Method and system for performing characteristic evaluation of medium using ultrasonic wave

Abstract

To provide a method and a system for performing ultrasonic characteristic evaluation of a medium.SOLUTION: An ultrasonic characteristic evaluation method of a medium includes: a step for generating a series of incident ultrasonic waves; a step for measuring a canonical reflection matrix Rui(t) defined between an input radiation base (i) and an output reception base (u); a step for determining one set of responses R of a medium acquired from the canonical reflection matrix Rui(t) on some points in a plurality of frequencies f and in a region around a reference point; a step for determining a frequency correction law Φ adapted to the reference point and determined in the frequency f from the responses of the medium in various points; and a step for determining a corrected response R' of the medium by applying the frequency correction law Φ on the plurality of frequencies f to the response R of the medium around the reference point.SELECTED DRAWING: Figure 5

Description

Technical Field

[0001] This specification relates to methods and systems for ultrasonic characterization of heterogeneous media. These methods and systems use an array of transducers placed in contact with the medium to emit ultrasonic waves into the medium and measure the waves backscattered by the inhomogeneity of the medium.

Background Art

[0002] In the field of acoustic imaging, it is required to evaluate the characteristics of a medium by actively probing the medium with ultrasonic waves. This is, in particular, the principle of ultrasonic examination in medical imaging.

[0003] FIG. 10 shows a conventional focusing process in a medium for generating an ultrasonic image of the medium. In this example, the medium includes an aberration layer having a sound velocity different from that in other parts of the medium. This results in a spatial distortion and a temporal dispersion (reverberation) of the acoustic wavefront, which in turn results in lateral and axial aberrations in the resulting ultrasonic image. These phenomena lead to a degradation of the resolution and contrast, as well as a degradation of the appearance of reverberation artifacts, which is particularly inconvenient, for example, in medical examinations.

[0004] In the left figure, an array of transducers placed opposite the medium is used to irradiate the medium with ultrasonic waves for imaging. The conventional method consists of applying ultrasonic waves to the medium using focused radiation using a technique known as beamforming. The waves generated by each transducer are focused at the spatial position r of the target focus in .=(x inIn order to interfere constructively at (x, y, z), a set of appropriate delays τ based on a homogeneous velocity model c0 is applied to the signals emitted by each transducer. Due to the physical diffraction limit, the ultrasonic waves emitted through the aperture of the ultrasonic probe are focused into an area often referred to as the "focus spot". Furthermore, the waves passing through the aberration layer are distorted and reflected several times, resulting in multiple wave echoes in the direction of the focus during emission.

[0005] In the central view of this drawing, the waves reflected at the focus are returned to the transducer array and then pass through the aberration layer again, further distorting the ultrasonic waves and increasing the echoes due to multiple reflections. Thus, each scatterer in the medium generates several echoes, producing several temporal pulses arriving at each transducer at different times, resulting in a significant temporal dispersion of the ultrasonic signal. The beamforming process applied to this type of signal can be used to construct an ultrasonic image with significant axial distortion, and as shown in the ultrasonic image of Figure 14, the same scatterer appears at several depths. Furthermore, the heterogeneous distribution of the speed of sound in the passing tissue affects the quality of the constructed image.

[0006] The right view of Figure 10 shows how, for a single scatterer, the signals received by each transducer can be deconvolved with respect to time and then inverted with respect to time in order to optimally perform the spatial and temporal focusing of the ultrasonic waves at the scatterer in question. This time-reversal focusing technique remains limited since it requires a medium containing a very small number of scatterers. In ultrasonic inspection, the problem is quite different since there are media with a random distribution of scatterers having multiple sub-resolutions that produce ultrasonic speckle.

[0007] Therefore, the usual assumption of a homogeneous medium with a constant speed of sound c0 in conventional imaging is often not met. The wave is then reverberated with multiple internal reflections in the path of the wave towards the focus. The result is a spatial and temporal distortion of the acoustic wavefront, which causes significant aberrations in the ultrasonic image and thus degradation in its resolution and contrast. These aberrations can impair the ultrasonic characterization.

Prior Art Documents

Patent Documents

[0008]

Patent Document 1

Non-Patent Documents

[0009]

Non-Patent Document 1

Non-Patent Document 2

Non-Patent Document 3

Non-Patent Document 4

Summary of the Invention

Problems to be Solved by the Invention

[0010] Patent Document 1 proposes a technique for correcting aberration in ultrasonic imaging based on post-processing operations of the reflection matrix of a medium. However, the method described in this document only considers IQ ultrasonic signals having a window at times near the expected ballistic time. Therefore, the phase shift applied to those signals to correct aberration is equivalent to the application of a time delay, and such a delay must have an amplitude smaller than the time resolution of the ultrasonic signal. Therefore, the technique described in Patent Document 1 is applied to relatively low-order aberration correction without time dispersion. Therefore, it cannot be used to correct reverberation or multiple scattering problems, which requires different delay laws to be determined for each frequency component of the ultrasonic signal.

[0011] An object of the present disclosure is to improve known ultrasonic probing methods for correcting aberration, in particular.

Means for Solving the Problems

[0012] In a first aspect, the present disclosure relates to a method for evaluating ultrasonic characteristics for medical analysis of a medium, the method comprising: - generating, by an array of transducers, a series of incident ultrasonic waves that are radiation-based (i) in a zone of the medium; - A canonical reflection matrix defined between an input radiation base (i) and an output reception base (u), having coefficients corresponding to signals caused by ultrasonic waves received by the transducer and reflected in the medium, the canonical reflection matrix R ui (t) is measured.

[0013] The method further includes - Regarding several frequencies f of the signal received from the reflected ultrasonic wave, and regarding the canonical reflection matrix R ui (t) of the sound speed model c0, a set of responses R of the medium is determined by focusing processing regarding several points of the spatial position r = (x p , z p ) in the region around the reference spatial position point r = (x, z) (step S130); p - By averaging or correlating the responses of the medium at several points (x, z) of a plurality of different spatial positions around the reference point, a frequency correction law Φ adapted to the reference point and determined at the frequency f is determined (step S140); - By applying the frequency correction law Φ regarding several frequencies f to the response R of the medium around the reference point, a corrected response R' of the medium is determined (step S180).

[0014] Thanks to these steps, the method has the advantage of being able to obtain a local estimate of an appropriate frequency correction law for correcting ultrasonic focusing processing by locally examining the medium with a probe. This correction is used to reduce or eliminate aberrations, for example, caused by multiple reflections of waves generated by one or more aberration zones in the medium.

[0015] The estimate is calculated from measured values obtained and recorded as a canonical reflection matrix. Therefore, the estimate may be calculated independently of the measurement acquisition phase, especially by changing various calculation parameters, thereby enabling various ultrasonic characteristic evaluation analyses to be performed in real time or retrospectively.​

[0016] Those correction calculations benefit from local information extracted around a reference point and also from local frequency information from the medium.

[0017] This method may be used in medical or veterinary imaging and also in all fields of ultrasonic imaging.

[0018] According to various embodiments of this method, one and / or other of the following techniques may be used.

[0019] According to one variant, the method further - combines the corrected responses at several frequencies f of the reference point r of the above spatial position p to determine the intensity I of the ultrasonic examination image point corresponding to the reference point r of the above spatial position p (step (S190)). c includes

[0020] According to one variant, - determining the set of responses R of the medium (S130) includes determining the responses obtained by focusing between a first point r in =(x in , z) of the spatial position corresponding to the input virtual transducer and a second point r out =(x out , z) of the spatial position corresponding to the output virtual transducer, the first point and the second point being identical (r in =r out ), all of the responses R being recorded in a confocal reflection matrix R with coefficients represented by R = [R(x, z, f)], - determining the frequency correction law Φ (S140) is obtained by correlating the responses of the medium at a plurality of different spatial position points (x, z) around the reference point, the coefficients of which are represented by Φ = [φ(f, r p )], - Determining the corrected response R' around the reference point (S180) is performed by applying the frequency correction law at each frequency f and calculating the product of the terms between the confocal reflection matrix R and the phase conjugate of the frequency correction law Φ, that is, by the following equation:

Equation

Equation

Equation

[0021] According to a modification, the method further includes - Determining the intensity I of the ultrasonic inspection image point at the spatial position (x, z) by combining the corrected responses R' of the ultrasonic inspection image points at the spatial positions (x, z) at a plurality of frequencies f, that is, by the following equation (S190). c including the step of determining (S190).

Equation

[0022] According to a modification, determining the frequency correction law (S140) includes constructing a correlation matrix C from the confocal reflection matrix R(z, f) (S141), and analyzing the correlation matrix C to determine the frequency correction law Φ (S142).

[0023] According to a modification, the correlation matrix C is determined in the frequency domain by the following equation:

Equation

[0024] According to a certain modification example, the above correlation matrix C is determined based on the image points at the spatial position (x, z) by the following formula, [Number] Here, R is the above-mentioned confocal reflection matrix, x and z are the coordinates of the image points in the region around the above reference point, * is the conjugate operator.

[0025] According to a certain modification example, analyzing the above correlation matrix C (S142) is the eigenvalue decomposition of the above correlation matrix C, and the above frequency correction law Φ is the first eigenvector U1 of the above correlation matrix C.

[0026] According to a certain modification example, analyzing the above correlation matrix C (S142) is to solve the equation including the above correlation matrix C and the above frequency correction law Φ, and the solution method of this equation corresponds to iterative time reversal or iterative phase reversal.

[0027] According to a certain modification example, determining the above frequency correction law (S140) is executed by an optimization algorithm that maximizes the confocal intensity of the ultrasonic image in the region around the above reference point.

[0028] According to a certain modification example, the correction processing steps (S140, S180) are repeated multiple times, In each iteration, the corrected confocal reflection matrix R’(z, f) obtained in the previous iteration is used instead of the focused reflection matrix R(z, f).

[0029] According to a certain modification example, in each iteration, the size of the region around the reference point r p of the above spatial position is reduced.

[0030] According to a modification, determining the confocal reflection matrix R(z,f) (S130) includes compensating for the temporal attenuation of the signal.

[0031] According to a modification, - Determining a set of responses R of the medium (S130) includes determining a response obtained by focusing processing between a first point r in =(x in ,z) of a spatial position corresponding to the input virtual transducer and a second point r out =(x out ,z) of a spatial position corresponding to the output virtual transducer, where the first point and the second point are located in a region of the same seismic intensity z, and the lateral positions x in and x out form a focusing base (x) at each depth z, and all of the responses R are recorded in a confocal reflection matrix R xx (z,f) having coefficients represented as R in ,x out ,z,f), xx - Determining the frequency correction law Φ (S140) is a sub-step performed at each depth z and each frequency f, - A sub-step (S150) of determining a dual reflection matrix R - (z,f) by orthogonally projecting the confocal reflection matrix R xx (z,f) onto a correction base (c), c - A sub-step (S160) of calculating the frequency correction law Φ = [φ(c,f,r )] determined for the correction base (c) such that the frequency correction law Φ is a spatial-frequency correction law from the dual reflection matrix R p (z,f), c - A sub-step of calculating the product of the terms between the dual reflection matrix R (z,f) and the phase conjugate of the frequency correction law Φ, that is, determined by the following equation, R c (z,f), c ’(z,f)=[Rc A corrected dual reflection matrix R around the reference point, having coefficients represented as ’(x, c, f, z) c including a sub-step (S170) for determining ’

Number

Number

Number

[0032] According to a variant, the method further - At several frequencies f, by combining the diagonal coefficients of R’(z, f) of the corrected focusing reflection matrix at that point, the intensity I of the spatial position ultrasonic image point (x, z) xx is determined (S190), that is c

Number

[0033] According to a variant, the forward projection (150) is a matrix product between the transition matrix and R(z, f) of the focusing reflection matrix, that is xx

Number

[0034] According to a variant, said correction base (c) is an input correction base or an output correction base.

[0035] According to one variant, the calculating (S160) of the frequency correction law comprises: The above dual reflection matrix R c Constructing a correlation matrix C from (z, f) (S161); and analysing the correlation matrix C to determine the frequency correction law Φ (S162).

[0036] According to one variant, the correlation matrix C is determined in the correction base (c) and in the frequency domain by the following formula:

number

[0037] According to one variant, said correlation matrix C is determined on the basis of the image points at spatial positions (x,z) according to the following formula:

number

[0038] According to a modification example, analyzing the correlation matrix C (S162) is the eigenvalue decomposition of the correlation matrix C, and the frequency correction law Φ is the first eigenvector U1 of the correlation matrix C.

[0039] According to a modification example, analyzing the correlation matrix C (S162) is to solve an equation including the correlation matrix C and the frequency correction law Φ, and the solution method of this equation corresponds to iterative time reversal or iterative phase reversal.

[0040] According to a modification example, the frequency correction law (S160) is calculated using an optimization algorithm that maximizes the confocal intensity of the ultrasonic image in the region around the reference point.

[0041] According to a modification example, the correction processing steps (S140, S180) are repeated multiple times, In each iteration, the orthographic projection (S150) is the corrected focusing reflection matrix R' xx (z, f) obtained during the back-projection (S180) of the previous iteration, xx is used instead of the focusing reflection matrix R

[0042] According to a modification example, in each iteration of the orthographic projection, it alternates between the orthographic projections in the input correction base and the output correction base.

[0043] According to a modification example, in each iteration, the correction base (c) of the orthographic projection (S150) is different.

[0044] According to a modification example, in each iteration, the reference point r of the spatial position pThe size of the area around is reduced.

[0045] According to a modification, determining the focusing reflection matrix R xx (z, f) (S130) includes compensating for the temporal attenuation of the signal.

[0046] According to a second aspect, the present disclosure relates to an ultrasonic property evaluation system for analyzing a medium, for example, in a medical context, the ultrasonic property evaluation system being configured to implement the method as described above. The system according to the second aspect includes - an array of transducers adapted to generate a series of ultrasonic waves incident on a zone of the medium and to measure the ultrasonic waves backscattered by the zone as a function of time, and - a computing device associated with the array of transducers and adapted to implement the method according to the first aspect.

Brief Description of the Drawings

[0047]

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DETAILED DESCRIPTION OF THE INVENTION

[0048] Further advantages and features of the above-described technology will become apparent from the following detailed description, which is presented in a non-limiting manner for illustrative purposes with reference to the drawings.

[0049] In the various embodiments described with reference to the drawings, like or identical components have the same reference numerals unless otherwise noted.

[0050] In the following detailed description, only certain embodiments are described in detail for the sake of clarity of explanation, but these examples are not intended to limit the entire scope of the principles disclosed herein.

[0051] The various embodiments and aspects described in this disclosure may be combined in many ways or simplified. In particular, the steps in the various processes may be repeated, exchanged, and / or executed in parallel, unless otherwise specified.

[0052] The present disclosure relates to methods and systems for ultrasonic characterization of media, and in particular, is applicable to medical imaging of biological or non-biological tissues. The media, for example, is a heterogeneous media such as we are trying to characterize in order to identify and / or characterize inhomogeneities, provide accurate information about the media under study, and detect unhealthy or damaged areas and / or tissues. For example, this data is very useful for medical applications such as the identification of lesions in the breast area, damaged muscle tissue, or deteriorated liver tissue. These characterization techniques are well-known for being non-invasive to the media, which has the advantage of being preserved, especially with respect to its nature and integrity.

[0053] Conventional ultrasonic imaging approach In the field of ultrasonic imaging, we often attempt to construct an image of the reflectivity of a media from the echoes backscattered by inhomogeneities in the media. It is the principle underlying the ultrasonic scanners used in medical imaging. It is used, in particular, to view the internal anatomical structures of a subject, individual, or animal. For the purpose of simplification, the media is considered to be homogeneous with a constant acoustic propagation speed c0 in order to construct an ultrasonic image.

[0054] Conventional ultrasonic methods generally use an array of piezoelectric transducers that radiate and / or receive ultrasonic signals independently or quasi-independently, with each transducer being present at a position u in a strip supporting the array. The transducer array arranged opposite the media is used to apply ultrasonic waves in a plurality of different ways to construct a representative image of the media. Conventional methods consist of applying ultrasonic waves to the media using focused radiation using a technique known as beamforming. The method involves spatial positioning (x) of the wavelets generated by each transducer in, z) so as to interfere constructively at the target focus, a set of appropriate delays τ(u in , x in , z, c0) based on a homogeneous velocity model c0 is applied to the signals emitted by each transducer. Due to the physical diffraction limit, the ultrasonic waves are emitted through the aperture of the ultrasonic probe and are focused into an area often called the "focus spot" with a lateral width δx.

[0055] By also performing digital focusing steps during reception, an ultrasonic image representing the characteristics of the medium under study can then be constructed. The echoes picked up by the transducer array are restored in phase by shifting them in time. The delay τ(u out , x out , z, c0) is the same as that applied during emission, and the variable u out indicates the position of each transducer. During the emission phase, if the velocity model c0 used corresponds to the reality of the medium being studied, all the signals interfere at the location point (x in , z) at the ballistic time t = z / c0. During reception, the signals from the same point (x out = x in ) interfere by the sum of the signals at the echo time t = 2z / c0. This sum results in the final result of the reception focus. This confocal method, which includes focusing both during emission and reception (dual focusing), enables the reflectivity of the medium to be directly imaged with a lateral resolution δx and good contrast. However, this method is time-consuming because it requires the radiator to be physically focused at each point of the medium, at each line of the image constructed as representing the medium, or at least at a given depth.

[0056] Matrix approach to ultrasonic imaging In recent years, the applicant of the present application has developed a matrix approach to ultrasonic imaging. This approach is based on constructing a canonical reflection matrix of the medium under study. This canonical reflection matrix is determined experimentally or by calculations or digital simulations that reproduce the experiment.

[0057] A first proposal for generating this canonical reflection matrix is to sequentially emit ultrasonic pulses from each transducer in the array. Its position is marked by u in coordinates, as shown in Fig. 1(a). This generates a diverging cylindrical (or spherical) incident wave. As shown in Fig. 1(b), the wave is reflected by scatterers in the medium, and the backscattered field is measured as a function of time by each of the transducers. By repeating this operation, sequentially using each transducer as a source, we determine the canonical reflection matrix R out ,u in ,t) composed of all the pulse responses R(u uu (t)=[R(u out ,u in ,t)]. Here, the matrix contains rich information describing the medium under study. However, this method assumes that the medium remains static during the measurement, which is particularly difficult in the case of medical examinations performed on living patients. Furthermore, since ultrasonic waves are applied to the medium by a single transducer, the recorded signal has an insufficient signal-to-noise ratio.

[0058] A second option for constructing the canonical reflection matrix is to apply ultrasonic waves to the medium using waves that are sequentially focused at a large number of points in the medium, generally as in the case of a standard ultrasonic scanner. Fig. 1(c) shows this transmit-focusing irradiation. For this focusing, a delay law is applied to each emitted signal. The reception shown in Fig. 1(d) is measured by all the position sensors u out , and the response is the canonical reflection matrix R(u out ,r in, t) is formed. However, the autofocusing at multiple points is still too slow.

[0059] A third method of constructing this canonical reflection matrix is to apply a series of plane-wave ultrasonic waves to the medium. This method avoids most of the problems inherent in the methods described above. Figure 1(e) shows the principle of this plane-wave irradiation. A delay law τ’ is applied to each radiated signal to form a wavefront inclined at an angle θ in with respect to the transducer array. At reception, as shown in Figure 1(f), the field R(u out , θ in , t) backscattered by the medium is measured by the position sensors for all u in with respect to each incident plane wave θ out . The set of these responses forms the canonical reflection matrix R uθ (t) = [R(u out , θ in , t)]. The dual autofocus method described above can be achieved digitally by temporally shifting the measured signals before coherently summing them. This method generates ultrafast imaging and elastography and is described in Non-Patent Document 1.

[0060] A third option for generating this canonical reflection matrix is to apply ultrasonic waves to the medium based on divergent waves, as shown in Figures 1(g) and 1(h). This enables a wider irradiation of the sound field than when using plane waves. This technique, especially used in super-resolution imaging, is described in Non-Patent Document 2.

[0061] Therefore, conventional imaging consists of focusing both in emission and reception at the same focus for each pixel in the image, as shown in Figure 2(a) (x in = x out ).

[0062] Matrix imaging consists of separating the emission and reception foci for the same echo time t, as shown in Figure 2(b). Therefore, the autofocus reflection matrix R xx (τ) = [R(xin , x out , z, τ) is determined, and the focusing reflection matrix corresponds to each spatial position r at different spatial positions for the input and output composite focal spots. in = (x in , z) and r out = (x out , z) consists of the response between the input virtual transducer and the output virtual transducer. The predicted depth z depends on the echo time t, that is, it satisfies z = c0t / 2. Here, τ represents the focusing-based time such that τ = t - 2z / c0. The origin of this time τ corresponds to the moment when the virtual source emits an ultrasonic pulse. The focusing reflection matrix is obtained from the canonical reflection matrix R ui (t) by focusing (for example, using beamforming). This matrix provides access to more information characteristics related to the medium under study than the information obtained using the confocal image mode of conventional imaging. This focusing reflection matrix may be synthesized in the time domain (beamforming) by using the delay law or in the frequency domain by applying an appropriate phase shift.

[0063] The focusing reflection matrix is described in particular in Non-Patent Document 3 and then in Non-Patent Document 4.

[0064] In those documents, the focusing reflection matrix R xx (z, τ) was considered between the virtual transducers at the ballistic time τ = 0 (t = 2z / c0). The diagonal coefficient (x xx = x out ) of the matrix R in (z, τ = 0) enables the construction of the composite confocal image at the depth z, while its off-diagonal coefficients provide information regarding the potential aberrations and multiple scattering effects that can change the quality of this same image.

[0065] In Patent Document 1, the focusing reflection matrix is considered in the ballistic time and, in particular, has been studied to correct aberration problems. However, the corrections applied correspond to the application of time delays, and those delays must have amplitudes smaller than the temporal resolution of the ultrasonic signal. Therefore, the technique described in Patent Document 1 is applicable only to relatively low-order aberration corrections that do not have time dispersion. Therefore, it cannot be used to correct reverberation or multiple scattering problems, which requires that different delay laws be determined for each frequency component of the ultrasonic signal.

[0066] Ultrasonic characteristic evaluation system FIG. 3 shows an example of an ultrasonic imaging system 1 that implements an ultrasonic imaging method for a medium such as a heterogeneous medium M according to the present disclosure. This system and method make it possible to form an ultrasonic image of at least a part (area of interest or field of view) of the medium.

[0067] System 1 includes - a probing system 20 or a probe 20, and - a computing device 30 for calculating an image from the signals received from the probe 20, and - a control panel 40 connected to the computing device 30 and including, for example, buttons 41 and a touch pad 42, and - a display device 50 for viewing the image and various elements or measurements.

[0068] The probe 20 is connected to the computing device 30 using a cable 21 or a wireless connection and can emit ultrasonic waves W into the medium M and receive ultrasonic waves W from the medium M, where the ultrasonic waves result from the reflection of the emitted ultrasonic waves at scattering particles or scatterers inside the medium.

[0069] Probe 20 may include an array 10 comprising a plurality of transducers 11. The array 10 may be, for example, a linear, curved, two-dimensional, or matrix array. The transducer 11 can convert an electrical signal into vibrations and vice versa. The transducer 11 is, for example, a piezoelectric ultrasonic transducer, and they may take the form of a rigid strip that is directly or indirectly brought into contact with the outer surface of the medium M so as to be connected to the medium and vibrate to emit and receive ultrasonic waves W. The array 10 of transducers 11 of the probe 20 is then associated with the computing device 30. The transducer array 10 may have 100 or more transducers 11.

[0070] The computing device 30 may include a receiving device that amplifies and / or filters the signals received from the probe 20, and a converter (analog / digital converter and digital / analog converter) that converts the signals into data representing the signals. The data may be stored in a memory in the computing device 30 and / or may be directly processed to calculate intermediate data (beamforming data or other data). The computing device 30 may perform any processing used to subsequently construct an image from the signal data received from the probe 20, such as beamforming.

[0071] The calculated image is - An image of the medium (B-mode image), usually in grayscale, for viewing an organ in the medium, and / or - An image indicating the velocity or flow in the medium (color image), useful for viewing, for example, blood vessels and associated flow in the medium, and / or - An image showing the mechanical properties of the medium (elasticity in the ShearWave (registered trademark) elastography mode, useful for identifying, for example, tumors inside the medium).

[0072] The "connection" or "link" between the probing system 20, the computing device 30, and the display device 50) refers to any type of wired connection of an electrical or optical type, or any type of wireless connection using any protocol such as WiFi (registered trademark), Bluetooth (registered trademark), or others. Those connections or links can be either unidirectional or bidirectional. The associated display device 50 can be of any type, whether touch or non-touch screen, connected or not.

[0073] The display device 50 is a screen used to display the image calculated by the computing device 30. The display device 50 may also display other information such as image scale, configuration information for calculation or processing, or any measurement value, or help information. The screen 50 may be articulated in the support arm 51 so as to improve positioning for the user. The screen 50 is usually a large screen (at least 20 inches) so as to be more easily visible to the user.

[0074] The control panel 40 is, for example, part of the system housing, and the part includes a panel housing having a substantially flat surface 40a tilted towards the user for one-handed operation. As shown in FIG. 3, the control panel 40 may include a control screen 49 for displaying various configuration information.

[0075] The computing device 30 is configured to perform computing and / or processing steps, in particular to perform the method steps according to the present disclosure. By convention, as shown in FIG. 4 showing the array 10 of transducers 11 on the surface of the medium M, the spatial reference of the medium M is defined by taking a first axis X and a second axis Z perpendicular thereto. For the sake of simplicity, the first axis X corresponds to the lateral direction in which the transducers 11 are aligned in the example of a linear array, and the second axis Z corresponds to the depth of the medium M with respect to this array 10 of transducers 11. The definition may be adapted to the context and thus, for example, may be extended to a three-axis spatial reference frame in the case of a two-dimensional array 10, may be extended to a polar reference frame in the case of a curved array 10, or may be extended to any other reference frame, depending on and / or adapted to the structure and shape of the array 10 of ultrasonic transducers. Thus, for the remainder of the present disclosure, we use the Cartesian reference frame XZ corresponding to the linear probe 20 for the sake of simplicity of explanation, but those skilled in the art will readily generalize and apply the results to any type of reference frame.

[0076] For the remainder of the present disclosure, the array 10 of transducers 11 is referred to for transmission and reception, and it is understood that in more general cases, several arrays of transducers may be used simultaneously. The transducer 11 may be both a transmitter and a receiver, or may be a transmitter only for some and a receiver only for others. Similarly, the array 10 may be composed of one to N transducers 11 of the same or different types.

[0077] The array 10 of transducers 11 is used, for example, both as a radiator and a receiver, or is composed of several sub - arrays of transducers, some for the emission of ultrasound and others reserved for reception. The transducer array means at least one transducer, an ordered or unordered sequence of transducers, a two - dimensional distribution of transducers (e.g., a matrix of transducers), or any spatial distribution of transducers.

[0078] In the present disclosure, in particular, when a calculation or processing step for implementing a method step is referred to, it is understood that each calculation or processing step may be implemented by software, hardware, firmware, microcode, or any suitable combination of them or related technologies. When software is used, each calculation or processing step may be implemented, for example, by computer program instructions or code that is interpretable or executable. Those instructions may be stored or transmitted to a storage medium readable by a computer (or a computing device), and / or may be executed by a computer (or a computing device) to carry out those calculation or processing steps.

[0079] Analysis of points in a medium using a focusing reflection matrix The present disclosure describes methods and systems used for evaluating the ultrasonic properties of a medium. In practice, the medium is assumed to be heterogeneous. These methods and systems are based on the definitions shown in FIG. 4.

[0080] In the medium, we define - a first point P1 at a spatial position r in in the spatial reference frame of the medium, and - a second point P2 at a spatial position r out in the spatial reference frame of the medium.

[0081] Those spatial positions r in and r outis written in bold and indicates that the element is a position vector taken in the spatial reference frame (X,Z) of the medium. Other representations and definitions of the point position are possible and accessible to any ultrasound technician.

[0082] In the present disclosure, the first point P1 has a lateral position x in The second point P2 has a lateral position x out The two points P1, P2 have the same expected depth z, also denoted as z in = z out which is controlled by the echo time t under consideration. Thus, the spatial positions of points P1 and P2 are respectively r in = (x in , z) and r out = (x out , z).

[0083] The two points P1 and P2 are selected to be very close to each other, that is, separated by a few millimeters, for example, a distance of 20 millimeters or less.

[0084] The ultrasonic characteristic evaluation method implemented by the computing device 30 of the system 40 includes the following steps. - Generating, by the array 10 of the transducer 11, a series of incident ultrasonic waves US with a radiation base i in the zone of the medium, and in - Measuring or constructing a canonical reflection matrix R (t) which is a canonical reflection matrix defined between the radiation base i at the input and the reception base u at the output, and which has coefficients corresponding to the signals caused by the ultrasonic waves received by the transducer and reflected by the scatterers in the medium. ui - A focused reflection matrix R including the response of the medium calculated by focusing from the canonical reflection matrix R (t) between the input virtual transducer TV in at the spatial position r in and the output virtual transducer TV out at the spatial position r out ui (t).xx Step of determining (z).

[0085] The acquired canonical reflection matrix R ui (t) may be a "real" matrix, i.e., composed of real coefficients in the time domain, and the electrical signals recorded by each of the transducers are real numbers. Alternatively, this matrix may be a "complex" matrix, i.e., composed of complex numerical values, for example, in the case of demodulation for phased beamforming and IQ beamforming.

[0086] The focused reflection matrix R xx may be represented in different ways. In the representation of the present disclosure, the first point P1 of the spatial position (x in , z) is taken as a reference. These representations may also be established with respect to the second point P2 of the spatial position (x out , z), or with respect to the midpoint ((x in + x out ) / 2, z) between P1 and P2 of the spatial positions, or with respect to any point designated as a reference point. Those skilled in the art will be able to make the necessary changes to the variables in the presented representations.

[0087] The response of the medium is calculated by focusing from the canonical reflection matrix R ui (t).

[0088] The response of the focused reflection matrix R xx (z) corresponds to the sound pressure field calculated with respect to the assumed sound speed c0 among all points in the medium having the lateral positions x in and x out and having the echo time t and located at the expected depth z. In other words, this focused reflection matrix R xx (z) is defined by R xx (z) = [R(x in , x out , z)].

[0089] The parameters of the depth z and the sound speed c0 in the medium affect the delay law used in the focusing process.

[0090] The input radiation base i is, for example, as described above in FIGS. 2(a) to 2(f) of the present disclosure, a wave base in which each wave is generated by one of the transducers 11 of the array 10, or a base of a plane wave with an angular tilt θ with respect to the axis X, or a base of a virtual source.

[0091] The reception base u is, for example, the base of the transducer 11. Alternatively, at the time of reception, other reception bases may be used. For example, a plane wave base (or a spatial Fourier base) may be used, or any other base that enables measurement of the ultrasonic field in an intermediate plane between the ultrasonic probe and the focal plane of the object under consideration by appropriate beamforming processing at the time of reception may be used.

[0092] Therefore, the ultrasonic generation step is performed between the radiation base i and the reception base u. Therefore, this ultrasonic generation step is defined for any type of focused or unfocused ultrasonic wave, such as a plane wave.

[0093] In the measurement step, the canonical reflection matrix R ui (t) is defined between the input radiation base i and the output reception base u. The matrix includes all the temporal responses of the medium measured at time t for each radiation i out by each transducer 11 having the spatial coordinate u in . It is understood that the element indicated by the subscript "in" indicates radiation (i.e., input), and the element indicated by the subscript "out" indicates reception (i.e., output). The canonical matrix may also be recorded and / or stored in, for example, the memory of a computing device or any other medium, whether removable or not, enabling permanent or temporary storage.

[0094] In the step of determining the focused reflection matrix R xx (z), it can be obtained by the following process. - The radiation base i and the input virtual transducer TV inUsing the forward wave propagation time between, the spatial position r in At the so-called input focus spot around the first point P1 of in , the input virtual transducer TV in Generating an input focus spot corresponding to the forward transfer matrix R ui (t)-based input focusing process, - The virtual output transducer TV out And using the backward wave propagation time between the transducer of the receiving base u, the spatial position r out At the so-called output focus spot around the second point P2 of out , the virtual output transducer TV out Generating an output focus spot corresponding to the forward transfer matrix R ui (t)-based output focusing process from.

[0095] These input and output focusing processes form an input / output focusing process, and hereafter, are called focusing process or, more simply, focusing.

[0096] In other words, in this ultrasonic characteristic evaluation method, the virtual input transducer TV in Corresponds to an ultrasonic "virtual source" located at the spatial position r in The virtual output transducer TV out Corresponds to an ultrasonic "virtual sensor" located at the spatial position r out These virtual source and sensor are spatially separated by the difference Δr = r out - r in In this case, they are separated only along the horizontal axis, Δx = x out - x in Only by in . Their predicted depths are the z parameters used in the focusing law in the case of the c0 sound speed model. Their actual depths depend on the axial position (depth) of the isochronous volume, i.e., on the echo time t and also on the sound speed distribution c(r) in the medium. The lateral dimension of the virtual transducer depends on the focus spot generated by focusing on this actual depth.

[0097] Furthermore, the focusing reflection matrix Rxx (z) may be determined or calculated by any of the following. - In the time domain, it can be explicitly described using the time parameter t, i.e., R xx is described as R(z,t), In practice, the data on the focusing reflection matrix R xx (z,t) is calculated between two predetermined time points. - Or, in the frequency domain, it can be explicitly described using the pulse parameter ω corresponding to the frequency f by ω = 2π / f, i.e., R xx is described as R(z,ω), In practice, the data on the focusing reflection matrix R xx (z,ω) is calculated between two pulses ω of the frequency bandwidth, for example, between the lower pulse ω− and the upper pulse ω+ with respect to the central pulse ω c .

[0098] Therefore, the calculation of the following method may be performed in the time domain or the frequency domain.

[0099] In the first case of calculating in the time domain, the focusing reflection matrix R in (z,t) of the medium between the input virtual transducer TV out and the output virtual transducer TV xx is obtained by focusing using the input and output beamforming calculations. The coefficients of this focusing reflection matrix R xx (z,t) can be determined by the following formula. [Number] Here, N in is the initial normalization coefficient, N out is the second normalization coefficient, R ui (t) is the confocal reflection matrix, R(u out ,i in ,t) is the radiation following the radiation with subscript i in the radiation base (i) in at the spatial position uout The confocal reflection matrix R at time t, recorded by the transducer in ui (t), which has the delay times r in and r out applied to it, A in (i in ,x in z) and A out (u out ,x out ,z) are predefined apodization coefficients that maintain a constant numerical aperture, for example, in both transmission and reception.

[0100] For example, the first normalization coefficient N in may be defined by the following equation,

Equation

Equation

[0101] These delay times r in and r outis usually calculated by a qualified person from an established sonic model. A relatively simplified hypothesis is to assume a homogeneous medium with a constant speed of sound c0 in the medium. In that case, the propagation time is directly obtained from the distance between the probe transducer and the virtual transducer. Therefore, the calculation of these delay times depends on the type of wave, the assumed speed of sound, and the transducer array geometry.

[0102] N in The number of elements in the emission base is, for example, 1 or more, and advantageously 2 or more. N out The number of elements in the reception base (for example) is 2 or more.

[0103] Therefore, the previous beamforming calculation formula is the double sum of the time responses recorded in the canonical reflection matrix R ui the first sum related to the emission base i reflecting the focus obtained during emission, and the second sum related to the reception base u related to the focus during reception. This calculation is performed for each point of the spatial coordinates of two points P1 and P2, that is, the expected spatial position r in =(x in ,z) and r out =(x out ,z).

[0104] Therefore, the result of this beamforming calculation formula is a time signal related to these two spatial coordinates (r in ,r out ), or related to these two lateral positions x in , x out .

[0105] Finally, the focused reflection matrix R xx (z,t) in the time domain can be transformed into the focused reflection matrix R xx (z,ω) in the frequency domain by Fourier transform, that is, by the following formula.

Equation

[0106] This Fourier transform may be performed by any type of discrete Fourier transform, whether or not it is normalized.

[0107] In the second case of the calculation in the frequency domain, the canonical reflection matrix R ui (t), since it is composed of the signals received by the transducer, can be transformed into the frequency domain by Fourier transform, i.e., by the following equation, into the canonical reflection matrix R ui (ω).

Equation

[0108] This Fourier transform may be performed by any type of discrete Fourier transform, whether or not it is normalized.

[0109] Therefore, the focusing reflection matrix R xx (z) or R xx (z,ω) can be obtained by focusing using the following matrix calculation, which is substantially equivalent to focusing using the time beamforming described above, i.e., by the following matrix product.

Equation

[0110] Aberration correction processing The objective of method S100 according to the present disclosure is to correct aberrations in the ultrasonic characterization of medium M. Aberrations are caused, for example, by fluctuations in the structure in the medium, which cause fluctuations in the speed of sound and reflectivity.

[0111] Method S100 according to the present disclosure is shown in FIG. 5. This method is implemented by the computing device 30 of system 40 and includes the following steps. - Generating, by the array 10 of transducers 11, a series of incident ultrasonic waves US with radiation base i in the zone of the medium, in step S110, and - A canonical reflection matrix R(t) defined between the radiation base i at the input and the reception base u at the output, having coefficients corresponding to the signals caused by the ultrasonic waves received by the transducers and reflected by the scatterers in the medium. ui Measuring or configuring step S120.

[0112] These steps S110 and S120 correspond to the above-described generation and measurement steps.

[0113] Method S100 according to the present disclosure further includes the following steps. - Determining a set of responses R from the medium, step S130.

[0114] This step S130 is similar to the step of determining the focusing reflection matrix R(z,f), but this step is different in that the responses are not necessarily organized as a matrix. They may correspond only to the confocal signals, i.e., only to the diagonal components of the focusing reflection matrix. Further, these responses are at several frequencies f and at spatial positions r xx =(x p =(x p ,z p) It is calculated at several points of the spatial position r=(x,z) in the region (analysis region) located around the reference point. The responses around the points of the reference point at several frequencies enable analyzing this region around the reference point and enable local correction of the aberration and / or dispersion and / or reverberation caused by the medium upstream of the focal plane.

[0115] In particular, the method includes the following steps. - For several frequencies f of the signal received from the reflected ultrasonic wave, and for the canonical reflection matrix R of the sound speed model c0 ui (t) from the reference point r of the spatial position p =(x p ,z p ) Determine a set of responses R of the medium obtained by focusing processing for several points of the spatial position r=(x,z) in the region around. Step S130.

[0116] Next, the method S100 according to the present disclosure includes a correction process including the following steps. - Determine the frequency correction law Φ adapted to the reference point and determined at the frequency f by averaging or correlating the responses of the medium at points (x,z) of a plurality of different spatial positions around the reference point. Step S140, - Determine the corrected response R' of the medium by applying the frequency correction law Φ for a plurality of frequencies f to the response R of the medium around the reference point. Step S180.

[0117] In this way, the method locally examines the medium with a probe, and in particular, by determining the correction law for each point of the medium M at the spatial position r p and for each frequency f of the ultrasonic wave, has the advantage of being able to correct the focusing reflection matrix for aberration.

[0118] Furthermore, the method may include the following steps. - By combining the corrected responses at several frequencies f of this reference point, the intensity I of the point in the ultrasonic image corresponding to the point of the spatial position r=(x,z) c Step S190 of determining.

[0119] In particular, this intensity is calculated by the sum of squares of the corrected responses R’ for at least some or all of the previously calculated frequencies f at the point of the spatial position r=(x,z). For example, this calculation may be limited to a predetermined frequency band for ultrasonic characterization of the medium.

[0120] 1 - First Embodiment The first embodiment of the method S100 of the present disclosure performs matrix calculations by performing focusing processing between the points of the input virtual transducer and the points of the output virtual transducer, which may or may not be separate from each other. Therefore, a large number of responses from the medium may be calculated, enabling very detailed analysis and specific correction processing to be performed in order to characterize the medium M.

[0121] FIG. 11 shows this method according to the first embodiment of the present disclosure. The transducer array arranged facing the medium is used to apply ultrasonic waves to an area of the medium having a random “speckle” reflectivity for imaging.

[0122] In the first diagram (A) of FIG. 11, using a technique known as beamforming or focusing, the spatial position r in 1 , r in 2 , and r in 3 A plurality of waves are sequentially radiated into the medium by focused radiation in several focal directions of. The waves pass through the aberration layer, causing spatially and temporally distorted focal spots around the focus. Here, the temporal dispersion of the focused waves is caused by the frequency dependence of the speed of sound in the aberration layer and / or by multiple reflection echoes caused by the aberration layer.

[0123] In the following three figures (B) in the drawings, during the return stroke, the waves reflected at each focus pass through the aberration layer again, which further increases the echoes caused by multiple reflections within the aberration layer, distorting the ultrasonic waves spatially and temporally again. Therefore, the time signal received by the transducer is very complex and all contain a large number of echoes linked to multiple reflections.

[0124] As shown in the fifth figure (C), by averaging or correlating the echoes caused by a plurality of foci in the region around the reference point of the spatial position r p a temporal response as generated by a virtual coherent reflector is obtained. This calculation is used to determine the spatial-frequency correction law (herein shown by the transducer base u).

[0125] Figure 6 (D) in this drawing illustrates how this inverse-convolved virtual response can be used as the optimal delay law applied to correctly focus at each focus, compensating for problems of aberration, dispersion, and / or multiple reflections.

[0126] The method of this first embodiment will be described in detail later.

[0127] Step S130 of determining a set of responses R of the medium includes determining the response obtained by the focusing process between a first point r in =(x in , z) of the spatial position corresponding to the input virtual transducer and a second point r out =(x out , z) of the spatial position corresponding to the output virtual transducer. The first point and the second point are located in the region around the reference point and are located at the same seismic intensity z. The lateral positions x in and x out of the first and second points form a focusing base (x) at each depth z.

[0128] Then, the response R is R xx (z, f)=[R(x in, x out , z, f)] and having coefficients that may be represented as the focusing reflection matrix R xx It is recorded in (z, f).

[0129] Determination of the frequency correction law Φ (S140) Next, as shown in FIG. 6, the step S140 of determining the frequency correction law Φ includes the following sub-steps performed at each depth z and each frequency f. - The focusing reflection matrix R xx By orthogonally projecting R(z, f) onto the correction base (c), the dual reflection matrix R(z, f) is determined in sub-step S150 c - The frequency correction law Φ = [φ(c, f, r p )] determined for the correction base (c) such that the frequency correction law Φ is a spatial-frequency correction law is calculated from the dual reflection matrix R(z, f) in sub-step S160 c - The corrected dual reflection matrix R' around the reference point having coefficients represented as R'(z, f) = [R'(x, c, z, f)] is determined in sub-step S170 by calculating the product of the terms between the dual reflection matrix R(z, f) and the phase conjugate of the frequency correction law Φ, that is, determined by the following equation c c ’(z, f) = c ’ c

Number

Number

Number

[0130] ​​​​Next, step S180 of determining the corrected response R' of the medium around the reference point involves determining a corrected focusing reflection matrix R c ’(z,f) by back-projecting the corrected dual reflection matrix R xx ’(z,f) onto the focusing basis (x).

[0131] Thus, the method advantageously enables correction of the focusing reflection matrix for aberrations by locally examining the medium with a probe and determining correction laws for each point of the medium M at a spatial position r p and for each frequency f of the ultrasonic waves.

[0132] The correction is performed in a correction basis c adapted to the aberration to be corrected. The correction basis c is an input correction basis or an output correction basis.

[0133] Examples of correction bases are as follows. - A plane wave basis or a spatial Fourier basis, - A transducer basis u, - A basis corresponding to the assumed position of an aberrator in the medium, i.e., for example, a plane between the transducer plane (transducer basis u) and the focusing plane (focusing basis x), - A basis corresponding to a plane determined by optimization, for example, by a correlation matrix for which the first eigenvalue is maximized.

[0134] The dual reflection matrix R c (z,f) (S150) According to an embodiment of the method according to the present disclosure, an orthographic projection S150 is used to determine the dual reflection matrix R c (z,f). The orthographic projection S150 may be performed by a matrix product between the transition matrix P and the focusing reflection matrix R xx (z,f), i.e., by the following equation.

Equation

[0135] The transition matrix P depends on the correction base c used.

[0136] For the correction base corresponding to the plane wave base (c = k), the transition matrix P is the Fourier transform operator.

[0137] Regarding the array 10 of linear transducers 11 for generating a two-dimensional image, the coefficients of the transition matrix P may be expressed by the following equation.

Equation

[0138] Regarding the array 10 of matrix-type transducers 11 for generating a three-dimensional image, the coefficients of this transition matrix P may be expressed by the following equation.

Equation

[0139] Regarding the correction base corresponding to the transducer base (c = u), the coefficients of the transition matrix P correspond to the normal derivative of the Green's function connecting each focus at the spatial position (x, z) and each transducer 11 at the spatial position (u, 0).

[0140] Regarding the array 10 of linear transducers 11 used for generating a two-dimensional image, the coefficients of the transition matrix P may be expressed by the following equation.

Equation

Equation

Equation

Equation

[0141] Regarding the array 10 of the matrix-type transducers 11 for generating a three-dimensional image, the coefficients of this transition matrix P may be expressed by the following equation.

Equation

Equation

[0142] Therefore, the coefficients of the transition matrix P may be expressed as follows.

Equation

[0143] Spatial-Frequency Correction Law (S160) According to the first embodiment shown in FIG. 7 regarding step S160 of calculating the spatial-frequency correction law, this calculation step S160 includes the following. The dual reflection matrix R determined in the orthographic projection step S140 c Constructing the correlation matrix C from (z, f) in S161, and Analyzing the correlation matrix C in S162 to determine the spatial-frequency correction law Φ.

[0144] The spatial-frequency correction law corrects the dual reflection matrix R c (z, f) at the correction base c to obtain the corrected dual reflection matrix R’ c (z, f) and is used for this purpose. Next, this correction at the correction base c is applied to the focusing base x by performing the back-projection S180 of the corrected dual reflection matrix R’ c (z, f) to obtain the corrected focusing reflection matrix R xx ’(z, f).

[0145] Correlation matrix (S161) According to the first modification of step S161, the correlation matrix C is determined in the correction base c and in the frequency domain by calculating the following equation for the elements of the correlation matrix C = C cc .

Equation

[0146] Reference matrix R ref in the above formula for the reflection matrix R cWhat is added to it compensates for the geometric components of the reflection matrix predicted by the sonic model c0 and separates the distorted and reverberated wavefront components. When viewed from the focal plane, this operation virtually moves each focus (x, z) to the origin of the reference frame. For a medium with a random reflectivity (ultrasonic speckle) and a sufficient number of foci (x, z) in the region around the reference point of the spatial position r p Regarding the correlation matrix obtained for the region around the reference point of r at p , it is equivalent to what is measured on the correction basis for the coherent virtual reflector, to the extent defined by the focal spot caused by the focusing process in the above region. That virtual reflector forms a guide star that is later used to determine the optimal spatio-temporal focusing law in the region around the reference point r p

[0147] According to the second embodiment of step S161, the correlation matrix C is determined in the correction basis c and in the frequency domain by calculating the following equation for the elements of the correlation matrix C = cc

Equation

Equation

Equation

[0148] ​​​ The second modification is equivalent to the first modification. It reveals the intermediate calculation of the dual strain matrix Dc. Therefore, although it is not as direct as the first modification, it enables the direct extraction of the focusing law by a simple singular value decomposition of the D c matrix.

[0149] Compared with previous work that only considered the strain matrix with a temporal window at a single central frequency, the originality of the strain matrix considered in this application lies in its frequency dependence, which provides access to a complex spatio-temporal focusing law that goes beyond a simple time-delay law. In addition to conventional aberrations, this has the advantage of compensating for reverberation and frequency dispersion problems.

[0150] According to the third modification of step S161, the correlation matrix C is determined at the base of the image points at the spatial positions (x, z) by calculating the following equation for the elements of the correlation matrix C = C rr Here,

Equation

[0151] The reference matrix R ref is used as the dual reflection matrix R in the above equation cWhat is added to this is to compensate for the geometric components of the reflection matrix predicted by the c0 sound speed model and separate the wavefront distortion and the reflected components. When viewed from the focal plane, this operation virtually moves each focus (x, z) to the origin of the reference frame. Therefore, a set of incoherent guide stars is formed, and the amplitude distribution thereof depends on the support of the focal spot and is further modulated by the random reflectivity of the medium. The calculation of the correlation matrix C in the focusing base makes it possible to determine the phase shift between each guide star in the medium, and subsequently, it is used to determine how the phases of multiple different configurations can be readjusted and combined to generate coherent guide stars.

[0152] According to the fourth modification example of step S161, the correlation matrix C is the corrected matrix C = C rr and is determined at the base of the image point at the spatial position (x, z) by the calculation of the following equation for the elements thereof.

Equation

Equation

Equation

[0153] Analysis (S162) According to the first modification of step S162, the analysis of the correlation matrix C is performed by eigenvalue decomposition of the correlation matrix C, and the space-frequency correction law Φ is the correlation matrix C in the correction base (c), that is, C = C cc which is the first eigenvector U1 of

[0154] When the correlation matrix is a Hermitian matrix (C = C † ), its eigenvalues are positive real numbers. Therefore, the correlation matrix C cc may be expressed by the following formula

Equation

Equation

[0155] Next, we check if the first eigenvector, i.e., Φ(r p ) is equal to U1, or its normalized version, Φ(r p ) = exp(j arg{U1}), i.e., the coefficients of the space-frequency correction law have the same unit amplitude, but its phase is equal to that of U1 (the symbol arg{X} specifies the phase of the vector X), or an inverse filter type correction, Φ(r p) has a spatial-frequency correction law Φ equal to exp(j arg{U1}) / |U1|. When the signal-to-noise ratio is insufficient, the first option is preferred (appropriate filter). However, generally, the second option will be preferred when the correction corrects only the phase distortion without acting as an amplitude filter. Finally, the third option is relevant when the aberration medium non-uniformly attenuates a predetermined component and / or frequency of the field that we desire to improve in order to obtain a more accurate estimate of the reflectivity.

[0156] According to a second variant of step S162, the correlation matrix C is the dual distortion matrix D defined previously in the second variant of step S161 c analyzed by singular value decomposition thereof. The correlation matrix C in the first variant of step S162 cc eigenvalue decomposition of, in fact, when having coefficients organized according to the following definition, the dual distortion matrix D c is equivalent to the singular value decomposition (SVD) thereof.

Number

[0157] Singular value decomposition is applied to a rectangular matrix and applied to the dual distortion matrix D c and is represented as follows,

Number

Number

[0158] Therefore, the space-frequency correction law Φ is either equal to the first eigenvector of the dual distortion matrix D c , i.e., Φ(r p ) = U1, or its normalized version, Φ(r p ) = exp(j arg{U1}), i.e., the coefficient of the space-frequency correction law has unit amplitude but its phase is equal to that of U1 (the symbol arg{X} designates the phase of vector X), or an inverse filter type correction, Φ(r p ) = exp(j arg{U1}) / |U1|.

[0159] The advantage of the singular value decomposition of the dual distortion matrix D cc compared to the eigenvalue decomposition of the correlation matrix C c lies in the computational speed of the numerical algorithm for the singular value decomposition.

[0160] This search for the space-frequency correction law Φ is also equivalent to solving the following equation.

Equation

Equation

[0161] Next, the spatial-frequency correction law Φ is obtained by the following equation,

Equation

Equation

Equation

[0162] In the case of n→∞, the iterative time reversal algorithm converges to the same first eigenvector U1 of the matrix D c . In fact, since it converges after a small number of iterations and can bring about faster calculations, there may be an advantage in using the iterative time reversal algorithm instead of SVD.

[0163] According to the third modification example of step S162, the correlation matrix C cc is analyzed by solving the following equation.

Equation

[0164] Next, the spatial-frequency correction law Φ is obtained by the following equation,

Equation

Equation

[0165] The advantage of the iterative phase inversion algorithm for the foregoing options is that it is a more reliable estimator of the phase of the compensation law Φ(r p ), and thus ultimately provides better compensation for the phase distortion caused by the aberration source.

[0166] According to a fourth modification of step S162, the correlation matrix C rr is analyzed by solving the following equation.

Equation

Equation

Equation

[0167] This vector W = [W(x,z)] defined on the focus basis contains the phases of each incoherent guide star synthesized by focusing in the region around the reference point r p .

[0168] Then, the phase conjugate of this vector W may be used to readjust their phases so that the incoherent virtual stars can be coherently recombined, thereby obtaining an estimator of the spatially and frequency-compensated law Φ unbiased by the random reflectivity of the medium. Mathematically, this operation is expressed as the following equation.

Equation

[0169] Distortion matrix D c The advantage of this approach for the SVD (second modification of step S162) or the iterative phase inversion algorithm (third modification of step S162) is that it converges to a correction law that is as isoplanar as possible, i.e., for each point in the region around the reference point r p it converges to an efficient correction law for each point in the region around it.

[0170] Spatial-frequency correction law (S160) According to the second embodiment shown in FIG. 8 of step S160 for calculating the spatial-frequency correction law, this calculation step S160 is based on the spatial position reference point r p in the surrounding region Ω p is executed by an optimization algorithm S163 that maximizes the intensity or confocal intensity of the ultrasonic image.

[0171] In other words, the spatial-frequency correction law Φ is determined by maximizing the following equation.

Equation

Equation

[0172] This ultrasonic image is determined, for example, by the triple sum of the frequency value f, the input correction base c in , and the output correction base c out .

[0173] Using the above definitions, we can obtain, for example, the following calculations.

Equation

[0174] The previous calculation is based on the input correction c in and the output correction c out The dual reflection matrix R obtained by the orthographic projection S150 onto c cc (c in , c out , f) and its coefficients may be expressed as follows.

Equation

[0175] This method of determining the spatial-frequency correction law Φ is repeated by ultrasonic image calculation. Even when the ultrasonic image is limited to the area around the spatial position reference point r p , the iteration of the optimization algorithm may take a long calculation time.

[0176] However, this method has the advantage of more accurately determining the spatial-frequency correction law Φ because it takes into account the reversibility of the aberration correction applied to the outgoing and return-path ultrasounds.

[0177] Corrected dual reflection matrix (S170) According to an embodiment of the method of the present disclosure shown in FIG. 6, the corrected dual reflection matrix S170, R c ’(z, f)=[R c ’(x, c, f, z)] is determined by performing the product of the terms between the dual reflection matrix R c (z, f) and the phase conjugate of the spatial-frequency correction law Φ, that is, by executing the following equation.

Equation

Equation

[0178] Corrected reflection matrix (S180) According to an embodiment of the method of the present disclosure, the corrected focusing reflection matrix R xx ’(z,f) is then determined by back-projecting the corrected dual reflection matrix R c ’(z,f) onto the focus base (x). The back-projection is performed by the matrix product between the transition matrix P defined above and the focusing reflection matrix R c ’(z,f), that is, according to the following equation. [Number] Here, the exponent † indicates the conjugate transpose matrix operation.

[0179] Correction process iteration (L1) According to an embodiment of the method of the present disclosure shown in FIG. 5, the correction process step, that is, - Step S140 of determining the frequency correction law Φ, which probably determines the dual reflection matrix R c (z,f), step S160 of calculating the frequency correction law Φ, and step S170 of determining the corrected dual reflection matrix R c ’(z,f), and step S140 including these steps, - Step S180 of determining the corrected focusing reflection matrix R xx ’(z,f) are repeated a number of times (twice or more) as represented by the L1 loop in FIG. 5.

[0180] In each iteration, the forward projection in step S150 uses the corrected focusing reflection matrix R xx (z,f) is replaced by the corrected focusing reflection matrix R xx ’(z,f) obtained during the back-projection in step S180 of the previous iteration.

[0181] Thus, in each iteration, the spatial-frequency correction law is improved to better account for one or more aberrations in the medium M.

[0182] According to this first variant of the iterative process, in each iteration of step S150 for determining the dual reflection matrix R c (z,f), different correction bases c are used, for example, to correct different aberrations located at different locations in the medium.

[0183] For example, the medium M may be discretized or modeled by a series of layers along the depth direction z, and the iterative correction base c corresponds to the planes of those successive layers. In other words, corrections corresponding to multiple aberrations in the medium M are applied during the iteration.

[0184] For example, the medium M may be spatially divided into a plurality of regions in a predetermined manner or automatically based on a first ultrasonic image of the medium M. Each iteration of the iterative process performs a correction in the correction base c corresponding to each region of the medium M.

[0185] According to this second variant of the iterative process, in each iteration of step S150 for determining the dual reflection matrix R c (z,f), an orthographic projection is used to go towards either the input correction base or the output correction base of the reflection matrix. In the latter case, the matrix R xx (z,f) is projected onto the correction base as follows.

Number

Number

[0186] In an iterative sequence, we may alternate between the use of an input correction basis and an output correction basis. Thus, the spatio-temporal correction law Φ is improved in each iteration and the aberration correction is improved.

[0187] According to this third variant of the iterative process, the dual reflection matrix R c in each iteration of step S150 for determining (z,f), the region around the spatial position point r p is used, the size of which becomes smaller and smaller during the iteration. In other words, in each iteration, the size of the calculation region around the reference point r p is reduced. The size of the region may mean the width in the x direction or the depth in the z direction, both, or any other convention regarding the size of this region adapted, for example, to the scan mode of the medium M.

[0188] Thus, the correction law Φ is increasingly better adapted to the aberration located close to the reference point of the spatial position r p .

[0189] Confocal image (S190) According to an embodiment of the ultrasonic characteristic evaluation method of the present disclosure, the method further includes the following steps. - The corrected focusing reflection matrix R xx ’(z,f) by combining the corrected responses R’ of the points at several frequencies f integrated over the bandwidth of the ultrasonic signal, i.e., from the diagonal coefficients of c determining the intensity I of the ultrasonic image point at the spatial position (x,z) in step S190. For example, the calculation is as follows.

Equation

[0190] The previously determined intensities at a plurality of points are used to construct a corrected confocal image of the medium M, which corresponds to a conventional ultrasonic image in which there are no aberration, reverberation, and sound velocity frequency dispersion problems in the medium under study.

[0191] 2 - Second Embodiment In the second embodiment of the method S100 of the present disclosure, for example, more direct calculations are mainly performed to confocal-determine the characteristics of the medium M. This simplified embodiment determines the intensity I of the ultrasonic image points c and can be useful for more quickly determining the ultrasonic image of the zone of interest in the medium M.

[0192] In this second embodiment, the focusing process is determined or calculated only between the same input virtual transducer points and output virtual transducer points. It is equivalent to determining the diagonal components of the focusing reflection matrix R xx (z, f) of the first embodiment and recording them in the confocal reflection matrix R(z, f), which greatly reduces the number of medium responses to be calculated.

[0193] FIG. 12 shows this method according to the second embodiment of the present disclosure. The transducer array arranged facing the medium is used to apply ultrasonic waves to an area of the medium having a random "speckle" reflectivity for imaging.

[0194] In the first diagram (A) of FIG. 11, using a technique known as beamforming or focusing, multiple waves are sequentially radiated into the medium by focusing radiation in the directions of several foci at spatial positions r in 1 , r in 2 , and r in 3 . The waves pass through the reverberant layer and arrive at the focus with multiple reflection echoes caused by the reverberant layer.

[0195] In the next three diagrams (B) in the drawing, during the return journey, the waves reflected at each focus pass through the reverberant layer again, newly increasing the echoes caused by multiple reflections within the reverberant layer. The time signals received by the transducer are very complex and all contain a large number of echoes linked to multiple reflections.

[0196] As shown in the fifth figure (C), in the region around the reference point of the spatial position r p By averaging or correlating the echoes caused by a plurality of foci in the region around the reference point of, a temporal response such as that generated by a virtual coherent reflector is obtained. This calculation is used to determine the frequency correction law applied to the signal to compensate for reverberations in the ultrasonic image.

[0197] Figure 6 (D) in this drawing illustrates how this time-reversed virtual response obtained by inverse convolution can be used as the optimal delay law applied to correctly focus at each focus, compensating for problems of time dispersion and / or multiple reflections.

[0198] The method of this second embodiment will be described in detail later.

[0199] This second embodiment of method S100 has the following characteristics.

[0200] The step S130 of determining a set of responses R of the medium includes determining the response obtained by a focusing process between a first point r in =(x in , z) of the spatial position corresponding to the input virtual transducer and a second point r out =(x out , z) of the spatial position corresponding to the output virtual transducer, where the first point and the second point are the same (r in =r out ), All of the responses R are recorded in the confocal reflection matrix R with coefficients represented by R = [R(x, z, f)].

[0201] Thus, compared to the first embodiment, the confocal reflection matrix R here has only a single lateral position parameter x instead of two independent lateral position parameters x in and x out .

[0202] Next, step S140 of determining the frequency correction law Φ is directly executed by correlating the responses of the medium at various spatial position points (x, z) around the reference point, and the coefficients of the frequency correction law are given by Φ = [φ(f, r p )].

[0203] Next, step S180 of determining the corrected response R' around the reference point is directly executed by applying the frequency correction law for each frequency f and also by calculating the product of the terms between the confocal reflection matrix R and the phase conjugate of the frequency correction law Φ, that is, by the following equation.

Equation

Equation

Equation

[0204] Thanks to this system, this method has the advantage of being able to correct the confocal reflection matrix with respect to aberration by locally examining the medium using a probe and directly determining the correction law, particularly with respect to the reference point of the spatial position r p of the medium M and also with respect to several frequencies f of the ultrasonic waves.[[]]

[0205] The frequency correction law Φ is calculated more directly and simply than in the case of the first embodiment by correlating the received responses, that is, without using a correction base or a dual reflection matrix.[[]]

[0206] Frequency correction law (S140)[[]] According to the first embodiment of step S140 for determining the frequency correction law shown in FIG. 9, this step S140 includes: constructing a correlation matrix C from the confocal reflection matrix R(z,f) in S141; analyzing the correlation matrix C to determine the frequency correction law Φ in S142.

[0207] Next, this step S140 for determining the frequency correction law is the same as step S140 for calculating the frequency correction law of the first embodiment. It does not require a dual reflection matrix and is directly implemented on the confocal reflection matrix. Therefore, the calculation is simplified, but possible variations of these method steps are also the same as those of the first embodiment, as will be described below.

[0208] According to the first variation of step S141, the correlation matrix C is determined in the frequency domain by the following calculation.

Equation

[0209] According to the second variation of step S141, the correlation matrix C is determined based on the image points at the spatial position (x,z) by the following equation.

Equation

[0210] According to the first variation of step S142, the analysis of the correlation matrix C is the eigenvalue decomposition of the correlation matrix C, and the frequency correction law Φ is the first eigenvector U1 of the correlation matrix C.

[0211] According to the second modification of step S142, the analysis of the correlation matrix C is to solve an equation regarding the correlation matrix C and the frequency correction law Φ, and the solution method of this equation corresponds to iterative time reversal or iterative phase reversal, similar to that described in the first embodiment.

[0212] According to the second embodiment of step S140 for determining the frequency correction law, the frequency correction law is determined by an optimization algorithm that maximizes the confocal intensity of the ultrasonic image in the region around the reference point, similar to that described in the first embodiment.

[0213] Correction process iteration (L1) As shown in FIG. 5, the correction process step, that is, - step S140 for determining the frequency correction law Φ, and - step S180 for determining the corrected confocal reflection matrix R'(z,f) are repeated a number of times (twice or more) as represented by the L1 loop in FIG. 5.

[0214] In each iteration, the step of determining the frequency correction law in step S140 uses the corrected confocal reflection matrix R'(z,f) obtained during the step of determining the corrected response of step S180 for the previous iteration, instead of the confocal reflection matrix R(z,f).

[0215] Therefore, in each iteration, the frequency correction law is improved to better take into account one or more aberrations in the medium M.

[0216] In each iteration of step S140, regions around the spatial position reference point r p having an increasingly smaller size may be used during those iterations. In other words, in each iteration, the size of the calculation region around the reference point r p is reduced. The size of the region may mean the width in the x direction or the depth in the z direction, both, or any other convention regarding the size of this region adapted, for example, to the scan mode of the medium M.

[0217] The correction law Φ is increasingly better adapted to the aberrations located close to the reference point of the spatial position r p than to those located further away.

[0218] Confocal image (S190) According to an embodiment of the ultrasonic characteristic evaluation method of the present disclosure, the method further includes the following steps. - The intensity I of the ultrasonic image point at the spatial position (x, z) c (x, z) is determined in step S190 by combining the corrected responses R' of that point at several frequencies f. For example, the calculation is as follows.

Equation

[0219] The previously determined intensities at a plurality of points are used to construct a corrected confocal image of the medium M, which corresponds to a conventional ultrasonic image in which there are no aberration, reverberation, and sound velocity frequency dispersion problems in the medium under study.

[0220] Results in a calibrated experimental medium (so-called "phantom") FIG. 13 shows a calibrated experimental medium, a so-called "phantom", for generating ultrasonic speckles, which has two cylindrical enclosures having a higher reflectivity than the surrounding medium and a plurality of reflectors (nylon threads) linearly arranged along two lines, one horizontal and the other vertical. At a distance from the point reflector, the speed of sound in the medium is about 1540 m / s. A layer of plexiglass® having a speed of sound of about 2750 m / s is placed on the phantom corresponding to the aberration layer. Then, on top of that layer, an array 10 of transducers 11 of the ultrasonic probe is placed. A plurality of plane waves of ultrasonic waves are applied to the medium at various angles between -40 degrees and +40 degrees with respect to the transducer plane. Ultrasonic waves in such a medium pass through media having different speeds of sound and undergo multiple reflections (echoes) between the interfaces of those media before reaching the phantom medium scatterers.

[0221] FIG. 14 shows an ultrasonic image acquired in the zone of interest in the experimental medium shown in FIG. 13. This ultrasonic image is acquired assuming a speed of sound of 1540 m / s in the volume of the medium to which the ultrasonic waves are applied. This ultrasonic image shows the problems of aberration and echoes caused by the plexiglass layer in the image by the point reflector. First, the image of each point reflector is stretched horizontally, indicating the degradation of the horizontal resolution of the image due to the difference between the speed of sound model c0 and the actual speed of sound distribution in the medium. Second, the image of each point reflector is repeated in the depth z direction behind each ballistic image of the reflector, indicating the echoes caused by the multiple reflection echoes inside the plexiglass layer. As a result, the ultrasonic image has distortions in both the horizontal and axial directions and is greatly disturbed. In the case of medical imaging, those problems result in low contrast, low resolution, and the appearance of artifacts in the ultrasonic image, which seriously interfere with the doctor's diagnosis.

[0222] FIG. 15 then shows the frequency correction law Φ obtained by the method according to the present disclosure in the region of the medium B1 of FIG. 14. In the second embodiment, this frequency correction law is obtained by repeatedly phase-inverting the frequency correlation matrix C = [[C(f,f’)] of the confocal signals from each point in the medium. First, this drawing shows the absolute value and phase as a function of the frequency of the frequency correction law, and then shows the time representation of the frequency correction law obtained by inverse Fourier transform. The phase of the frequency correction law corresponds to the phase shift applied to each frequency component of the ultrasonic signal. Equivalently, the time correction law corresponds to the time delay law that should be associated with the received ultrasonic signal in order to (partially) compensate for the reverberation problem and obtain a more satisfactory ultrasonic image.

[0223] The time representation of the frequency correction law includes the first large-amplitude echo, the echo time of which is less than the ballistic time and corresponds to the error of the propagation model with respect to the speed of sound in the medium. Some subsequent echoes correspond to multiple reflections in the pre- plexiglass layer. This frequency correction law makes it possible to correct the aberration on average in the B1 region of the experimental medium, which corresponds to the "speckle" region in the medium. Then, this law is used to improve the corrected ultrasonic image of this area of interest in order to characterize the medium, especially as can be seen from FIG. 16(b) described below.

[0224] FIG. 16 shows the improvement achieved by the process according to the present disclosure.

[0225] The left image (a) in this drawing is an ultrasonic image obtained using a focusing method generally used in the prior art of an experimental medium having an assumed speed of sound c0 of 1540 m / s and without aberration correction. The image has a low resolution and is just of medium quality.

[0226] The right image (b) in this drawing is an image obtained using the described process so as to correct for the speed of sound and multiple reflection aberrations. A significant improvement can be seen in the spatial resolution of the image of the point reflector in the medium and in the (partial) suppression of the multiple reflection echoes. The background image also shows a greater difference in amplitude between the virtual reflector and the surrounding speckles. Thus, the reverberation compensation process significantly improves the quality of the ultrasonic image, particularly the contrast.

[0227] Figure 17 shows an ultrasonic image obtained facing the zone of interest in the experimental medium of FIG. 13, as in FIG. 16(b), after applying compensation for aberrations and reverberations according to the first embodiment, i.e., by applying the spatial-frequency correction Φ = [Φ(k x ,f)] determined on a plane-wave basis. This law is obtained by iterative phase inversion of the spatial-frequency correlation matrix C kk = C({k x ,f},{k’ x ,f’}) obtained by averaging the correlations at all points in the field of view. As in the case of FIG. 16(b), this global correction only partially compensates for the aberrations and reverberations. Unlike FIG. 16(b), three regions C1, C2, and C3 are identified in this image in order to apply the method of the present disclosure locally and iteratively.

[0228] Figure 18 shows the results of determining the spatial-frequency correction law Φ in the first region C1 of FIG. 17, the region C2 of FIG. 17, and then the region C3 of FIG. 17. Thus, in the first line (a) of FIG. 18, the spatial-frequency correction law Φ in the first region C1 is represented by its spectrum (|C x ×Φ|) as a function of the lateral component k kk of the wavevector and the frequency f (left-hand image), and also by its phase (arg[Φ]) as a function of k x and the frequency f (right-hand image). The second line (b) of FIG. 18 represents the spatial-frequency correction law Φ in the second C2 region using the same format. Another spatial-frequency correction law Φ is determined for the third C3 region in the ultrasonic speckles.

[0229] Next, FIG. 19 shows the improvements achieved by the method according to the present disclosure using a local spatio-temporal correction law including corrections C1, C2, and C3.

[0230] The left image (a) in this drawing is an ultrasonic image obtained using a focusing method generally used in the prior art of the experimental medium, which has an assumed speed of sound c0 of 1540 m / s and does not perform aberration correction. The image has low resolution and is severely degraded by the reverberation phenomenon.

[0231] The central image (b) in this drawing is an image obtained by the described method, which enables global correction of the speed of sound and multiple reflection aberration over the entire region of interest of the image. This correction averages the aberration over the entire region of interest, which is already an improvement. This image is similar to that shown in FIG. 17.

[0232] The right image (c) in this drawing is an image obtained by the described method by locally repeating the calculation of the spatio-frequency correction law as shown in FIG. 18 for regions C1, C2, and C3 shown in FIG. 17. The correction performed on the spatio-frequency correction law significantly improves the spatial resolution of the image and removes most of the echoes caused by multiple reflections inside the plexiglass layer. Finally, the relative amplitude between the point reflector and the surrounding speckles is much better, showing the contrast gain provided by the local compensation for aberration and reverberation.

[0233] Ultrasonic characteristic evaluation system The ultrasonic characteristic evaluation system 1 for the medium M according to this is illustrated in FIG. 3. It is - An array 10 of transducers 11 adapted to generate a series of ultrasonic waves incident on a zone of the medium and measure the ultrasonic waves backscattered by the zone as a function of time, - A computing device 30 connected to the transducer array and adapted to implement a method including the following steps. The method includes: - Generating, by an array 10 of transducers 11, a series of incident ultrasonic waves US with a radiation base i in a zone of the medium. in Step S110. - Measuring a canonical reflection matrix R(t) that is defined between a radiation base i at the input and a reception base u at the output, and has coefficients corresponding to signals caused by ultrasonic waves received by the transducer and reflected in the medium. ui Step S120. - Determining a set of responses R of the medium obtained by focusing on several points of the spatial position r=(x,z) of a region around a reference point r=(x,z) of the spatial position with respect to several frequencies f and from the canonical reflection matrix R(t) of the sound speed model c0. Step (S130). ui - Determining a frequency correction law Φ adapted to the reference point and determined at the frequency f from the responses of the medium at several points (x,z) of different spatial positions. Step (S140). p - Determining a corrected response R' of the medium by applying the frequency correction law Φ for several frequencies f to the response R of the medium around the reference point. Step (S180). p ,z p ) - Determining a frequency correction law Φ adapted to the reference point and determined at the frequency f from the responses of the medium at several points (x,z) of different spatial positions. Step (S140). - Determining a corrected response R' of the medium by applying the frequency correction law Φ for several frequencies f to the response R of the medium around the reference point. Step (S180).

Claims

1. An ultrasonic characteristic evaluation process (S100) of a medium, - By the array (10) of transducers (11), in the zone of interest of the medium, a series of incident ultrasonic waves (US) that are a radiation base (i) ｉｎ are generated in step (S110); - A canonical reflection matrix defined between an input radiation base (i) and an output reception base (u), the canonical reflection matrix R having coefficients corresponding to signals caused by ultrasonic waves received by the transducer and reflected in the medium ｕｉ measuring (step S120) (t), and wherein the method - For several frequencies f of the signal received from the reflected ultrasonic wave, and for the acoustic velocity model c ０ of the canonical reflection matrix R ｕｉ from the reference point r of the spatial position in (t) ｐ =(x ｐ , z ｐ ) by performing focusing processing on several points of the spatial position r=(x, z) in the region around, determining a set of responses R of the medium (step S130); - determining a frequency correction law Φ adapted to the reference point and determined at a frequency f by averaging or correlating the responses of the medium at points (x, z) at a plurality of different spatial positions around the reference point (step S140); - further comprising a correction process including determining a corrected response R' of the medium by applying the frequency correction law Φ for a plurality of frequencies f to the response R of the medium around the reference point, the process.

2. - The reference point r of the above spatial position ｐ By combining the corrected responses at some frequencies f of the above, the reference point r of the above spatial position ｐ The intensity I of the ultrasonic inspection image point corresponding to ｃ Further includes the step (S190) of determining The method according to claim 1.

3. - determining a set of responses R of the medium (S130) includes determining a response obtained by a focusing process between a first point r ｉｎ = (x ｉｎ , z) of a spatial position corresponding to the input virtual transducer and a second point r ｏｕｔ = (x ｏｕｔ , z) of a spatial position corresponding to the output virtual transducer, and the first point and the second point are identical (r ｉｎ = r ｏｕｔ ), ｉｎ = (x ｉｎ , z) and a second point r ｏｕｔ = (x ｏｕｔ , z) of a spatial position corresponding to the output virtual transducer, and the first point and the second point are identical (r ｉｎ = r ｏｕｔ ), All of the responses R are recorded in a confocal reflection matrix R having coefficients represented by R = [R(x, z, f)], - Determining the above frequency correction law Φ (S140) is performed by correlating the responses of the medium at a plurality of different spatial positions (x, z) around the reference point, and the coefficient is Φ = [φ(f, r ｐ )] is represented by, - determining the corrected response R' around the reference point (S180) is performed by calculating the product of terms between the confocal reflection matrix R and the phase conjugate of the frequency correction law Φ by applying the frequency correction law at each frequency f, that is, by the following formula, 【Number 1】 where all of the corrected responses R' are recorded in a corrected confocal reflection matrix R' having coefficients represented by R' = [R'(x, z, f)], the symbol 【Number 2】 is a Hadamard product satisfying the following formula, [Number 3] The method according to claim 1 or 2.

4. - further comprising combining the corrected responses R' of the ultrasonic inspection image points at spatial positions (x, z) at a plurality of frequencies f, that is, by the following formula, [Number 4] The intensity I of the ultrasonic inspection image point at the above spatial position (x, z) ｃ The step (S190) of determining The method according to claim 3.

5. Determining the frequency correction law (S140) comprises constructing a correlation matrix C from the confocal reflection matrix R(z, f) (step S141); analyzing the correlation matrix C to determine the frequency correction law Φ (step S142). The process according to claim 3 or 4.

6. The correlation matrix C is determined in the frequency domain by the following formula, 【Number 5】 where R is the confocal reflection matrix, x, z are the coordinates of points in the region around the reference point, * is a conjugate operator. The method according to claim 5.

7. The correlation matrix C is determined based on the image points at the spatial position (x, z) by the following formula, 【Number 6】 where R is the confocal reflection matrix, x, z are the coordinates of the image points in the region around the reference point, * is a conjugate operator. The method according to claim 5.

8. Analyzing the correlation matrix C (S142) is the eigenvalue decomposition of the correlation matrix C, and the frequency correction law Φ is the first eigenvector U of the correlation matrix C １ is as follows. The method according to one of claims 5 to 7.

9. Analyzing the correlation matrix C (S142) is to solve an equation including the correlation matrix C and the frequency correction law Φ, and the solution method of this equation corresponds to iterative time reversal or iterative phase reversal. The method according to one of claims 5 to 7.

10. Determining the frequency correction law (S140) is executed by an optimization algorithm that maximizes the confocal intensity of the ultrasonic image in the region around the reference point. The method according to one of claims 3 to 9.

11. The steps of the correction process (S140, S180) are repeated multiple times. In each iteration, the corrected confocal reflection matrix R'(z, f) obtained in the previous iteration is used instead of the in-focus reflection matrix R(z, f). The method according to one of claims 3 to 10.

12. In each iteration, the size of the region around the reference point r of the above spatial position is reduced, ｐ ​ The method according to claim 11.

13. Determining the confocal reflection matrix R(z, f) (S130) includes compensating for the time decay of the signal. The method according to one of claims 3 to 12.

14. - Determining a set of responses R of the medium (S130) includes determining a response obtained by a focusing process between a first point r ｉｎ = (x ｉｎ , z) corresponding to an input virtual transducer and a second point r ｏｕｔ = (x ｏｕｔ , z) corresponding to an output virtual transducer, and the first point and the second point are located in a region of the same seismic intensity z, The horizontal positions x of the above first and second points ｉｎ and x ｏｕｔ form a focusing base (x) at each depth z, and all of the above responses R are R ｘｘ (z, f) = [R](x ｉｎ , x ｏｕｔ , z, f) and are recorded in a focusing reflection matrix R ｘｘ (z, f) having coefficients - Determining the frequency correction law Φ (S140) is a sub-step performed at each depth z and each frequency f, where - The above-mentioned focusing reflection matrix R ｘｘ By orthogonally projecting (z, f) onto the correction base (c), the dual reflection matrix R ｃ A sub-step (S150) for determining (z, f), and - Such that the above frequency correction law Φ is a spatial / frequency correction law, the above frequency correction law Φ = [φ(c, f, r ｐ ), which is determined for the above correction base (c), is calculated from the above dual reflection matrix R ｃ (z, f) in a sub-step (S160), and - The dual reflection matrix R ｃ By calculating the product of the term between (z, f) and the phase conjugate of the frequency correction law Φ, that is, R determined by the following equation ｃ ’(z, f) = [R ｃ ’(x, c, f, z)], the corrected dual reflection matrix R around the reference point having the coefficient represented as ｃ ’ and a sub-step (S170) for determining 【Number 7】 Here, The symbol * represents a phase conjugation operation. The symbol 【Number 8】 is a Hadamard product that satisfies the following equation. 【Number 9】 - Determining the corrected response R' of the medium around the reference point (S180) involves the corrected dual reflection matrix R' ｃ By back-projecting (z, f) onto the focusing base (x), a corrected focusing reflection matrix R ｘｘ '(z, f) is determined, including The method according to claim 1 or 2.

15. - At several frequencies f, the diagonal coefficients of the corrected focusing reflection matrix R' ｘｘ (z, f) are combined to determine the intensity I of the ultrasonic image point at the spatial position (x, z) ｃ (S190), that is 【Number 10】 Further including The method according to claim 14.

16. The orthographic projection (150) is the matrix product between the transition matrix and the above-mentioned focusing reflection matrix R ｘｘ (z, f), that is, 【Number 11】 Executed by Here, P(z, f)=[P(c, x, z, f)] is the transition matrix at each frequency f between the in-focus base (x) and the correction base (c) at depth z. The method according to claim 14 or 15.

17. The correction base (c) is an input correction base or an output correction base. The method according to one of claims 14 to 16.

18. Calculating the frequency correction law (S160) The above dual reflection matrix R ｃ Constructing a correlation matrix C from (z, f) (S161), Includes analyzing the correlation matrix C to determine the frequency correction law Φ (S162). The method according to one of claims 14 to 17.

19. The correlation matrix C is determined in the correction base (c) and in the frequency domain by the following equation, where 【Number 12】 Here, R ｃ is the above dual reflection matrix, R ｒｅｆ is the model reflection matrix of the model medium. In the above model medium, the speed of sound is the predicted speed of sound c of the medium ０ and the plane reflector is located at a depth z x and z are the coordinates of a point in the region around point r ｐ and * is a conjugate operator. The method according to claim 18.

20. The correlation matrix C is determined based on the image points at the spatial positions (x, z) by the following equation, where 【Number 13】 Here, R ｃ is the above dual reflection matrix, R ｒｅｆ is the model reflection matrix of the model medium. In the above model medium, the speed of sound is the predicted speed of sound c of the medium ０ and the plane reflector is located at a depth z x and z are the coordinates of the image points in the area around the point r ｐ and * is a conjugate operator. The method according to claim 18.

21. Analyzing the correlation matrix C (S162) is eigenvalue decomposition of the correlation matrix C, and the frequency correction law Φ is the first eigenvector U of the correlation matrix C １ is that. The method according to one of claims 18 to 20.

22. Analyzing the correlation matrix C (S162) is to solve an equation including the correlation matrix C and the frequency correction law Φ, and the solution method of this equation corresponds to iterative time reversal or iterative phase reversal. The method according to one of claims 18 to 20.

23. The frequency correction law (S160) is calculated using an optimization algorithm that maximizes the confocal intensity of the ultrasonic image in the region around the reference point. The method according to one of claims 14 to 22.

24. The steps (S140, S180) of the correction process are repeated multiple times. In each iteration, the orthographic projection (S150) is the corrected focus reflection matrix R' obtained during the back-projection (S180) of the previous iteration ｘｘ Let (z, f) be the focus reflection matrix R ｘｘ which is used instead of (z, f), The method according to one of claims 14 to 23.

25. In each iteration of the orthographic projection (S150), it alternates between the orthographic projections in the input correction base and the output correction base. The method according to claim 24.

26. In each iteration, the correction base (c) of the orthographic projection (S150) is different. The method according to claim 24.

27. In each iteration, the size of the region around the reference point r of the above spatial position is reduced, ｐ ​ The method according to claim 24.

28. The above-mentioned focusing reflection matrix R ｘｘ Determining (z, f) (S130) includes compensating for the temporal attenuation of the above-mentioned signal The method according to one of claims 14 to 27.

29. A system (1) for evaluating the ultrasonic characteristics of a medium (M), - An array (10) of transducers adapted to generate a series of ultrasonic waves incident on the zone of interest of the medium and measure the ultrasonic waves backscattered by the zone of interest as a function of time; - A computing device (30) connected to the array of transducers and adapted to implement the method according to one of claims 1 to 28. System.

Images