneous medium that one seeks to characterize in order, for example, to identify and / or characterize heterogeneities. Optionally, these methods and systems can be applied to the non-destructive testing of products, such as metal parts or other. These characterization techniques are thus non-invasive in the medium, which is then preserved.

[0077] Figure 3 illustrates an example of an ultrasonic characterization system 40 for implementing the methods for ultrasonic characterization of a medium such as a heterogeneous medium 20, according to the present description. The system 40 comprises at least one network 10 of transducers 11, for example a linear or two-dimensional or matrix network; the transducers are for example ultrasonic piezoelectric transducers which may conventionally be in the form of a rigid bar placed in direct or indirect contact with the medium 20. The network of transducers is for example part of a probing device 41 (usually called a probe); the network of transducers is connected to a computing unit 42, which may itself be connected or associated with a display device 43; the computing unit emits and records electrical signals to and / or coming from each of the transducers 11.The ultrasonic transducers then transform these electrical signals into ultrasonic waves and vice versa. By "connection" or "link" between the probing device 41, the computing unit 42 and the display device 43, we mean any type of wired connection of the electrical or optical type, or any type of wireless connection using any protocol such as WiFi™, Bluetooth™ or others. These connections or links are one-way or two-way.

[0078] The calculation unit 42 is configured for the implementation of calculation or processing steps, in particular for the implementation of method steps according to the present description. By convention, a spatial reference frame of the medium 20 is defined, by taking a first X axis and a second Z axis perpendicular thereto. For simplification, the first X axis corresponds to the transverse direction in which the transducers 11 are aligned for a linear array, and the second Z axis corresponds to the depth of the medium 20 relative to this array 10 of transducers 11. This definition can be adapted to the context and thus, for example, extended to a three-axis spatial reference frame in the case of a two-dimensional array 10.

[0079] In Figure 3 as in the rest of the description, reference is made to a network of transducers for transmission and reception, it being understood that, in a more general case, several networks of transducers may be used simultaneously. Similarly, a network may consist of one (1) to N translators, of identical type or of different natures. The transducers may be both transmitters and receivers, or only transmitters for some and only receivers for others.

[0080] The transducer array serves for example as both a transmitter and a receiver, or is made up of several sub-arrays of transducers, some being dedicated to the transmission, others to the reception of ultrasonic waves. By transducer array is meant at least one transducer, an aligned or non-aligned sequence of transducers, or a matrix of transducers.

[0081] When in the present description, reference is made to calculation or processing steps for the implementation in particular of method steps, it is understood that each calculation or processing step can be implemented by software, hardware, firmware, microcode or any appropriate combination of these technologies or neighboring technologies. When software is used, each calculation or processing step can be implemented by computer program instructions or code which can be for example interpreted, or executed. These instructions can be stored or transmitted to a storage medium readable by a computer (or computing unit) and / or be executed by a computer (or computing unit) in order to implement these calculation or processing steps.

[0082] Analysis of a point in the middle by focused reflection matrix

[0083] The present description describes methods and systems for ultrasonic characterization of a medium. In practical cases, the medium is assumed to be heterogeneous. These methods and systems are based on definitions represented in Figure 4:

[0084] We define in the middle:

[0085] - a first point PI of spatial position r in the spatial reference frame of the middle,

[0086] - a second point P2 of spatial position r out in the spatial reference frame of the middle.

[0087] These spatial positions r in and r out are noted in bold, to signify that these elements are position vectors, vectors taken in the spatial reference frame of the middle (X, Z). Other representations and definitions of the positions of the points are possible and ac- transferable to any specialist in the ultrasound profession.

[0088] These two points PI and P2 are chosen at a relatively short distance from each other, that is to say a few millimeters from each other, and for example twenty (20) millimeters or less, at ultrasonic frequencies.

[0089] As shown in Figure 4, the ultrasonic characterization method implemented by the calculation unit 42 of the system 40 comprises:

[0090] - a step of generating a series of incident ultrasonic waves USin in a area of said medium, by means of an array 10 of transducers 11, said series of incident ultrasonic waves being an emission base i; and

[0091] - a step of generating an experimental reflection matrix R ui (t) defined between the transmission base i at the input and a reception base u at the output;

[0092] - a step of determining a focused reflection matrix RFoc(r in , r out , ôt) which comprises responses of the medium between a virtual input transducer TVin of spatial position r in and a virtual output transducer TVout of spatial position r out, the responses of the virtual output transducer TVout being taken at a time instant offset by an additional delay öt relative to a time instant of the responses of the virtual input transducer TVin.

[0093] The responses of the focused reflection matrix RFoc(r in , r out, ôt) correspond to an acoustic pressure field calculated at any point in the medium.

[0094] The emission base i at the input is for example a base of waves each generated by a single one of the transducers 11 of the network 10 or a base of plane waves of angular inclination 0 relative to the axis X, as described previously in the description of figures 1A to 1C.

[0095] The reception base u is for example the base of the transducers 11. Optionally, another reception base can be used for reception.

[0096] Thus, the step of generating the ultrasonic waves is understood between the emission base i and the reception base u. This step of ultrasonic generation is therefore defined for any type of ultrasonic waves of the focused or non-focused type, such as plane waves.

[0097] In the matrix generation step, the experimental reflection matrix R ui (t) is defined between the emission base i at the input and a reception base u at the output. This matrix contains all the temporal responses of the medium, measured at time t by each transducer 11 of spatial coordinate u out and for each emission i in . It is understood that the elements denoted with the index "in" refer to the emission (i.e. the input) and the elements denoted with the index "out" refer to the reception (i.e. the output). This experimental matrix can also be recorded and / or stored, for example in the memory of the calculation unit, or on any other medium, removable or not, allowing permanent or temporary storage.

[0098] More precisely, in the step of determining the focused reflection matrix RFoc(r in , r out , ôt), we apply:

[0099] - an input focusing process from the reflection matrix exp rimental R ui (t) which uses a time of flight on the way between the emission base (i) and the virtual transducer at input TVin and which creates a so-called input focal spot around the first point PI of spatial position r in , said input focal spot corresponding to the virtual input transducer TVin,

[0100] - an output focusing process from the reflection matrix exp rimental R ui (t) which uses a return flight time of the waves between the virtual output transducer (TVout) and the transducers of the reception base (u) and which creates a so-called output focal spot around the second point P2 of spatial position r out, said output focal spot corresponding to the virtual output transducer TVout,

[0101] - an additional delay ôt which is a time delay added to the outward flight times and back during focusing processes.

[0102] These input and output focusing processes actually form an input-output focusing process, referred to in the remainder of this description as the focusing process.

[0103] In other words, in this ultrasonic characterization method, the virtual input transducer TVin corresponds to an ultrasonic "virtual source" located at the spatial position r in in the medium and the virtual output transducer TVout corresponds to an ultrasonic "virtual sensor" located at the spatial position r out. This virtual source and sensor are spatially separated by the difference in their spatial positions Ar = r out - r in • Us are also temporally separated by the additional delay ôt, which is an arbitrary delay and adjustable independently of the spatial distance lArl. Thus, the method is able to probe the medium around the point PI and / or the point P2, spatially and / or temporally, which makes it possible to obtain new information in these two dimensions (spatial and temporal) on the propagation of the waves.

[0104] For example, a calculation of the focused reflection matrix RFoc(r in , r out, ôt) of the medium between the virtual input transducer TVin and the virtual output transducer TV out by said input and output focusing processes, is an improved path forming method, which can be expressed by the following simplified formula:

[0105] RF<)C(ljn, rout, Ôt) — v 12. 12 ^ui (' hn, Emt- ^out' hn; ^0 ) linen uout

[0106] (Equ. 1)

[0107] in which

[0108] Nin is the number of elements of the emission base i,

[0109] Nout is the number of elements of the reception base u at output,

[0110] R ui (t) is the experimental reflection matrix, of which Roi ( Uout ' Vin- t ( r™, rout' Uout' hn, St ) ) is the element of the experimental reflection matrix R ui (t) recorded by the transducer u out following the emission i in at time r.

[0111] The time r is the sum of the outward flight time rin of the ultrasonic wave between the transducers of the transmission base i and the virtual input transducer TVin of spatial position r in (first point PI), of the return flight time rout of the ultrasonic wave between the virtual output transducer TVout of spatial position r out (second point P2) and the transducers of the reception base u, and of the additional delay ôt, as explained by the following formula:

[0112] (On- ^out' *in') ^in (On> hn) ^out (^out) "V St

[0113] (Equ. 2)

[0114] The flight times rin and rout are calculated from a sound speed model. The simplest hypothesis is to assume a homogeneous medium with a constant sound speed c 0 ■ In this case, the flight times are directly obtained from the distances between the probe transducers and the virtual transducers.

[0115] The number of elements of the transmission base Nin is for example greater than or equal to one (1), and advantageously greater than or equal to two (2). The number of elements of the reception base Nout is for example greater than or equal to two (2).

[0116] This improved path formation formula is therefore a double sum of the time responses recorded in the experimental reflection matrix R ui, a first sum according to the emission basis i translating a focusing at emission and a second sum according to the reception basis u linked to a focusing at reception, this calculation being carried out for the spatial coordinates of the two points PI and P2 (of spatial positions r in , r out ). The result of this improved path formation formula is therefore a time signal for these two spatial coordinates (r in , r out ), but which is also a function of the additional delay ôt between the input and the output, this additional delay being adjusted arbitrarily.

[0117] Such a channel formation formulation can also be supplemented by input and output weighting terms, often called apodization in reception and / or transmission. The entire series of channel formation formulas can thus be supplemented with these weightings by a technician in the field.

[0118] The recorded experimental reflection matrix R ui (t) may be a “real” matrix, i.e. composed of real coefficients in the time domain, the electrical signals recorded by each of the transducers being real numbers. Alternatively, this matrix may be a “complex” matrix, i.e. composed of complex values, for example in the case of demodulation for in-phase and quadrature channel formation (known in English as “beamforming IQ”).

[0119] We thus obtain a focused reflection matrix RFoc(r in , r out , ôt) which contains time signals. This focused reflection matrix is five (5) dimensional in the case of a linear probe; two spaces for the spatial positions r in and r out, as well as the additional delay ôt, which is very different and much richer in information than in focused reflection matrices of the prior art.

[0120] In this analysis, thanks to the additional delay ôt, the virtual input transducers TVin and output TVout are not defined at the same time instant, which makes it possible to virtually highlight the propagation of the ultrasonic wave between the first point PI of the virtual input transducer TVin and the second point P2 of the virtual output transducer TVout. This additional delay ôt can be positive or negative, which makes it possible to probe the focusing of the ultrasonic wave at the second point P2 respectively before and after a reference time instant of the paths of the ultrasonic wave in the medium.

[0121] This reference time instant is called the ballistic time tb. This ballistic time is the round trip time of the ultrasonic wave between the transducers of the transmission base i to the virtual input transducer TVin, then between the virtual output transducer TVout, and the transducers of the reception base u.

[0122] This ballistic time tb is defined by the following formula:

[0123] t b = ( || u out -r out || + || u in -r in || ) / c0

[0124] (Equ. 3)

[0125] in which:

[0126] c0 is the assumed speed of sound of the medium (speed of propagation of ultrasonic waves).

[0127] Thanks to these provisions, the method makes it possible to probe the medium very locally at the second point P2 relative to the first point PI, with an additional delay ôt between the signals from these two points. This local information is entirely contained in the values of the time response calculated from the focused reflection matrix, RFoc(r in , r out, ôt) of the medium and which can be used a posteriori (and without new emission and / or acquisition) to characterize each point of the medium.

[0128] Thus, it is possible to deduce from this temporal response after channel formation, an estimate of the reflectivity of the medium by considering the absolute value of the confocal signals characterized by equal spatial positions at input and output r in = r out and at the zero additional delay ôt = 0 (i.e. at the ballistic time without this additional delay). This estimate of the reflectivity of the medium is the value of a pixel of an ultrasound image of the medium. Thus, to construct an ultrasound image, one can scan or choose a set of spatial positions r = r in = r out which correspond to a set of pixel positions in the ultrasound image.

[0129] The ultrasound image I(0)(r) can then be constructed from the focused reflection matrix RFoc(r in, r out, ôt) by taking r = r in = r out, and ôt = 0, that is:

[0130] / °\r) =RFoc(rin, rout = rn, Ôt = O)

[0131] (Equ. 4) Propagation images around a midpoint

[0132] The ultrasonic characterization method implemented by the calculation unit 42 of the system 40 can then be completed by constructing one or more propagation images from the focused reflection matrix RFoc(r in , r out, ôt), this or these propagation images being determined for one or more values of the additional delay ôt, for a virtual input transducer TVin (first points PI) and for a plurality of virtual output transducers TVout (second points P2), the virtual output transducers TVout being located at spatial positions r out around the virtual input transducer TVin of spatial position r in .

[0133] In the case of a single propagation image, this propagation image is determined from the focused reflection matrix RFoc(r in , r out, ôt) for a single predetermined additional delay ôt.

[0134] This propagation image represents the way in which an ultrasonic wave propagates between the virtual transducers, and for example near the virtual input transducer, and at a time instant equal to the additional delay (time instant taken relative to the ballistic time).

[0135] The system 40 is then optionally capable of displaying one or more propagation images on the display device 43.

[0136] The calculation unit 42 can also calculate a series of propagation images for several additional temporally successive delays, for example to construct a propagation film of the ultrasonic wave around the virtual input transducer TV in (first point PI). This propagation film can possibly be displayed on the display device 43 or on any other media.

[0137] The additional temporally successive delays taken to construct this propagation film are taken in our example in an additional delay interval.

[0138] For example, the additional delay interval may take the form of a time range adapted to go from the virtual input transducer TVin of spatial position r in to all the virtual output transducers TVout of spatial position r out. This additional delay interval is then for example noted [-ôtmin, +ôtmax], with ôtmin = zout max-zin / Co and ôtmax = zOutmin-Zin / c0, where zin and zout are respectively the depths in the positive direction of the second Z axis of the virtual input transducer TVin. of spatial position r in and of the virtual output transducer TVout of spatial position r out; And

[0139] For example, the additional delay interval can be symmetrical around the zero value (ôt=0) and of amplitude ôtmax, this additional delay interval being noted [-ôtmax , +ôtmax]. For example, it can be defined by ôtmax = max(IArl) / c 0 for the TVout output transducers used for the propagation image.

[0140] The reference image A of Figure 5 shows an ultrasound image of a phantom or study example medium, which includes predetermined heterogeneities of several types. In this medium, a rectangular analysis zone ZAout is considered (composed of second points P2 of virtual output transducers TVout) which is scanned by calculation to construct one or more propagation images around the first point PI of virtual input transducer TVin of spatial position r in , here located in the middle of the analysis zone ZAout. The analysis zone can be positioned at any position independently of the position of the virtual input transducer. However, it is particularly interesting that the analysis zone surrounds the virtual input transducer.

[0141] The virtual input transducer TVin (first point PI) is, in this reference image A, located on or near a reflective element (echogenic target) of the medium.

[0142] The reference images B to F of Figure 5 are propagation images of the analysis zone ZAout of image A of Figure 5, for five (5) additional delay values ø. These additional delays are -3.86 ps, -1.93 ps, 0 ps, 1.93 ps, 3.86 ps in our illustrative example. Each propagation image is composed of:

[0143] - of a first image of index 1 (for example Bi) corresponding to the amplitude of the values of the focused reflection matrix for a set of points in the analysis area ZAout, and

[0144] - of a second image of index 2 (for example B2) corresponding to the real part values of the focused reflection matrix for the same set of points in the ZAout analysis area.

[0145] In these images, the level of the amplitude or the level of the real part is represented by a gray level whose scale appears on the images Bi and B2 of figure 5. The points or pixels of these propagation images have the spatial position Ar = r out - r in, that is to say the relative position of the virtual output transducers TV out of spatial position r out with respect to the position r in of the virtual input transducer TVin. In the figure illustrating this example, the coordinates are noted Ax on the abscissa, and Az on the ordinate on these images.

[0146] These propagation images illustrate the explanations given previously about the focused reflection matrix calculated with an additional delay ø: They allow the propagation of a coherent wave to be visualized. In particular, for the negative additional delays going towards zero, this coherent wave is convergent towards the first PI point of the virtual input transducer TVin, and it is ideally concentrated and focused into a focal spot delimited by the diffraction limits for the zero additional delay (β = 0). This coherent wave is then divergent for positive and increasing additional delays.

[0147] This coherent wave results from a digital time reversal process of the echoes coming from the virtual source located at the virtual input transducer of spatial position r in and measured by the transducers of the probe. By performing the channel formation in reception for a set of spatial positions r out around the virtual input transducer of spatial position r in, and at the various additional times ôt, we illustrate the focusing in reception outside the confocal position (i.e. r in = r out ).

[0148] As these propagation images are obtained for a first point PI of the virtual input transducer TVin located on or near a reflective element (echogenic target) of the medium, the coherent background is easily identifiable on these propagation images and has a good signal-to-noise ratio compared to the surrounding signals.

[0149] The reference image A of figure 6 shows the same ultrasound image as that of figure 5, for which another rectangular analysis zone ZA'out is considered (of the same dimension in this example) which is scanned by calculation to construct propagation images around another first point PI' of virtual input transducer TV'in of spatial position r in .

[0150] This other first point PI' of virtual input transducer TV'in is here associated with a resolution cell containing a set of under-resolved scatterers, randomly arranged and having a comparable reflectivity. At the wavelength scale, such a medium is called "ultrasonic speckle" and is characterized by a random reflectivity resulting from the destructive and constructive interactions between each of the under-resolved scatterers, responsible for the granular effect of the B-mode ultrasound image.

[0151] The reference images B to F of figures 6 are propagation images of this other analysis zone ZA'out of image A of figure 6, for the same 5 additional delay values as for images B to F of figures 5.

[0152] The amplitudes and real parts of the values of the focused reflection matrix for a set of second points of this other analysis zone ZA'out are represented here in the same way.

[0153] These propagation images for a diffuser also show a coherent ultrasonic wave (circled with dashed lines) that converges, focuses at the first point PI' of the virtual input transducer TV'in, and then diverges. However, it It is more difficult to discern this coherent wave due to the echoes generated by the diffusers located upstream or downstream of the focal plane, which have a reflectivity comparable to that of the virtual source studied.

[0154] In addition and reciprocally to the previous definition of the propagation images, it is also possible to construct one or more propagation images between a plurality of virtual input transducers TVin (first points PI) and a virtual output transducer TVout (second points P2). Thus, the propagation image(s) are constructed from the focused reflection matrix RFoc(r in , r out , ôt), this or these propagation images being determined for one or more values of the additional delay ôt, for a virtual output transducer TVout (second point P2) and for a plurality of virtual input transducers TVin (first points PI), the virtual input transducers TVin being located at spatial positions r in around the virtual output transducer TVout of spatial position r out.

[0155] The definitions of the propagation images with respect to the input and output transducers are in fact reversed. Due to the reciprocity of wave propagation, the images produced are very similar and the various calculations and determinations made from these propagation images and explained below can be carried out in a similar manner. For the sake of simplicity, this detailed description will only explain the first meaning between an input transducer and a plurality of virtual output transducers. But it will be understood that, in each of the definitions appearing in this document, it is possible to invert the elements with the index "out" and the index "in", and the names "input" and "output".

[0156] Furthermore, it is also possible to use both types of propagation images (according to the first and second direction), and to combine them or to average these two propagation images to obtain a more representative and more contrasted average propagation image of the propagation of waves in the medium. It is also possible to combine results derived or determined from these two types of images to obtain a result that is often more precise.

[0157] The focused reflection matrix RFoc(r in , r out, ôt) as defined previously uses the spatial positions r in , r out of the virtual input transducers TVin and output transducers TVout. These spatial positions are absolute positions in a spatial reference frame. However, it is also possible to use a single absolute spatial position and a relative spatial position with respect to this absolute spatial position. For example, one can take the absolute spatial position r in of the virtual input transducer and the relative spatial position Ar out of the virtual output transducer, with Ar out = r out - r in • Conversely, one can take the absolute spatial position r out of the virtual output transducer and the relative spatial position Ar in of the virtual input transducer, with Ar in = r in - r out. Each of the calculations and / or determinations of the This description may be made using any of the preceding definitions, or any other similar and / or equivalent definition. Coherent wave extraction

[0158] The ultrasonic characterization method implemented by the calculation unit 42 of the system 40 can be completed by applying a combination step in which a linear combination of a set of propagation films is carried out, each propagation film of the set being taken between a chosen virtual input transducer TVin of different spatial position r in, and virtual output transducers TVout of spatial position r out such that r out = Ar out + r in, with Ar out being predefined and identical for all the propagation films of the set, and the chosen virtual input transducers being neighbors of each other.

[0159] In other words, a set of neighboring spatial positions of selected virtual input transducers TVin is selected, this set of spatial positions forming a zone of interest for correlation, more simply called a spatial correlation zone ZC, and making it possible to correlate the propagation films of these virtual input transducers. This spatial correlation zone is for example a rectangular zone around a reference point. It can also be the image in its entirety or any zone of symmetrical or non-symmetrical shape. The neighboring spatial positions are for example spatial positions close to each other.

[0160] By this combination of a set of several propagation films, we then obtain a coherent wave propagation film improved for example in terms of coherence and contrast. The images of this new propagation film called coherent wave propagation film are obtained for the same additional delays ôt, and for the same relative positions Ar out.

[0161] This new coherent wave propagation film can then be associated with a reference virtual input transducer TVinref of spatial position r in>ref which represents the virtual input transducers chosen from the set of propagation films (the virtual input transducers of the spatial correlation zone).

[0162] According to a first example, the reference virtual input transducer TVinref is a virtual input transducer of spatial position corresponding to the average of the spatial positions of the chosen virtual input transducers. Thus, in this previous variant, the spatial position of the reference virtual input transducer can be expressed by:

[0163] r _ 1 V r rin. ref “ r= 'ln 'm rin

[0164] (Equ. 5)

[0165] rin being the chosen virtual input transducers,

[0166] Nfn being the number of virtual input transducers chosen, composing the zone spatial correlation.

[0167] According to another example, the reference virtual input transducer TVinref is a virtual spatial position input transducer corresponding to a weighted average of the spatial positions of the chosen virtual input transducers, said weighting being for example based on the reflectivity value of each point of the chosen virtual input transducers. Thus, in this variant, the spatial position of the reference virtual input transducer can be expressed by:

[0168] E r in ■ | RFoc ( r in = r out , ôt = 0 ) | p __ r in_________________________________________ E ^Foc(r in = r„„ t , 5( = 0)| r in

[0169] (Equ. 6)

[0170] For example, this linear combination is determined or carried out by a singular value decomposition, noted SVD during which a singular value decomposition calculation is carried out on the set of propagation films to obtain a singular vector V i associated with the singular value of greatest absolute value, this singular vector V i then being the coherent wave propagation film associated with said virtual reference input transducer TVinjref and for the same additional delays ø.

[0171] The plurality of propagation films of the set is here processed by singular value decomposition to combine several films, i.e. several measurements or experiments of the acoustic disorder of a region close to a virtual input transducer, which makes it possible to improve the contrast of the propagation film, and thus advantageously improve its exploitation.

[0172] To perform this singular value decomposition calculation (in particular because current usual singular value decomposition tools operate on two-dimensional matrices), it is possible to construct a concatenated focused reflection matrix RFoc' in which the rows of this concatenated focused reflection matrix RFoc' are the indices of the virtual input transducer TVin chosen with spatial position r in, and the columns of this concatenated focused reflection matrix RFoc' are the concatenated propagation films { Arout, ôt} (set of images) for each virtual input transducer TVin chosen, these propagation films being taken for the same temporal succession of additional delays ôt. This concatenated focused reflection matrix is thus the focused reflection matrix RFoc refocused on the input focus point r in .

[0173] For example, we denote this concatenated focused reflection matrix RFoc' by:

[0174] RFoc' = [ÆFoc(rin, { Arout, Ôt}) ] = [FFoc(rin, { rin +Arout, ôl})]

[0175] This step of decomposition into singular values SVD then provides a singular vector V i which maximizes the correlations between each of the sources of the transducers chosen virtual input transducers TVin. The singular vector V i is associated with the singular value of singular value decomposition of largest absolute value. The singular vector V i is then the coherent wave propagation film associated with a virtual input transducer of reference TVin ref and for the same additional delays ôt.

[0176] The use of singular value decomposition SVD therefore makes it possible to combine several wave propagation films while freeing oneself from the random reflectivity introduced by the speckle-type regime. The coherent wave being an element common to each of the propagation films, it emerges during the combination process, while the contributions of the diffusers located outside each virtual input transducer TVin are erased by destructive interference. This amounts to filtering the propagation films to extract the coherent background.

[0177] The reference image A of Figure 7 presents the same ultrasound image as those of Figures 5 and 6. In this figure, we consider an example of an analysis zone ZAout associated with a virtual input transducer chosen from among the set of virtual input transducers TVin chosen, these chosen virtual transducers being represented on this image A by a grid of rectangular points. The points of this grid represent the set of virtual input transducers TVin chosen, called the coherence zone ZC (i.e. the neighboring virtual input transducers chosen) to carry out the coherent combination of the propagation films.

[0178] Reference images B to F of Figure 7 are coherent wave propagation images of the analysis area ZAout of image A of Figure 7 for several additional delay values ôt which represent the first singular vector V i. The same representation of first amplitude image and second real part image as that presented for the previous figures is used in this example.

[0179] The images in Figure 7 show that the coherent part of the ultrasonic background can also be extracted for a set of first points PI (virtual input transducer TVin) located in the speckle. Indeed, in these images, a single coherent wave is observed which moves from the bottom to the top, concentrating at the position of the virtual input transducer TVin, whereas the propagation images not processed by the singular value decomposition process SVD of this experiment would resemble those presented in reference images B to F of Figure 6.

[0180] The singular value decomposition makes it possible to extract very reliably a coherent background from the propagation images / movies. For example, in Figure 8A, the first curve A1 corresponds to the amplitude of the signal at the confocal point as a function of the additional delay β (here between -3 ps and +3 ps) of one of the propagation movies obtained for a virtual input transducer TVin belonging to the coherence zone ZC. confocal point is the point of the propagation images defined by Ax = Az = lArl = 0 (r in = r out ) represented in our example by the cross located in the center of each propagation image and which corresponds to the position of the virtual input transducer. This curve Al is very chaotic in the case shown, because the confocal position Irl coincides with a so-called "speckle" type zone. The coherent wave is then completely or partially hidden by the echoes coming from diffusers located upstream or downstream of this confocal zone. In this figure, curve A2 corresponds to the amplitude of the signal of the coherent wave propagation film (first singular vector V i ) resulting from the singular value decomposition of the previous propagation film, and for the same confocal point. This curve A2 shows a single maximum centered at the additional delay ot zero, which demonstrates good background focusing even for this specific case concerning a low-reflecting element.

[0181] Figure 8B shows the frequency spectra of the signals of Figure 8A, the curve S1 corresponding to the frequency spectrum of the signal of curve A1, and the curve S2 corresponding to the frequency spectrum of the signal of curve A2. However, a loss of the coherent background time resolution is observed (visible in Figure 7), which results in a reduction in the spectral width of the signals studied. If necessary, this phenomenon can be corrected using a spectrum equalization step.

[0182] Coherent wave propagation images are analogous to propagation images associated with an echogenic scatterer but whose spectral width has been reduced.

[0183] These curves A2, S2 illustrate the effectiveness of the singular value combination / decomposition step for extracting or filtering coherent wave propagation films with a single maximum (a single main wave). Coherent wave in ballistic frame of reference

[0184] The calculation of the focused reflection matrix RFoc(r in , r out, ôt) assumes a model of speed of the ultrasonic waves in the medium (for example, a constant speed of sound c 0). Indeed, the outward flight times rin and the return flight times rout of the wave are calculated conventionally with geometric formulas for calculating the distance between the transducers 11 and each point in the medium, and with this assumption of constant speed of sound.

[0185] Therefore, the propagation images, propagation movies and coherent wave propagation movies calculated previously include this assumption of constant sound speed c 0. In these images and movies, coherent wave propagation results from a digital time reversal process based on the assumed sound speed model. This wave therefore propagates at the assumed sound speed c 0 ■ At time 5t = 0, it is located at the depth of the virtual input transducer TVin (the central cross in these figures), i.e. for Az = 0. The time of flight of the wave coherent therefore follows the following ballistic propagation relation:

[0186] &(Arout) = - sign (Az^) ■ |Arout| / c0

[0187] (Equ. 7)

[0188] in which:

[0189] c0 is the speed of sound in the medium,

[0190] lAr out I is the modulus of the vector between the virtual input transducer TVin and the virtual output transducer TVout, Ar out = r out - r in ,

[0191] where is the additional delay,

[0192] Azout is the component along the second Z axis of the spatial position vector Ar out

[0193] In other words, in these propagation images, the theoretical wave which propagates at the sound speed c 0 forms an arc of a circle centered on the origin of the image (i.e. the virtual input transducer TVin of spatial position r in ). The ballistic propagation relationship therefore links the relative position Ar out to the additional delay ôt by the sound speed c o. The negative sign underlines the fact that this is a digital time reversal process.

[0194] It is then possible to extract from the propagation film or the coherent wave propagation film, a background focusing image in the ballistic frame of reference, an image which is called the wavefront image and which follows this theoretical wave at the speed of sound c 0: For each propagation image or coherent wave propagation image, at an additional delay ot, the values (acoustic pressure value) which are located on this arc of a circle (i.e. which respect the previous ballistic propagation relation) are extracted. A new image is thus constructed, called the wavefront image which represents the evolution of the propagation film or coherent wave propagation film in the ballistic frame of reference. This wavefront image is therefore an image of the wavefront in the ballistic frame of reference.

[0195] According to a first variant, the image of the wavefront is determined indirectly by calculating a propagation film or coherent wave propagation film, and by extracting the appropriate data from this film as explained above to determine the image of the wavefront during the additional delay interval.

[0196] The ultrasonic characterization method implemented by the calculation unit 42 of the system 40 can therefore be completed by applying a step of determining an image of the wavefront for a virtual input transducer TVin or for a virtual reference input transducer TVin ref and for an additional delay interval, said image of the wavefront being determined from:

[0197] - images of a propagation film or a coherent wave propagation film, And

[0198] - of a ballistic propagation relation of the type:

[0199] <5f(Arout) — - sign ( Az ) ■ |Arout| / c0 which allows values to be extracted from each of the images of the films to construct the image of the wavefront.

[0200] According to a second variant, an image of the wavefront is determined directly from the experimental reflection matrix Rui(t), by imposing the ballistic propagation relation above.

[0201] The ultrasonic characterization method implemented by the calculation unit 42 of the system 40 can therefore be completed by applying a step of determining an image of the wavefront for a virtual input transducer TVin and for an additional delay interval, said image of the wavefront being determined from:

[0202] - of the focused reflection matrix RFoc(r in , r out, ôt) and

[0203] - of a ballistic propagation relation of the type

[0204] Ôf(Arout) = - sign ( Azout ) ■ | Arout| / c0, which allows values to be extracted from the focused reflection matrix to construct the wavefront image.

[0205] In all these variants, the image of the wavefront makes it possible to estimate the pressure field (transmission-reception response) generated by the virtual input transducer TV in or reference transducer TVinref from the echoes measured by the transducers of the probe.

[0206] Note that the signals contained in the wavefront image are a sub-matrix of the focused reflection matrix. Therefore, for the calculations, we can limit ourselves to signals that verify the ballistic propagation relation above. In this case, the wavefront image is the focused reflection matrix RFoc(r in , r out , ôt).

[0207] The points or pixels of these wavefront images have the spatial position Ar out = r Out - r in , that is to say a relative position with respect to the position r in of the virtual input transducer TVin. Thus, the coordinates are noted Ax on the abscissa, and Az on the ordinate on these images. These wavefront images can also be determined for a three-dimensional imaging method. Other coordinates are then used to represent wavefront images in various planes.

[0208] Figure 9A shows the amplitude of such a wavefront image and Figure 9B shows the real part of this wavefront image. In this Figure 9B, we see a phase jump of ir radians when passing the focal point of the virtual input transducer TVin (spatial position r in with coordinates Ax=Az=0 in this figure). This phase jump is known as the Gouy phase jump. The wavefront image makes it possible to clearly illustrate this phenomenon.

[0209] As for propagation images, it is possible to reverse the role played by the virtual input transducers TVin and the virtual output transducers TVout. In this case, an estimate of the pressure field generated by the output focusing is obtained. Determination of the integrated speed of sound

[0210] The method and system for ultrasonic characterization of a medium according to the present disclosure and implemented by the calculation unit 42 of the system 40 is also capable of determining the integrated speed of sound at a point in the medium. The integrated speed of sound is an estimate of the average value of the speed of sound between the transducers of the sounding device 41 and a point in the medium. More precisely, this integrated speed of sound integrates all of the local speeds of sound of the zones crossed by the outward and return path of the ultrasonic sound.

[0211] In this case, the method comprises:

[0212] - a step of determining a wavefront image for a virtual transducer input TVin and for an additional delay interval, said wavefront image being determined as described previously as a function of a sound speed c 0 in the medium,

[0213] - a step of determining a depth position Az(0) of the center of the spot focal length in the wavefront image for the virtual input transducer TVin, and

[0214] - a step of calculating an integrated speed of sound c(1) from the following formula:

[0216] (Equ. 8)

[0217] in which zin is the component along a second Z axis of the spatial position vector r in of the virtual input transducer TVin.

[0218] By "center of the focal spot in the wavefront image" is meant for example the position of the maximum of the focal spot in the wavefront image; that is to say the position of the pixel having the largest value of the entire wavefront image. It should be noted that in the wavefront image, only one focal spot is observed, and its position is therefore unique. Thus, the position of the center of the focal spot is also unique, and represents the depth position Az(0)(r in ) to be used to correct the speed of sound c 0, for the midpoint corresponding to the spatial position r in of the virtual input transducer TVin.

[0219] For example, the center of the focal spot is determined by searching in the wavefront image for the spatial position of the point of greatest value, and the depth position Az(0) of the center of the focal spot is then the component in the direction of the depth Z axis, corresponding to the Az axis, of this point of greatest value.

[0220] Note that the depth position Az(0) is determined for each virtual input transducer TVin taken in the medium or conversely for each virtual output transducer TVout taken in the medium. More generally, this depth position depends on each point of spatial position r considered and can be noted Az(0)(r) with r = r in or r = r out.

[0221] Indeed, in the images of the propagation film or the wave propagation film coherent, the ultrasonic wave focuses at the instant of the additional delay ôt zero (ôt=0) only if the speed of sound c 0, used for the calculation of the focused reflection matrix RFoc(r in , r out , ôt) through the calculations of time of flight on the way out and time of flight on the way back, and for the calculation of the image of the wavefront through the ballistic propagation relation, is a value of speed of sound which corresponds to a correct integrated speed of sound for the real medium between the transducers 11 of the sounding device 41 and the point of the medium corresponding to the virtual input transducer TVin of spatial position r in .

[0222] For example, Figure 10 illustrates this process. In this Figure 10, the images referenced A, B and C show images of the wavefront obtained with predefined sound speeds of 1440 m / s, 1540 m / s and 1640 m / s respectively. In these images of the wavefront, a focal spot is observed which moves along the ordinate axis Az, i.e. in depth (Z direction). The graph referenced D then shows the three intensity curves CIA, CIB and CIc of these images of the wavefront on this ordinate axis Az, i.e. the axis for which Ax = 0.

[0223] For example, the depth position Az(0)(r in ) of the focal spot is obtained as illustrated in Figure 10, i.e. by determining the depth position of the maximum of the values of the wavefront image on the ordinate axis Az, such that Ax = 0. The depth position Az(0)(r in ) of the focal spot in the wavefront image is performed by searching in the wavefront image for the position on the ordinate axis Az having a maximum value in this wavefront image, this ordinate axis Az corresponding to a zero abscissa Ax in the wavefront image.

[0224] For example, for the intensity curve CIA of graph D, the depth position Az(0)(r in ) is approximately 4.5 mm, which will lead to an estimate of the integrated speed of sound c(1)(r in ) greater than the initially assumed speed of sound c(0), at the position r in of the chosen virtual input transducer TVin, so that the vertical position along the axis Az of the focal spot of image A will be moved upwards and therefore towards the point of origin (Ax = Az = 0) of the virtual input transducer, which corresponds to a recalibration by calculation of the integrated speed of sound for this point in the middle of the virtual input transducer TVin.

[0225] Therefore, in practice, one can possibly be satisfied with calculating the values of the image of the wavefront on the Az axis, for which Ax=0, to determine a speed of sound or integrated speed of sound.

[0226] Thus, the method of ultrasonic characterization of a medium, to determine an integrated speed of sound, comprises the following steps:

[0227] - a step of generating a series of incident ultrasonic waves USin in a area of said medium, by means of a network 10 of transducers 11, said series of waves incident ultrasound being an emission base i; and

[0228] - a step of generating an experimental reflection matrix R ui (t) defined between the transmission base i at the input and a reception base u at the output;

[0229] - a step of determining a focused reflection matrix RFoc(r in , r out , ôt) which comprises responses of the medium between a virtual input transducer TVin of spatial position r in and a virtual output transducer TVout of spatial position r out, the responses of the virtual output transducer TVout being taken at a time instant offset by an additional delay öt relative to a time instant of the responses of the virtual input transducer TVin,

[0230] - a step of determining an image of the wavefront for the virtual transducer input TVin and for an additional delay interval, said wavefront image being determined as a function of the sound speed c 0 in the medium, and said wavefront image being determined from:

[0231] - of the focused reflection matrix RFoc(r in, r out, ôt) and

[0232] - of a ballistic propagation relation of the type

[0233] &(Arout) = - sign ( &Zout ) ■ |Arout| / c0, which allows values to be extracted from the focused reflection matrix to construct the wavefront image, and in which:

[0234] ôt is the additional delay,

[0235] lAr out I is the modulus of the vector between the virtual input transducer TVin and the virtual output transducer TVout, with Ar out = r out - r in ,

[0236] Azout is the component along a depth Z axis of the spatial position vector Ar out,

[0237] - a step of determining a depth position Az(0) of the center of the spot focal length in the wavefront image, and

[0238] - a step of calculating an integrated speed of sound c(1), from the formula next:

[0240] (Equ. 9)

[0241] in which zin is the component along the Z axis in depth of the spatial position vector r in of the virtual input transducer TVin.

[0242] Optionally, this method can be iterated one or more times as defined previously, by calculating a new integrated sound speed c(n+1) from the determination of an image of the wavefront obtained with the previous integrated sound speed c(n), from the determination of a depth position Az(n) of the center of the focal spot, and from the calculation of the new integrated sound speed c(n) by the same iteration formula:

[0243] (n+1) / I (n)[ VE AV X-Hn) V 1rin - ? rinNl + —z~

[0244] (Equ. 10)

[0245] In practice, this iterative process converges extremely quickly to an optimal integrated sound speed that corresponds to the best integrated sound speed for the transducers 11 of the sounding device and the chosen middle point (virtual input transducer).

[0246] Furthermore, in a variant, this method for determining the speed of integrated sound can be improved by carrying out, between the step of determining an image of the wavefront and the step of determining the depth position Az(0)(r in ) of a focal spot, a step of improving the image of the wavefront in which a linear combination is carried out of a set of images of the wavefront corresponding to a given coherence zone ZC, each image of the wavefront of the set being taken between a chosen virtual input transducer TVin of different spatial position r in, and virtual output transducers TVout of spatial position r out such that r out = Ar out + r in, with Ar out being predefined and identical for all the images of the wavefront of the set, and the chosen virtual input transducers being neighbors of each other.We thus obtain an improved wavefront image or coherent wavefront image associated with a virtual reference input transducer TVinjref, this virtual reference input transducer TVinjref representing the virtual input transducers of all the wavefront images used associated with the chosen coherence zone ZC, and for the same relative positions Ar out.

[0247] For example, the reference virtual input transducer TVinjref is a virtual spatial position input transducer corresponding to the average of the spatial positions of the chosen virtual input transducers or a weighted average of the spatial positions of the chosen virtual input transducers, as already explained previously in the case of propagation films.

[0248] In summary, in the method of the present disclosure, the following steps are added:

[0249] - between the step of determining an image of the wavefront and the step of determining mination of the depth position Az(0)(r in ) of a focal spot, a step of improvement of the wavefront image is carried out in which a linear combination of a set of images of the wavefront corresponding to a coherence zone is carried out, each image of the wavefront being taken between a chosen virtual input transducer (TVin) of different spatial position r in, and virtual output transducers (TVout) of spatial position r out such that r out = Ar out + r in , with Ar out being predefined and identical for all the images of the wavefront of the set, and the chosen virtual input transducers being neighbors of each other, to obtain a improved wavefront image associated with a virtual reference input transducer (TVinref), this virtual reference input transducer TVinref being characteristic of the virtual input transducers of all the wavefront images used and associated with the coherence zone ZC, and

[0250] - in the step of determining a depth position Az(0)(r in ), the image of the enhanced wavefront is used instead of the wavefront image, the depth position of the center of the focal spot is relative to the spatial position of the virtual reference input transducer TVinref, and this depth position of the center of the focal spot allows to estimate an integrated sound speed c(1)(r in>ref ) at the spatial position of the virtual reference input transducer TVinref.

[0251] The enhanced wavefront image (coherent wavefront image) is then used (instead of the wavefront image) to determine the axial position of the center of the focal spot. This distance or depth position Az(0)(r in>ref ) is then characteristic of an incorrect sound speed model and can be used to estimate the integrated sound speed c(1)(r jn>ref ) associated with the spatial position r jn>ref of the virtual reference input transducer TVinjref.

[0252] According to one embodiment, the linear combination is determined by a singular value decomposition SVD calculation of the set of images of the wavefront to obtain a singular vector W i associated with the singular value of singular value decomposition of greatest absolute value, this singular vector W i then being the improved image of the wavefront corresponding to said virtual reference input transducer TVin ref and for the same additional delays ôt.

[0253] The plurality of images of the wavefront of the set can here be processed by decomposition into singular values to combine several measurements or experiments of the acoustic disorder of a region close to a virtual input transducer, which makes it possible to overcome fluctuations linked to the disorder and to improve the contrast of the image of the wavefront, and its exploitation.

[0254] Furthermore, it is possible to determine an optimal sound speed of the medium (realistic for the medium as a whole) by calculating an integrated sound speed as described above, and taking for the linear combination of the set of wavefront images, a set of wavefront images corresponding to selected virtual input transducers (TVin) which cover substantially the whole of an area of interest of the medium. In particular, these selected virtual input transducers can be distributed regularly over the whole area of interest of the medium, with a predetermined spacing. For example, these selected virtual input transducers can represent 20% or more of the number of virtual input transducers used for example to construct an ultrasound image of the medium covering the area to be studied.

[0255] Note that the depth distances or positions Az(0)(r in ) or Az(0)(r jn>ref ) can be interpreted as an output focusing error due to the aberrations suffered during the backpropagation step of the echoes coming from the spatial positions r in or r jn>ref. The integrated sound speed measurement can also be determined by probing the aberrations suffered by the wavefronts during the forward path. This measurement is described by reversing the designations "in" and "out" in the equations above by interchanging the role of the virtual input and output transducers, to obtain another integrated sound speed estimate c(1)out.

[0256] Furthermore, it is possible to improve the integrated sound speed estimation by combining the integrated sound speed measurements or estimations obtained from the aberrations generated on the outward and / or return journeys, i.e. the integrated sound speeds c(1)in and c(1)out.

[0257] The process is then completed by the following steps:

[0258] - the role of the virtual input transducer(s) and the trans(s) is reversed. virtual output transducers for determining an integrated sound speed c(1)(r out ) with respect to a virtual output transducer, and

[0259] - we combine the integrated speed of sound c(1)(r in ) with reference to the virtual transducer input and the integrated sound velocity c(1)(r out ) with reference to the output virtual transducer to obtain an improved integrated sound velocity. Integrated sound speed images

[0260] The ultrasonic characterization method implemented by the calculation unit 42 of the system 40 can be completed by constructing one or more integrated sound speed images, this or these integrated sound speed images being determined by at least one calculation of an integrated sound speed as described above and for a plurality of points in the medium corresponding to virtual input transducers TVin (first points PI) of spatial position r in .

[0261] Figure 11 illustrates two examples of such images.

[0262] In the first example corresponding to images A1 and A2 of figure 11, the medium is of phantom type with a reference speed of sound given for substantially cref = 1542 m / s. Image A1 is the standard ultrasound image, while image A2 is the integrated sound speed image obtained by the previous method. This integrated sound image A2 makes it possible to estimate an average value of the speed of sound in the medium of 1544 m / s with a standard deviation of + / - 3 m / s, which is entirely in agreement with the reference sound speed value of this medium.

[0263] In the second example, corresponding to images B1 and B2 of Figure 11, the medium is a laminated medium with a first layer of almost 20 mm thickness, with a fibrous structure and a sound speed of substantially 1570 m / s positioned on the same phantom-type medium having a sound speed predetermined by construction of substantially 1542 m / s. Image B1 is the standard ultrasound image of this medium, while image B2 is the integrated sound speed image obtained by the method disclosed previously. This integrated sound image B2 reflects a higher sound speed in the first layer of the order of 1580 m / s and a lower sound speed below, but not identical to that of the expected sound speed and corresponding to that of this medium studied in the first example. This effect is due to the fact that the sound speed calculated by the method is an integrated sound speed which corresponds to an average or integrated sound speed over the entire outward and return path of the waves between the transducers 11 and the point of the medium. Correction of axial aberrations

[0264] The method and system for ultrasonic characterization of a medium according to the present disclosure and implemented by the calculation unit 42 of the system 40 is also capable of determining an axial correction.

[0265] The method for ultrasonic characterization of a medium, to determine a temporal and local characterization of an ultrasonic focusing with an axial correction comprises the following steps already explained to obtain a focused reflection matrix, that is to say:

[0266] - a step of generating a series of incident ultrasonic waves USin in a area of said medium, by means of an array 10 of transducers 11, said series of incident ultrasonic waves being an emission base i; and

[0267] - a step of generating an experimental reflection matrix R ui (t) defined between the transmission base i at the input and a reception base u at the output;

[0268] - a step of determining a focused reflection matrix RFoc(r in , r out , ôt) which comprises responses of the medium between a virtual input transducer TVin of spatial position r in and a virtual output transducer TVout of spatial position r out, the responses of the virtual output transducer TVout being taken at a time instant shifted by an additional delay öt relative to a time instant of the responses of the virtual input transducer TVin, and

[0269] - a step of determining a wavefront image for a virtual transducer input TVin and for an additional delay interval, said wavefront image being determined as described previously as a function of a sound speed c 0 in the medium,

[0270] - a step of determining a depth position Az(0)(r in ) of the center of the focal spot in the wavefront image.

[0271] By "center of the focal spot in the wavefront image" is meant for example the position of the maximum of the focal spot in the wavefront image; i.e. the position of the pixel having the largest value in the entire wavefront image. The center of the focal spot and the depth position can be found / determined according to one of the techniques already explained above.

[0272] This method further comprises a step of determining a corrected focused reflection matrix RFoc (1) (r in , r out, ôt) by a translation of the responses of the focused reflection matrix RFoc (r in , r out, ôt) by a spatial translation in the depth direction Z, said spatial translation being a function of the depth position Az (0)(r in ) determined previously.

[0273] According to a first variant, the spatial translation is carried out by spatial translation of the axial component of the virtual output transducer TVout of spatial position r out (along the depth Z axis) by a correction value Azcoir(r in ) equal to 2.Az(0)(r in ), to obtain the corrected focused reflection matrix RFoc (1) (r in , r out , ôt), such that: RFoc (rül, rouj, ôt) — RFoc(rjn, { xou!, zoui + Azcol.r(rou()}, ôt)

[0275] (Equ. 11)

[0276] A corrected ultrasound image I (1)(r in ) can then be constructed from the corrected focused reflection matrix RFoc (1) (r in , r out, ôt) characterized by r = r in = r out, and ôt = 0 to obtain:

[0277] RFoc(1)(rin, rout = rn, ôt = 0)

[0278] (Equ. 12)

[0279] Conversely, the spatial translation can also correspond to the spatial translation of the components along the depth Z axis of the virtual input transducer TVin of spatial position r in with a correction value AzCOIT(r in ) equal to 2.Az (0)(r in ) to obtain the following corrected focused reflection matrix RFoc (1) (r in , r out, ôt):

[0280] î) (ôt RFoc( { z^ + Az^ (rin)}, rout, ôt)

[0281] (Equ. 13)

[0282] Note that the depth position Az(0) is determined for each virtual input transducer TVin taken in the medium and is characteristic of the aberration undergone during the return journey. By reversing the notations "in" and "out", it is possible to determine the position Az(0)(r out ) characteristic of the aberration undergone during the outward journey, for each virtual output transducer TVout taken in the medium. In other words, more generally, this depth position depends on each point of spatial position r considered and can also be noted Az(0) = Az(0)(r) with r = r in or r = r out.

[0283] According to a second variant, the spatial translation is carried out by:

[0284] - calculation of a correction value Azcoir(r) equal to Az(1)(r) which is determined by the following formula: Az(l)(r) = z(l)(r) - zin

[0285]

[0286]

[0287]

[0288]

[0289]

[0290]

[0291]

[0292]

[0293]

[0294]

[0295]

[0296]

[0297]

[0298]

[0299]

[0300] (Eq. 14) in which we apply this equation for r = rin and r = rout z = zin and z = zout is the component along a depth Z axis of the spatial position r in of the virtual input transducer TVin or of the spatial position r out of the virtual output transducer TVout, - calculation of the corrected focused reflection matrix RFoc (1) (r in , r out, ôt) by spatial translation of the components along the depth Z axis of the virtual input transducer TVin of spatial position r in of said correction value AzCOIT(r in ) and of the virtual output transducer TVout of spatial position r out of said correction value AzCOIT(r out ), such that: ( i ) RB oc (Tjn, rout, ôt ) — RI oc ( { x H), + Azcorr(rjn)}, [ xout, z()Ul + Azcon.(rout) ], ôt ) This previous calculation can also be expressed as a function of the integrated speed of sound c(1)(r) using the following formula: (Eq. 15) in which zin is the component along a second Z axis of the spatial position vector r in of the virtual input transducer TVin, and - the calculation of translation Az(l)(r) by: Az(l)(r) = z(l)(r) - zin with (Eq. 16) According to modifications of the two previous variants, translations can be implemented by a spatial Fourier transform calculation, phase shift by a phase ramp whose slope depends on the correction value, then inverse spatial Fourier transform. This implementation has the advantage of allowing the combination of translation and interpolation for new spatial coordinates. As an example, the method thus implemented performs: - a step of determining a spatial frequency matrix RFreqz(r in , xout, k zout, ôt) which is a spatial Fourier transform according to a depth direction of the focused reflection matrix RFoc(r in , r out, ôt), according to the equation: x out , k z out , — TjF ^^RFocÇr^, r out ,

[0302] (Equ. 17)

[0303] in which

[0304] TFzout is the spatial Fourier transform along the depth direction Azout,

[0305] kzout is the corresponding wave number included in the interval [w' / c0, o)+ / c0], with the pulsations w and <',+ which are the limiting pulsations of the bandwidth of the ultrasonic waves, and

[0306] xout is the transverse component in the direction of the X axis, of each virtual output transducer TVout of spatial position r out ..

[0307] - a step of determining a corrected focused reflection matrix RFoc (1) (r in , r out, ôt) corresponding to the inverse spatial Fourier transform along the same depth direction, of the product of the spatial frequency matrix RFreqz(r in , xout , kzout, ôt) by a phase ramp of the depth correction value Azcoir, i.e. equal to 2.Az(0)(r in ) according to the previous variants, and determined for each spatial position of the virtual input transducer TVin, and in which the following formula is applied:

[0308] nr? ( , s* x F »17 / „ . > 1out^'corr 1 RFoc (ijni ^out' 51 ) — TF^ RFreq^ rjn, xout, kzmj!, Ôt^cj

[0309] (Equ. 18)

[0310] in which

[0311] eix is the complex exponential function,

[0312] Azcoit is the correction value determined by the depth position of the center of the focal spot in the wavefront image.

[0313] The spatial Fourier transform in the Azout direction can for example be explained by the following spatial discrete Fourier transform formula:

[0314] RFreq? (rin, xout, k^ oul, ôt) - TFzout [RFoc (rin, rout, ôt)] 103151 = £ RFoc ( a} e A^out

[0316] (Equ. 19)

[0317] Other formulations of Fourier transform and spatial Fourier transform exist.

[0318] The inverse spatial Fourier transform in the Azout direction can then be explained by the following reciprocal formula: 103191 RFoc" (^,^,,^)=1^1 [RFreq_ (rln, x„„ *) e ^<>ut L «. • J

[0320] V"1 » 17 / / s. \ ~l out^corr 'kz. out^out = L RFreq_(rin,xoM, kz oufôt) ee kz, yes

[0321] (Equ. 20)

[0322] According to a third variant, the responses are axially translated by a calculation or determination of a corrected focused reflection matrix RFoc (1) (r in , r out, ôt) with a new sound speed cj ( r ) which replaces the assumed sound speed c 0 ■

[0323] The method of this third variant thus further comprises the following steps for obtaining an axially corrected focused reflection matrix:

[0324] - a step of calculating an integrated speed of sound c(1)(r) from the formula next:

[0326] (Equ. 21)

[0327] in which zin is the component along a second Z axis of the spatial position vector r in of the virtual input transducer TVin, and

[0328] - a step of determining a corrected focused reflection matrix RFoc (1) (r in , r out, ôt) which comprises responses of the medium between a virtual input transducer TVin of spatial position r in and a virtual output transducer TVout of spatial position r out, the responses each being obtained with a corrected sound speed depending on the virtual input transducer.

[0329] For each of these variants, the corrected focused reflection matrix RFoc (1) (r in , r out , ôt) is an axial correction of the focused reflection matrix, i.e. a focused reflection matrix whose axial aberrations have been corrected. Thanks to this corrected focused reflection matrix, it advantageously becomes possible to construct an ultrasound image with reduced axial aberrations. Thus, the distances in the axial direction in this corrected ultrasound image are more precise and allow, for example, the obtaining of better quality images.

[0330] The corrected focused reflection matrix RFoc (1) (r in , r out, ôt) is obtained by a spatial translation, which is either a spatial position translation in the Z direction of the axial component of one or both virtual transducers (TVin and / or TVout), or a translation by change of sound speed c. These alternatives make it possible to improve the channel formation step which is similar to a process of translating temporal information given by the experimental signals of the experimental reflection matrix R ui (t) (also often referred to as RF signals) into spatial information via the relation t = z / c. Thus, the spatial positions of the middle points are corrected axially in the depth Z direction, which makes it possible to obtain images with more precise vertical positioning.

[0331] For example, Figure 12 illustrates this process. In this Figure 12, the image referenced A corresponds to an ultrasound image obtained with a sound speed c 0 of co = 1540 m / s which is the speed of sound in the phantom, but not that in the water layer above the phantom which has a sound speed of ceau = 1480 m / s. We therefore usually obtain an ultrasound image A with a resolution and a degraded contrast due to the heterogeneity of the environments studied. Known aberration correction techniques make it possible to obtain the laterally improved B-referenced image, which gives a better quality image than conventional techniques. However, in this image the depth positions of the reflective elements are not corrected (see the horizontal arrows between images A and B).

[0332] The image referenced C corresponds to an ultrasound image obtained by the axial correction proposed in the method presented above. In this image C, the reflective elements are slightly displaced upwards (towards the external surface), which shows the influence of the reduced speed of sound in water compared to that of the phantom. Thus, thanks to this axial correction, the axial positions (in depth) of the points of the image are closer to the true nature of the observed medium and the distances measured in such an image are closer to the exact values.

[0333] It is further possible to improve the technique of any of the three variants above, by determining improved wavefront images using combinations of a set of wavefront images and determining the speed of sound both at the input and at the output as explained previously in the integrated speed of sound determination section, and for example by a singular value decomposition technique.

[0334] The plurality of images of the wavefront of the set are here processed by decomposition into singular values to combine several measurements or experiments of the acoustic disorder of a region close to a virtual input transducer, which very advantageously makes it possible to improve the contrast of the image of the wavefront, and its exploitation.

[0335] Ultrasound image corrected for axial aberrations

[0336] The ultrasonic characterization method for determining an axial correction and implemented by the calculation unit 42 of the system 40 can then be completed by constructing one or more corrected ultrasound images, a corrected ultrasound image being determined by calculating an ultrasound intensity value for a plurality of points in the medium each corresponding to a virtual input transducer TVin of spatial position r in from a corrected focused reflection matrix RFoc (1) (r in , r out, ôt) and by imposing a virtual output transducer TVout coincident with the virtual input transducer TVin, i.e. r in = r out.

[0337] Determination of a preferred direction of anisotropy of the medium diffusers

[0338] The method and system for ultrasonic characterization of a medium according to the present disclosure and implemented by the calculation unit 42 of the system 40 is also capable of locally determining a preferred direction of an anisotropy of the diffusers in the medium.

[0339] Scatter anisotropy characterizes any scatterer capable of generating echoes in a preferred direction when it is insonified according to a particular incident direction. This anisotropy therefore concerns any diffuser whose dimensions are larger than the wavelength. In particular, in the case of medical imaging, we will be interested in fibers, organ walls, surgical instruments such as biopsy needles, etc.

[0340] In this case, the method comprises steps similar or identical to those already explained above, up to:

[0341] - a step of determining a wavefront image for a virtual transducer input TVin and for an additional delay interval, said wavefront image being determined as described previously as a function of a sound speed c 0 in the medium.

[0342] The method further comprises:

[0343] - a step of determining a preferred direction of the focal spot in the wavefront image by image processing of said wavefront image.

[0344] For example, Figure 13 illustrates this process. In this Figure 13, the image referenced A corresponds to an ultrasound image with a spatial variation of the direction of anisotropy of the tissues. The medium imaged in this ultrasound corresponds to a muscle of a patient (a calf in this example) in which several regions are observed with fibers inclined in very different directions. This application to an image of a muscle is only one example of an anisotropic medium for which the method can be applied. However, such a usual ultrasound image gives distorted general information. State-of-the-art ultrasound does not allow reliable observation of this anisotropy which is a local characteristic of the medium, because the propagation of ultrasonic waves in such a medium is neither at constant speed nor propagating in a rectilinear direction from the transducers of the probe.

[0345] The images referenced B, C, D, and E of this figure 13 correspond to the wavefront images constructed for the small regions of the ultrasound image connected by the arrows. These wavefront images are here processed by singular value decomposition of a plurality of virtual transducers in each of these regions to capture or probe a plurality of experiences of the acoustic disorder of this region and thus to improve the contrast of the wavefront image produced, and its analysis.

[0346] All these images of the wavefront B, C, D and E show a very elongated focal spot in the vertical direction (direction of the depth axis Az), but with a different inclination. This inclination of the focal spot in the wavefront image is local inclination information which is very correlated with the real value of inclination of the muscle fibers in the region considered. The inclination axis of the focal spot is in fact substantially perpendicular to the direction of the fibers, in particular at the center of the image, places where the incident ground has a direction substantially in the depth Z direction.

[0347] Thus, the method determines the preferred direction of the focal spot in the wavefront image by image processing on this wavefront image.

[0348] According to a first variant, the method can for example extract a contour of the focal spot by a threshold at a level lower than the maximum value in this image of the wavefront, for example at 50% or 70% of this maximum. From this contour, one can deduce the preferred direction or main direction (the direction of greatest dimension for the focal spot), and the secondary direction (the direction of least dimension). However, other image processing techniques are possible to extract the preferred direction of the focal spot.

[0349] According to a second variant, the method can for example:

[0350] - transform the image of the wavefront U(rin, Axout, Azou£) from a reference frame into co Cartesian ordinates to a reference frame in polar coordinates, of the type U(rin, A.sout, A^^)

[0351] - sum the values of said image of the wavefront of the reference frame in coordinates polar, on a plurality of radial distance deviation values Asoub to obtain an angular sensitivity function f(r in , A0out) for a plurality of angular values A0out,

[0352] - determine the optimal angular value A0maxout(r in ) corresponding to the maximum of the angular sensitivity function, said optimal angular value A0maxout(r in ) corresponding to the preferred direction of the focal spot associated with the virtual input transducer TVin.

[0353] We thus have:

[0354] A^ (rin) = max [EU (rin, Asout, A^t)]

[0355] (Equ. 22)

[0356] Figure 14 shows an example of an angular sensitivity function curve f(r in , A0out) of said image of the wavefront of the reference frame in polar coordinates corresponding to Figure 13B, said angular sensitivity function being in this illustrative example normalized to have a maximum value equal to one (1). This curve has a maximum around A0 = -11° which is the estimated angle of the local preferred direction at the point considered in the middle of this example.

[0357] Optionally, a correction corresponding to the viewing angle of the considered point of the medium seen from the transducers is applied to the angular value A0out to obtain an angular anisotropy value yout(r in ), which is characteristic of the anisotropy direction of the diffusers located at the spatial position of the virtual input transducer.

[0358] This estimation is carried out here from correlation of the output signals. Next, we can estimate another angular anisotropy value yin(r out ), which is characteristic of the anisotropy direction of the diffusers located at the spatial position of the virtual output transducer. Advantageously, it is possible to combine the two angular anisotropy values yout(r in ) and yin(r out ), in order to obtain a better local characterization of the anisotropy direction of the medium.

[0359] According to one example, the method could be completed by the following steps:

[0360] - the role of the virtual input transducer(s) and the trans(s) is reversed. virtual output transducers to determine a preferred direction relative to a virtual output transducer, and

[0361] - we combine the preferred direction with reference to the virtual input transducer and the preferred direction with reference to the virtual output transducer to obtain an improved preferred direction.

[0362] According to another example, the method could be completed by the following steps:

[0363] - the role of the virtual input transducer(s) and the trans(s) is reversed. virtual output transducers to determine an angular anisotropy value relative to a virtual output transducer Fout(rout), and

[0364] - we combine the angular value of anisotropy with reference to the virtual transducer input fo(lt(rin) and the angular anisotropy value with reference to the virtual output transducer Eout(rout) to obtain an improved angular anisotropy value.

[0365] An example of anisotropy angular value calculation can be given by the following formula (in the first case of anisotropy angular value with reference to the virtual input transducer Eout(rîn)):

[0366] y (rin) = - 2( (rin) - 0 t (rin)) * out\ \ * have ' yes \ m / j

[0367] (Equ. 23)

[0368] Such an anisotropy angular value calculation comes for example from calculations explained in the document "Specular Beamforming", Alfonso Rodriguez-Molares et al., published in IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control (Volume: 64, Issue: 9, Sept. 2017).

[0369] We add a definition of a viewing angle of the spatial position point r in of the virtual input transducer, for example of the type:

[0370] A < _ «5ut ^out(^in) — M+ ^out ( I*in ) COS (^oUt(^in) ) E“out “out " ou c° s (^ out (laughed n ) )

[0371] (Equ. 24)

[0372] with

[0373] 0^ ( rn ) = atan ( j

[0374] in which:

[0375] iÇm(r) are the maximum and minimum values of spatial positions of transducers in the network.

[0376] Other formulas for calculating the angular value of anisotropy are possible for the technician in the field in order to obtain more realistic values of the preferred direction angle.

[0377] Figure 15 shows an ultrasound image on which are superimposed lines corresponding to estimates of preferred directions for a set of points distributed over the ultrasound image. There is a high degree of consistency between the estimated preferred directions and the underlying structures visible on the ultrasound image. The proposed method advantageously makes it possible to adequately estimate the preferred directions over the entire ultrasound image.

[0378] The measurement of this preferred direction, the angle of inclination of the focal spot for its largest dimension, is an important parameter for improving the quality of the ultrasound image in this region: Its knowledge can make it possible to adapt the characteristics of the incident ultrasonic waves USin; for example by choosing plane waves with a specific inclination or waves focused in a specific location. This also makes it possible to adapt the apodizations chosen in receptions during the channel formation step.

[0379] Measuring this local preferred direction can allow the degree of anisotropy of a larger region to be analyzed, and thus the potential existence of lesions in the tissue to be determined and their location to be located.

[0380] Thus, the method of ultrasonic characterization of a medium, to locally determine a preferred direction of an anisotropy, comprises the following steps:

[0381] - a step of generating a series of incident ultrasonic waves USin in a area of said medium, by means of an array 10 of transducers 11, said series of incident ultrasonic waves being an emission base i; and

[0382] - a step of generating an experimental reflection matrix R ui (t) defined between the transmission base i at the input and a reception base u at the output;

[0383] - a step of determining a focused reflection matrix RFoc(r in , r out , ôt) which comprises responses of the medium between a virtual input transducer TVin of spatial position r in and a virtual output transducer TVout of spatial position r out, the responses of the virtual output transducer TVout being taken at a time instant offset by an additional delay öt relative to a time instant of the responses of the virtual input transducer TVin,

[0384] - a step of determining an image of the wavefront for the virtual transducer input TVin and for an additional delay interval, said wavefront image being determined as a function of the sound speed c 0 in the medium, and said wavefront image being determined from:

[0385] - of the focused reflection matrix RFoc(r in, r out, ôt) and

[0386] - of a ballistic propagation relationship of the type

[0387] &(Arout) = - sign ( ^Z t ) ■ |Arout| / c0, which allows values to be extracted from the focused reflection matrix to construct the wavefront image, and in which:

[0388] ôt is the additional delay,

[0389] lAr out I is the modulus of the vector between the virtual input transducer TVin and the virtual output transducer TVout, with Ar out = r out - r in ,

[0390] Azout is the component along a depth Z axis of the spatial position vector Ar out,

[0391] - a step of determining a preferred direction of the focal spot in the wavefront image by image processing of said wavefront image.

[0392] It is possible to improve the proposed technique by determining enhanced wavefront images using combinations of a set of wavefront images as explained previously in the integrated sound speed determination section, and for example by a singular value decomposition technique. In this case, the preferred direction obtained from an enhanced wavefront image makes it possible to characterize the anisotropy of the medium corresponding to a chosen coherence zone and is attributed to the spatial position r jn>ref of the virtual reference transducer.

[0393] The plurality of images of the wavefront of the set are here processed by decomposition into singular values to combine several measurements or experiments of the acoustic disorder of a region close to a virtual input transducer, which makes it possible to improve the contrast of the image of the wavefront, and thus its exploitation.

[0394] In the process, the following steps can thus be added:

[0395] - between the step of determining an image of the wavefront and the step of determining mination of the preferred direction of the focal spot, a step of improving the wavefront image is carried out in which a linear combination is carried out of a set of wavefront images corresponding to a coherence zone, each wavefront image being taken between a chosen virtual input transducer (TVin) of different spatial position r in, and virtual output transducers (TVout) of spatial position r out such that r out = Ar out + r in , with Ar out being predefined and identical for all the wavefront images of the set, and the chosen virtual input transducers being neighbors of each other, to obtain an improved wavefront image associated with a reference virtual input transducer (TVinref), this reference virtual input transducer TVinref being characteristic of the virtual input transducers of the set of wavefront images used and associated with the coherence zone ZC, and

[0396] - in the preferred direction step of the focal spot, the image of the wavefront improved is used instead of the wavefront image, the preferred direction of the focal spot is relative to the spatial position of the virtual reference input transducer TVin ref.

[0397] Furthermore, by reversing the role of the virtual input transducers TVin and output transducers TV out, that is, by reversing the notations "in" and "out", it is possible to determine the preferred direction A0maxin(r out ) of the focal spot associated with the virtual output transducer TVout of spatial position r out The combination of the two preferred directions associated with the position r, that is, A0maxin(r) and A0maxout(r) makes it possible to improve the measurement of diffuser anisotropy.

[0398] Thanks to this calculation of preferred direction and these images, it is possible to characterize the anisotropy of the scatterers of the medium, or to characterize for example an anisotropic structure in the medium, such as a needle introduced into a tissue, or a wall separating different tissues. By scatterer anisotropy is understood any element larger than the wavelength of the ultrasonic waves.

[0399] Analysis of temporal signals for confocal points

[0400] The method and system for ultrasonic characterization of a medium according to the present disclosure and implemented by the calculation unit 42 of the system 40 is also capable of carrying out a local spectral analysis of an ultrasonic focusing.

[0401] In such an analysis, we are particularly interested in confocal responses, that is to say a virtual input transducer TVin of spatial position r in superimposed on the virtual output transducer TVout of spatial position r out; that is to say with r in = r out =r.

[0402] The additional delay ö is then used to probe the temporal response of the diffusers selected by these virtual transducers.

[0403] In this case, the method comprises the following steps already explained to obtain a focused reflection matrix, but applied to the same spatial position, i.e. to a confocal position:

[0404] - a step of generating a series of incident ultrasonic waves USin in a area of said medium, by means of an array 10 of transducers 11, said series of incident ultrasonic waves being an emission base i; and

[0405] - a step of generating an experimental reflection matrix R ui (t) defined between the transmission base i at the input and a reception base u at the output;

[0406] - a step of determining a focused reflection matrix RFoc(r, ôt) which comprises responses of the medium between a virtual input transducer TVin of spatial position r in and a virtual output transducer TVout of spatial position r out, the virtual input and output transducers being superimposed at the same spatial position r, with r in — r on — r, and the responses of the virtual output transducer T^out being taken at a time instant shifted by an additional delay ot relative to a time instant of the responses of the virtual input transducer TVin.

[0407] The method then comprises the following steps for performing the local spectral analysis:

[0408] - a step of determining a frequency matrix RFreqt(r, œ) which is a time Fourier transform of the focused reflection matrix RFoc(r, ôt)

[0409] RFreq^r, w) = TF t [RFoc(r,

[0410] (Equ. 25)

[0411] in which

[0412] TFt is the time Fourier transform, and

[0413] co is a pulsation with co = 2irf, f being the frequency corresponding to said pulsation.

[0414] The time Fourier transform can be explained for example by the following time discrete Fourier transform formula:

[0415] RFreq^r, œ) = TF t [ RFoc (r, ôt) ] = £ A RFoc(r, Ôt )e ül ' ôt

[0416] (Equ. 26)

[0417] Other formulations of Fourier transform and time Fourier transform exist, for example in discrete or integral form, with or without normalization, and can also be used.

[0418] RFreqt(r, co) then contains a local estimate of the spectrum of echoes backscattered by the medium. More precisely, these echoes come from scatterers which are included in the monochromatic focal spot centered on the position r. In the absence of aberration, these dimensions are therefore predicted by the diffraction limits defined at the central frequency of the echoes backscattered by the medium.

[0419] This method can therefore be supplemented by any medical imaging technique based on a frequency analysis of backscattered echoes in order to improve the spatial resolution. More precisely, this process makes it possible to carry out a spatial channel formation in reception for each frequency, before carrying out any spectral analysis. Note that the confocal configuration advantageously makes it possible to limit the phenomena of impulse diffractions.

[0420] For example, this method can be completed by a filtering step during which a frequency filtering of the elements of the frequency matrix RFreqt(r, co) is carried out. In particular, it is possible to carry out a low-pass, band-pass or high-pass frequency filtering, to extract desired components in the responses of the focused reflection matrix, depending on the intended application. For example, the frequency filtering can possibly be adapted to extract harmonic components of a fundamental frequency of the incident ultrasonic waves USin.

[0421] For example, Figure 16 illustrates this process. In this Figure 14, the image re Referenced A illustrates an ultrasound image of a medium containing bubbles. These bubbles are resonant structures in the medium that disturb the ultrasound image, because they continue to oscillate after the passage of an incident wave. They thus generate echoes that reach the receiving transducers with a flight time greater than the ballistic flight time, which produces artifacts in the ultrasound image downstream of the bubble. Image referenced B in Figure 14 shows an enlargement of image A in which we observe a bright echo of a bubble at the spatial position r = [x, z] = [11, 17] mm, and of its downstream artifact located below this position (i.e. vertically in depth). Images referenced C1 and C2 correspond to the propagation image respectively in amplitude and in real part, for an additional delay of zero.

[0422] The focused reflection matrix RFoc(r, ôt) of the method makes it possible to study the temporal signals of the oscillation of this bubble. The images referenced DEF in figure 14 correspond respectively to the plots of the real part, the amplitude and the frequency spectrum of the response RFoc(r, ôt) at the spatial position point r corresponding to the position of this bubble. In images D and E, a second echo is observed around 1.5 ps after the main echo centered at ôt = 0. Image F shows a first spectrum plot excluding this second echo and a second spectrum plot with this second echo. This second spectrum plot includes a main frequency around 6 MHz which corresponds to the incident background frequency, and another frequency around 3 MHz which corresponds to the resonance (oscillation) frequency of the bubble.

[0423] The method thus carries out a spectral analysis which makes it possible, for example, to identify resonance frequencies of bubbles or any other resonant structure in the observed medium.

[0424] It is thus possible to filter, for example by a predetermined bandpass filter, the responses of the focused reflection matrix, and then to calculate an ultrasound image using these filtered responses which will be improved. The effect of the resonances can then be attenuated or eliminated in the ultrasound image.

[0425] Conversely, it is possible to construct resonance frequency images by retaining only these resonances in the responses of the focused reflection matrix. Note that the resonance frequency of a bubble is linked to its size, and can make it possible to estimate a local pressure in the medium.

[0426] In a second example, RFreqt(r, œ) can be used to study the attenuation of the medium. Indeed, this phenomenon depends on the frequency. Since high frequencies are more attenuated than low frequencies, it is possible to deduce an attenuation coefficient, for example, by comparing the spectrum of echoes coming from two different depths in the observed medium. The technique described above for estimating the local spectrum of echoes coming from a given area is therefore very suitable. for the determination of attenuation. For this, the method can be supplemented, for example, with a step of determining an average spectrum at a depth S(z, œ) determined by an average of the spectra of the frequency matrix at a predetermined depth z in the medium.

[0427] For example, this average spectrum at a depth is calculated by the following formula, which is a normalized average, averaged over a set of spatial positions of the same depth z and lateral coordinate x included over a predetermined interval.

[0428] x / RFreq^r, w) 1 w) - maX RFreqf ( r, w ) ] [

[0429] (Equ. 27)

[0430] For example, Figure 17 illustrates this calculation of the average depth spectrum, by constructing an image of all the spectra for all the depths of an ultrasound image. In this Figure 17, the image referenced A illustrates an in-vivo ultrasound image of the calf of a breasted individual and the image referenced B presents the average depth spectra with a gray level scale. This image of depth spectra shows the strongest attenuation of high frequencies for great depths.

[0431] Using such an image, it is possible to estimate the evolution of the attenuation as a function of the depth thanks to the entire frequency content by adjustment techniques between a theoretical and / or experimental model, and such an image.

[0432] In a third example, the method can also be completed with a step of determining the spectral width of correlation ôco(r) for the point of spatial position r, by calculating the width at half-height of the autocorrelation of each spectrum of the frequency matrix RFreqt(r, œ), that is to say by the following formula:

[0433] / , f ôw(r) = FWMH\-^ J RFreqf r, (jo)RFreqt (r, œ + da^düj

[0434] (Equ. 28)

[0435] in which

[0436] FWMH is the full width half maximum calculation function

[0437] ()* is the complex conjugation function,

[0438] M and "F which are limit pulsations, A a) = - co is the interval of the limiting pulsations, i.e. the considered bandwidth of ultrasonic waves.

[0439] Thanks to the spatial resolution of the matrix RFreqt(r, œ), the spectral correlation width ôco(r) is a local value which can be used to characterize the nature of the scatterers contained in the monochromatic focal spot centered on the spatial position r. If the focal spot contains a single non-resonant scatterer, the width The correlation spectral width ôœ(r) is of the order of magnitude of the bandwidth of the ultrasonic signal. If the focal spot contains a set of randomly distributed scatterers of the same intensity (ultrasonic speckle regime), the correlation spectral width value ôco(r) becomes much smaller than the bandwidth Aco.

[0440] The method may also comprise a step of determining at least one spectral correlation image, said spectral correlation image being obtained by determining the spectral widths ôco(r) for a plurality of points of the medium each corresponding to a point of the medium of spatial position r.

[0441] For example, Figure 18 illustrates this process. In this Figure 16, the image referenced A is an ultrasound image of a phantom medium containing several different elements: point targets and an echogenic cylinder. The corresponding image referenced B is the spectral correlation image of the previous ultrasound image and obtained by calculating the spectral correlation width ôco(r) for a set of points in this medium. In this image B, the edges of the cylinder and the point targets have a spectral correlation width ôco(r) larger than the rest of the medium which is made up of a large number of randomly distributed under-resolved scatterers.

[0442] Thanks to this calculation of correlation spectral width and these images, it is possible to characterize the nature of the targets in the medium. For example, it is possible to differentiate between a bright speckle grain and a single scatterer. For example, this can help in the identification of bubbles for contrast imaging, or micro-calcifications characteristic of the presence of tumors, particularly in the case of breast cancer.

Claims

Claims

1. Method for ultrasonic characterization of a medium, for performing a local spectral analysis in the medium, the method comprising: - a step of generating a series of incident ultrasonic waves (USin) in an area of said medium, by means of an array (10) of transducers (11), said series of incident ultrasonic waves being an emission base i; and - a step of generating an experimental reflection matrix R ui (t) defined between the emission base i at the input and a reception base u at the output; - a step of determining a focused reflection matrix RFoc( r, ôt) which comprises responses of the medium between a virtual input transducer (TVin) of spatial position r in and a virtual output transducer (TVout) of spatial position r out, the virtual input and output transducers being superimposed at the same spatial position r, with r in = r out = r,and the responses of the output virtual transducer (TVout) being taken at a time instant shifted by an additional delay ôt relative to a time instant of the responses of the input virtual transducer (TVin), and - a step of determining a frequency matrix RFreqt(r, co) which is a time Fourier transform of each cell of the focused reflection matrix RFoc(r, ôt), this time Fourier transform being: RFreq^r, œ) = TF t[RFoc{ r, ôf)] in which TFt is the time Fourier transform, and co is a pulsation with co = 2irf, f being the frequency corresponding to said pulsation.,

2. Method according to claim 1, further comprising a filtering step during which a frequency filtering of the cells of said frequency matrix is carried out.

3. A method according to claim 2, wherein the filtering extracts harmonic components of a fundamental frequency of the incident ultrasonic waves (USin).

4. Method according to one of claims 1 to 3, further comprising a step of determining an average spectrum at a depth S(z, co) determined by an average of at least a part of the spectra of the frequency matrix at a predetermined depth z in the medium.

5. The method of claim 4, wherein a first average spectrum is determined at a first depth of the medium, a second average spectrum is determined at a second depth of the medium, and the first average spectrum and the second average spectrum are compared to derive an attenuation value of the medium.

6. Method according to one of claims 1 to 5, further comprising a step of determining the spectral width of correlation ôco(r) for the point of spatial position r, by calculating the width at half-height of the autocorrelation of each spectrum of the frequency matrix RFreqt(r, œ), that is to say by the following formula: / r < -' '+ Ôw(r) - FWMHy^ J RFreqf(r^ w}RFreq* (r, œ + dœ} dcc in which FWMH is the function for calculating the width at half-height ()* is the complex conjugation function, and nd which are limit pulsations, Aco is the interval of the limit pulsations.

7. The method of claim 6, further comprising a step of determining at least one spectral correlation image, said at least one spectral correlation image being obtained by determining the spectral correlation widths ôco(r) for a plurality of medium points each corresponding to a medium point of spatial position r.

8. Method according to one of claims 1 to 7, wherein in the step of determining the focused reflection matrix: the calculation of the responses of the virtual input transducer (TVin) corresponds to an input focusing process from the experimental reflection matrix R ui (t) which uses a forward flight time of the waves between the transmission base and the virtual input transducer (TVin) to create an input focal spot at the spatial position r in , the calculation of the responses of the virtual output transducer (TVout) corresponds to an output focusing process from the experimental reflection matrix R ui (t) which uses a return flight time of the waves between the virtual output transducer (TVout) and the transducers of the reception base u, to create an output focal spot at the spatial position r out, the additional delay ôt being a time delay added to the flight times to the back and forth during the focusing processes.

9. A method according to one of claims 1 to 8, wherein the focused reflection matrix is calculated by the following formula: RFoc (rta, rout, ôt) = NEE. E Rui (uollt, iin, t (rilq, rout, uout, iin, 5t)) 1in uout in which Nin is the number of elements of the emission base (i), Nout is the number of elements of the reception base (u) at output, R ui (t) is the experimental reflection matrix, of which Ruj ( UOut ' ^out' 5t ) ) is the element of the experimental reflection matrix R ui (t) recorded by the spatial position transducer u out following the emission of index i in in the emission base and at time r, r is a time which is the sum of the outward flight time rin of the ultrasonic wave between the transducers of the emission base (i) and the virtual input transducer (TVin) of spatial position r in, and of the return flight time rout of the ultrasonic wave between the output transducer (TVout) of spatial position r out and the transducers of the reception base u, and of the additional delay ôt, as explained by the following formula: T (in, I*out' ^out' ^iir hn) ^out) St

10. System (40) for ultrasonic characterization of a medium (20), for performing a local spectral analysis in the medium, the system comprising: - an array (10) of transducers adapted to generate a series of incident ultrasonic waves in a zone of the medium, and to record as a function of time the ultrasonic waves backscattered by said zone; and - a calculation unit (42) connected to the transducer network and adapted to implement the method according to one of the preceding claims.

Images