Method for characterizing a target object in a medium

Abstract

Method for characterizing a target object in a medium The present disclosure relates to a method for characterizing a target object in a medium. The method comprises: obtaining a reference matrix F(q) associated with the target object, measuring a reflection matrix R associated with the medium being probed, and projecting the reflection matrix R onto the reference matrix F(q) to estimate a probability P(q) that the object is in a state q. Figure for abstract: Figure 1

Description

Title of the invention: Method for characterizing a target object in a medium Prior art

[0001] Ultrasound, i.e. ultrasound imaging, provides a non-invasive method for visualizing the internal structure of a material, an animal, a human body or certain of its parts (e.g. organs).

[0002] Examples of different ultrasound imaging modes may include a B-mode (i.e., a brightness mode), a Doppler mode, or a ShearWave® Elastography mode (i.e., a shear wave elastography mode).

[0003] In ultrasound, an array of piezoelectric transducers is typically placed opposite the medium to be imaged. These elements can emit / receive ultrasonic waves independently over a wide spectral band. From a series of insonifications of the medium by this array, the echoes backscattered by the heterogeneities of the medium are recorded by these same transducers or by others. The signals thus recorded are then stored in a response matrix. This matrix can be acquired for different types of incident waves.

[0004] A basic acquisition sequence consists of emitting each incident wave with one element at a time and, for each emission, recording the field reflected by the medium on all the elements of the array. This canonical basis, or basis of transducers, was first used to describe the principle of iterative time reversal, cf. the “DORT” method described by: Claire Prada, Mathias Fink, “Eigenmodes of the time reversal operator: A solution to selective focusing in multiple-target media,” Wave Motion, Volume 20, Issue 2, 1994, Pages 151-163, ISSN 0165-2125. This canonical basis can be used in the field of non-destructive testing, where it is called “full matrix capture.”

[0005] In addition, there are ultrasound imaging technologies that use coherent plane-wave compounding for very high frame rate ultrasonography and transient elastography, cf. Montaldo G, Tanter M, Bercoff J, Benech N, Fink M. Coherent plane-wave compounding for very high frame rate ultrasonography and transient elastography. IEEE Trans Ultrason Ferroelectr Freq Control. 2009 Mar;56(3):489-506. doi: 10.1109 / TUFFC.2009.1067. PMID: 19411209.

[0006] In this context, FR3114159 describes a method for ultrasonic characterization of a medium comprising a step of generating a series of incident ultrasonic waves, a step of generating an experimental reflection matrix R ui(t) defined between the emission base (i) at the input and a reception base (u) at the output, a step of determining a focused reflection matrix R rr =| / ?(rm, rout, ôt)] of the medium between a virtual input transducer (TVin) calculated from an input focus of the experimental reflection matrix and a virtual output transducer (TVout) calculated from an output focus of the experimental reflection matrix, the responses of the virtual output transducer (TVout) being taken at a time instant shifted by an additional delay ôt relative to a time instant of the responses of the virtual input transducer (TVin). This focused reflection matrix plays a pivotal role in the development of matrix ultrasound for the purposes of quantification and correction of aberration and multiple scattering problems in ultrasound imaging. Disclosure Statement

[0007] The method and system described in this document relate to technologies for detecting, locating and characterizing a target object, in particular objects that are difficult to image, for example objects in a scattering medium. This description applies in particular, but not exclusively, to medical or veterinary imaging for locating and characterizing targets in biological environments (for example micro-calcifications, bubbles, needles or lesion markers in ultrasound imaging). It can also be applied to the detection of defects useful for non-destructive testing in industry.Although the experimental demonstrations presented in this document are carried out in reflection in the field of ultrasound imaging, this disclosure can also be applied in transmission to all fields of wave physics (for example radar technologies, microscopy, seismology) for which one or more multi-element networks make it possible to measure the response matrix of a medium in reflection and / or in transmission of the latter.

[0008] In particular, it may be desirable to more reliably detect the position and / or orientation of a target object in a medium under study, also called a region of interest. For example, if the target object is a medical device (e.g. a marker) implanted in a human body, it is desirable to precisely locate its position in the human tissue, for example in the context of a surgical procedure such as removal of a tumor or suspicious mass.

[0009] According to a more general example, it may be possible to characterize a target object in a medium, for example, not only to locate its position, but also to obtain other information on the object or its environment (temperature, pressure, etc.), for example its shape and / or the structure of the object, the size of the object, the composition of the object, and / or follow the evolution of these parameters nature, structure, composition as a function of time.

[0010] According to another modality, the state of the object can be used to characterize the surrounding environment (pressure, temperature, mechanical properties, etc.), the response of the object also depending on the environment surrounding the region of interest.

[0011] As explained in more detail below, conventional techniques (e.g., B-mode ultrasound imaging) often do not allow for accurate detection or characterization of a target object, for example, due to the presence of a scattering medium generating ultrasonic speckle. Speckle can be considered as a granular profile, which can vary from one location to another in the medium. Speckle can be explained by the coherent formation of the echo from many small scatterers within the medium. Some objects are also difficult to image or even undetectable with conventional imaging techniques due to their geometry or their acoustic or mechanical properties.

[0012] Thus, a method for characterizing a target object in a medium is provided according to a particular exemplary embodiment of the disclosure. The method comprises: obtaining a reference matrix F(q) associated with the target object (e.g. associated with a state q of the target object), obtaining a reflection matrix R of the medium, and projecting the reflection matrix R onto the reference matrix F(q) to estimate a probability P(q) that the object is in a state q.

[0013] Therefore, as disclosed in the present application, since a reflection matrix of the medium (and therefore of the contained target object) is obtained, and since this reflection matrix can be projected onto a reference matrix of the target object (i.e. which "describes" the target object), the target object can be characterized reliably and precisely in the medium, independently of any disturbance factor of the medium.

[0014] In other words, the reference matrix can be designed, predetermined and used to search in a medium of interest and / or detect the target object more reliably and accurately.

[0015] Therefore the reference matrix F(q) can be used to characterize the target object.

[0016] For example, the medium may be breast tissue comprising a marker. A Breast tissue typically causes ultrasound speckle. The presence of a target object (e.g., a marker) is difficult to detect on a conventional B-mode ultrasound image. In contrast, the use of a reference matrix F(q) associated with the target object allows detection with excellent contrast and localization with a precision well below the diffraction limit of the medium.

[0017] According to a particular exemplary embodiment, the target object comprises at least one of: a predefined element of the environment, such as a fabric of the environment, such as for example a muscle fiber, and an external object inserted into the medium, such as a medical device, for example a biomarker-type marker, all or part of a biopsy device, a needle or a probe.

[0018] According to a particular embodiment, the state q of the object comprises at least one parameter from: the relative position and / or the relative orientation of the object in the medium, the orientation of the object in the medium, the shape and / or the structure (initial and / or current) of the object, the size of the object, the composition of the object, local intensive parameters of the surrounding medium, such as the temperature, the pressure, the composition, the mechanical properties and / or the concentration of a compound of the surrounding medium.

[0019] According to a particular exemplary embodiment, the state q of the object can be measured at different times and can thus be characterized dynamically.

[0020] For example, obtaining the reflection matrix may comprise obtaining reflection matrices measured at different times t. Each of the reflection matrices may be projected onto the reference matrix to measure the dynamics of the state of the object.

[0021] Accordingly, the estimated probability that the target object is in a particular state can provide information about the characteristics of the object or its environment. For example, if the object is estimated with a high probability to have a particular size and to be in a particular position, this size and this position can partially or completely characterize the object.

[0022] The state of the target can also be expressed in the form of a matrix Q: Each column qj (in vector form) of the matrix Q can correspond to a state parameter of the target object, for example qi: Position, q 2: Orientation, etc.

[0023] According to a particular exemplary embodiment, obtaining a reference matrix F(q) comprises obtaining a dictionary of reference matrices F(q) associated with the target object.

[0024] The matrix dictionary makes it possible, for example, to exploit the matrix signature of a target object to characterize it precisely, for example to detect it with excellent contrast in a medium which generates speckle when it is insonified, for example by ultrasonic waves.

[0025] According to a particular exemplary embodiment, projecting the reflection matrix R comprises: projecting the reflection matrix R onto the set of reference matrices F(q) to estimate a probability P(q) that the object is in a state q.

[0026] According to a particular exemplary embodiment, projecting the reflection matrix R comprises applying a matrix filter to the reflection matrix R.

[0027] According to a particular exemplary embodiment, the matrix filter comprises one or more normalized scalar products between the reflection matrix R and the set reference matrices F(q), or the matrix filter includes an artificial intelligence model.

[0028] Also, the normalized scalar product may be a correlator and / or a mathematical function. The result of this mathematical function may be the estimated probability.

[0029] The artificial intelligence model is for example a neural network.

[0030] According to a particular exemplary embodiment, the reflection matrix R is a reflection matrix expressed in the focused basis or in another basis, such as plane wave bases, transducers, etc. The input data for the artificial intelligence model may comprise the reflection matrix R and the reference matrix F(q). The output of the artificial intelligence model may comprise the estimated probability. The model may be pre-trained for the task of estimating the probability.

[0031] According to a particular exemplary embodiment, the reference matrices F(q) of the dictionary depend on a reference state of the target object or its environment, the state optionally at least one of: the position, the orientation, the shape, the structure, the size, the composition and / or the local intensive parameters of the surrounding environment such as the temperature, the pressure or the concentration of a compound.

[0032] According to a particular exemplary embodiment, obtaining the dictionary of reference matrices F(q) comprises: a measurement (for example of experimental type) of a first reference matrix corresponding to a reflection matrix R 0(q 0 ) for a first state q 0 of the target object, and / or a measurement (for example of experimental type) of a first set of reference matrices for a first set of states q of the target object and / or associated with several states q of the target object.

[0033] Primarily, a reference matrix may correspond to or may be a reflection matrix according to the present disclosure. However, the reference matrix has a specific function, namely to serve as a reference (e.g., in the context of a dictionary). However, the manner in which it is obtained may be the same, for example, in the context of a measurement.

[0034] The difference between the reference matrix and the reflection matrix may therefore lie in the context in which it is measured. While a reference matrix according to the present disclosure may be measured during an experiment, in order to obtain a reference of a target object, the reflection matrix according to the present disclosure may be measured on a particular support (e.g. a patient) during deployment.

[0035] Therefore, the reference matrix(s) can be obtained during the preparation of the method or system and be stored in advance, the reflection matrix can be obtained "on the fly” (e.g. in real time or near real time) during the deployment of the method or system. The projection of the reflection matrix reflection on the reference matrix can also be done "on the fly" (e.g. in real time or near real time).

[0036] According to a particular exemplary embodiment, obtaining the dictionary of reference matrices F(q) comprises: the numerical calculation of a second reference matrix for a second state q of the target object, from the first reference matrix, for example measured for a state q of the target object.

[0037] According to a particular embodiment for which the state q is the position r of the target object, the second reference matrix is ​​digitally simulated from the first reference matrix measured for a first position r 0 of the object by a virtual translation of the target object into a new position r, this operation being optionally carried out in a focused base, the base of the transducers, or in the plane wave base.

[0038] The second reference matrix can be simulated numerically, for example using a model of wave propagation from an array of transducers to the target object and a model of wave scattering by the target object.

[0039] The choice of the basis, in which the virtual translation should be carried out, can be dictated by a minimization of the induced computational cost.

[0040] According to a particular exemplary embodiment, the dictionary of reference matrices comprises the first and second reference matrices.

[0041] According to a particular exemplary embodiment, the dictionary of reference matrices is adapted / adjusted / optimized using at least one of the following methods:

[0042] - adaptation of the matrix filter according to the first reference matrix in order to make the matrix filter more specific to the target object being searched for relative to the surrounding environment;

[0043] - optimization of the frequency spectrum of the dictionary to improve the contrast between the target object and a noise associated with the environment;

[0044] - and construction of the dictionary from an estimator (q) of the matrix inverse of the first reference matrix R 0(q 0).

[0045] According to a particular embodiment, the first measured reference matrix R 0(q 0) and / or the reflection matrix R is obtained by an imaging and / or ultrasound echography method.

[0046] According to a particular exemplary embodiment, obtaining the first measured reference matrix and / or the reflection matrix comprises: - a step of generating a series of incident waves (USin) in a medium, by means of an array (10) of transducers (11), said series of incident waves being an emission base (i); and - a step of generating an experimental reflection matrix R ui(t) defined between the emission base (i) at the input and a reception base (u) (i.e. a transducer base) at the output for an echo time t; - a step of determining a focused reflection matrix R rr= [7?(r in, r out, ôt)] being a focused base, the focused reflection matrix R rr comprising responses of the medium R(r in, r out, ôt) between a virtual input transducer (TVin) of spatial position r in and a virtual output transducer (TVout) of spatial position r out, the responses of the virtual output transducer (TVout) being taken at a time instant shifted by an additional delay ôt relative to a time instant of the responses of the virtual input transducer (TVin).

[0047] The waves may include ultrasonic waves.

[0048] The focused reflection matrix can be obtained digitally by a path forming process; i.e. by "beamforming".

[0049] According to a particular exemplary embodiment, obtaining a reference matrix F(q ) comprises: constituting a dictionary of reference matrices in a fully synthetic manner by numerically simulating a first reference matrix of a virtual reflector (for example a reflectivity mirror of orientation a and size lc.) for a first state q0, and by numerically calculating a second reference matrix for a new state q of the target object from the first reflection matrix R 0(q 0).

[0050] Therefore the dictionary of reference matrices can also be constituted in a completely synthetic manner, that is to say without experimental measurement.

[0051] The present disclosure also relates to a method for recognizing a target object in a medium, the method comprising a method according to any one of the preceding aspects.

[0052] The present disclosure also relates to a method for generating a mapping of a medium comprising a target object, comprising a method according to any one of the preceding aspects, and / or generating the mapping, in particular as a function of the estimated state of the target object.

[0053] According to a particular exemplary embodiment, the mapping of the environment comprises an image of the environment (for example obtained by a predefined method) and an identification of the superimposed target object, in which the identification of the target object is determined by a method according to one of the preceding aspects.

[0054] For example, a point at the location of the target object or an image (which may be a schematic image or a photo) of the target object is superimposed on the middle image at the corresponding location.

[0055] The present disclosure also relates to a computer program comprising instructions which, when the program is executed by a computer, lead the latter to implement the method according to any of the preceding aspects.

[0056] The present disclosure according to a particular embodiment also relates to a system for characterizing a target object in an environment. The system comprises a processor configured to: - obtain a reference matrix F(q) associated with the target object, - obtain a reflection matrix R of the medium, - project the reflection matrix R onto the reference matrix F(q) to estimate a probability P(q) that the object is in a state q.

[0057] The system may have functionalities that correspond to the operations of the method according to the present disclosure.

[0058] For example, the system may be a computer that may be associated with an ultrasound imaging system. It is also possible that the system is an ultrasound imaging system.

[0059] The characteristics and advantages of the disclosure will appear on reading the description which follows, given solely as a non-limiting example and made with reference to the appended figures. In particular, the examples illustrated in the figures can be combined unless there is a clear inconsistency. Brief description of the figures

[0060] Other characteristics and advantages of the present disclosure will emerge from the description of the particular and non-limiting exemplary embodiments of the present disclosure below, with reference to the appended figures 1 to 12, in which:

[0061] [Fig. 1] schematically shows a method for characterizing a target object in a medium according to examples of the present disclosure.

[0062] [Fig.2] shows a schematic drawing of an ultrasound imaging system according to examples of the present disclosure.

[0063] [Fig.3] schematically shows the principle of a method for decomposition of the time reversal operator according to an example.

[0064] [Fig.4] schematically shows a diagram summarizing the different steps of the matrix projection method from a calibration measurement of the reflection matrix of the target object according to examples of the present disclosure.

[0065] [Fig.5] schematically shows a proof of concept according to a first experiment comprising matrix imaging of steel spheres in strongly scattering granular media according to examples of the present disclosure.

[0066] [Fig.6] schematically shows a device and a method for obtaining an experimentally measured reference matrix R 0(q 0) in the context of the first experiment according to examples of the present disclosure. It describes also the information contained in this matrix according to its spatial and temporal components.

[0067] [Fig.7] schematically shows a method for detecting and localizing a lesion marker in the ultrasound speckle according to a second experiment, according to examples of the present disclosure.

[0068] [Fig.8] schematically shows an example of matrix mapping of the muscle fibers of a calf, in which the reference matrix dictionary is constituted entirely synthetically according to the present disclosure

[0069] [Fig.9] schematically shows the virtual translation of the position of the target object according to examples of the present disclosure.

[0070] [Fig. 10] schematically shows the transmission and reception of a plane wave associated with an angle of incidence from which the data is to be filtered in the matrix R(q=qo) according to examples of the present disclosure.

[0071] [Fig. 11] schematically shows position likelihood maps for each target resulting from the matrix projection according to examples of the present disclosure.

[0072] [Fig. 12] schematically shows a spectrum of the singular values ​​aî of the matrices R(qj=qo) associated with the spheres according to examples of the present disclosure. Description of the embodiments

[0073] In the various figures, provided for illustration purposes, the same numerical references designate identical or similar elements except in the case of obvious inconsistency.

[0074] [Fig. 1] schematically shows a method for characterizing a target object in a medium according to examples of the present disclosure.

[0075] The target object may comprise, for example, a predefined element of the medium or region of interest, such as a tissue of the medium and / or a biocompatible or non-biocompatible object, inserted into the medium, such as a medical device, for example a marker, such as a marker used in surgery, a biopsy device, a needle or a probe.

[0076] The state q of the target object may comprise for example the position of the object in the medium, the orientation of the object in the medium, the shape and / or the (current) structure of the object, the size of the object, the composition of the object, or local intensive parameters of the medium such as the temperature, the pressure or the concentration of a compound of the medium surrounding the region of interest and / or a variation of the state of the object.

[0077] According to a particular exemplary embodiment, the state q of the object can be measured at different times and can thus be characterized dynamically.

[0078] The method according to examples of the present disclosure may be an ultrasound imaging method. However, other types of imaging or scanning methods are possible, as described below.

[0079] The method may for example be used to recognize a target object in an environment.

[0080] The method may also be used to generate a map of an environment comprising a target object or likely to contain a target object. According to a particular exemplary embodiment, the map of the environment consists of an image of the environment (for example obtained by a predefined method) and an identification of the superimposed target object (for example a probability map of presence of the target object), in which the identification of the target object is determined by a method as described below. For example, a point at the location of the target object or an image (which may be a schematic image) of the target object which is superimposed on the image of the environment.

[0081] The method comprises an SI operation to obtain a reference matrix F or a dictionary of reference matrices F(q) associated with a state q of the target object.

[0082] The reference matrices F of the dictionary may depend on a reference state of the target object, the state optionally at least one parameter among: the position, the orientation, the shape and / or the structure, the size, the composition of the object or local intensive parameters of the environment such as the temperature, the pressure or the concentration of a compound of the surrounding environment.

[0083] According to an optional operation Sla, obtaining the reference matrix F(q) may comprise experimentally measuring a first reference matrix called reflection matrix R 0(q 0) for a state q 0 of the target object, and / or experimentally measuring a first set of reference matrices for a first set of states q

[0084] Furthermore, the operation Sla may comprise obtaining a second reference matrix for other values ​​of the state q of the target object as a function of the first reference matrix. For example, if the state q is the position r of the target object, the second reference matrix may be numerically simulated from the first reflection matrix measured for a position r 0 by a translation of the target object to a new position r. This virtual translation of the object may be carried out in a new state q, optionally in a focused basis, the basis of the transducers, or the plane wave basis.

[0085] The reference reflection matrix R 0(q) can also be simulated numerically, for example using a model of wave propagation from an array of transducers to the target object and a model of wave scattering by the target object.

[0086] According to an optional operation Slb (taken as an alternative to the operation Sla or in combination), obtaining a reference matrix F(q) may comprise the constitution of a dictionary of reference matrices in a synthetic manner (i.e. obtained via simulations and / or calculations). For example, a first reflection matrix of a virtual reflector in a predefined state (for example a mirror scattering whose states are position r 0, orientation a and size lc.) can be simulated numerically. A second reference matrix R 0(q) for a second state q of the target object (e.g. at another position r of the mirror) can be simulated numerically as a function of the first reference matrix. The dictionary of reference matrices can also be built up entirely synthetically, i.e. without experimental measurement.

[0087] According to an optional operation Sic, the reference matrix F(q) or the dictionary of reference matrices can be optimized using at least one of the following methods:

[0088] * adaptation of the matrix filter according to the first reference matrix in order to make the matrix filter more specific to the target object sought in relation to the surrounding environment;

[0089] * optimization of the dictionary frequency spectrum to improve the contrast between the target object and a noise associated with the environment;

[0090] * construction of the dictionary from an estimator Ro'(«) of the inverse matrix of the first reference matrix R 0(q).

[0091] In an operation S2, the reflection matrix R of the medium can be obtained by an ultrasonic echography method, for example as described in file FR3114159.

[0092] According to a particular exemplary embodiment, obtaining the reference matrix (i.e. experimentally measuring a first reference matrix and / or a first set of reference matrices) and / or obtaining the reflection matrix comprises:

[0093] - a step of generating a series of incident waves (USin) in a medium, at by means of an array (10) of transducers (11), said series of incident waves being an emission base (i); and

[0094] - a step of generating an experimental reflection matrix R ui(t) defined between the transmitting base (i) at the input and a receiving base (u) (i.e. a transducer base) at the output;

[0095] - a step of determining a focused reflection matrix R rr =[R(r in, r out, ôt)] in a focused base, the focused reflection matrix R rr comprising responses R(r in, r out, ôt) of the medium between a virtual input transducer (TVin) of spatial position r in(rin) and a virtual output transducer (TVout) of spatial position r Out(rout), the responses of the virtual output transducer (TVout) being taken at a time instant shifted by an additional delay ôt relative to a time instant of the responses of the virtual input transducer (TVin).

[0096] In an operation S3, the reflection matrix R is projected onto the reference matrix F(q) to estimate a probability P(q) that the object is in state q

[0097] In particular, the projection of the reflection matrix R may comprise projecting the reflection matrix R onto the set of reference matrices F(q) of the dictionary to estimate a probability P(q) that the object is in a state q.

[0098] According to an optional operation S3a, projecting the reflection matrix R may comprise applying a matrix filter to the reflection matrix R. This matrix filter comprises a normalized scalar product between the reflection matrix R and the set of reference matrices F(q), or the matrix filter comprises an artificial intelligence model constructed from the reference matrices. In other words, the matrix filter may be a correlator (normalized scalar product) and / or a mathematical function. The result of this correlator or this mathematical function may be the estimated probability. The artificial intelligence model is for example a neural network.

[0099] [Fig.2] shows a schematic drawing of an ultrasound imaging system 10 according to examples of the present disclosure. It is noted that the system 10 according to the present disclosure may also be a type of system other than an ultrasound imaging system, as illustrated below.

[0100] The system 10 may have functionalities that correspond to the operations of the method according to the present disclosure.

[0101] The system may be configured to characterize a target object in a medium. The system includes a processor configured to:

[0102] obtain a reference matrix F(q) associated with the target object,

[0103] obtain a reflection matrix R of the medium, and

[0104] project the reflection matrix R onto the reference matrix F(q) to estimate a probability P(q) that the object is in a state q

[0105] The ultrasound imaging system 10 may comprise:

[0106] - a probe 20,

[0107] - a processing unit 30 for processing an image on the basis of the signals received by the probe (for example corresponding to the processing unit 11 of [Fig. 1]),

[0108] - a control panel 40 connected to the processing unit, said control panel control comprising for example buttons 41 and a touch pad 42, and

[0109] - a screen 50 allowing images to be viewed.

[0110] The probe 20 may be connected to the processing unit 30 by a cable 21 or by a wireless connection, and it makes it possible to emit ultrasonic waves W into a medium M and to receive ultrasonic waves W from the medium M, said received ultrasonic waves resulting from reflections of said emitted ultrasonic waves on scattering particles inside said medium. The probe 20 may be formed or contain a transducer array comprising a plurality of transducers, each converting an electrical signal into a vibration and vice versa. A transducer is for example a piezoelectric element. The transducer array may comprise one hundred or more transducers. The transducer array is linear or curved and is often arranged through a lens on an outer surface of the medium M so as to be coupled to the medium and to vibrate and to emit or receive ultrasonic waves W.

[0111] The processing unit 30 may comprise receiving devices for amplifying and / or filtering the signals received from the probe 20, and converters (analog-to-digital converters and digital-to-analog converters) for transforming the signals into data representing the signal. The data may be stored in a memory of the processing unit or processed directly to calculate intermediate processed data (beamforming data). The processing unit 30 may use any known processing method for processing the image based on the signals received from the probe, such as beamforming. The processed ultrasound image data may be:

[0112] - a simple image of the medium (reflectivity image of the medium obtained in B mode) usually in grayscale to visualize the organs within the medium, or

[0113] - an image showing the velocity or flow in the medium (Doppler image), for useful example for visualizing blood vessels in the medium, or

[0114] - an image showing a mechanical characteristic of the medium (elasticity), for useful example for identifying tumors within the medium (e.g., ShearWave™ Elastography (SWE) image data) as described below.

[0115] The display screen 50 may be a screen for viewing the image processed by the processing unit 30.

[0116] The display screen may be articulated on a support arm 51 for better positioning of the user.

[0117] The control panel 40a is for example a part of the system housing 31, said part comprising a panel housing having a substantially planar surface inclined towards the user to be manipulated by a hand of said user.

[0118] The ultrasonic probe 20 may comprise, for example, one or more transducer elements (not shown in [Fig.l]), each being configured to convert an electrical signal received from the system 10 into ultrasonic waves. The transducer elements may be configured to transmit (a) the waves into the medium and / or to receive (b) a plurality of ultrasonic signals from the medium, possibly in response to the transmission (a).

[0119] The system 10 may be a medical system, for example an ultrasound system. For example, the system may be associated with an ultrasound probe 20, in order to collect ultrasound data from a medium, for example composed of living tissues and / or in particular human or animal tissues.

[0120] However, the system 10 may be any type of electronic system. For example, the system may also be another type of medical system than an ultrasound imaging system. Accordingly, the probe 20 may be any type of imaging device or sensor, using waves other than ultrasound waves (for example, waves having a wavelength different from the wavelength of ultrasound and / or waves that are not sound waves).

[0121] Examples of medical imaging systems include an ultrasound imaging system, an X-ray imaging system (particularly for mammography), and an MRI (Magnetic Resonance Imaging) system.

[0122] According to other examples, the system 10 may include at least one processing unit (or processor) and additionally a memory (not shown). In examples, the processing and memory unit may be incorporated into the system or may be a computer or computing device communicatively linked thereto. Depending on the exact configuration and type of computing device, the memory (which stores the instructions for evaluating the ultrasound data or performing the methods described herein) may be volatile (such as RAM), non-volatile (such as RAM, flash memory, etc.), or a combination thereof. In addition, the system 10 may also include storage devices (removable and / or non-removable), including, but not limited to, magnetic or optical disks or tapes.

[0123] The system 10 may be a single computer operating in a networked environment using logical connections with one or more remote computers. The remote computer may be a personal computer, a server, a router, a network PC, a peer device, or another common network node, and generally includes several or all of the elements described above as well as others not mentioned. The logical connections may include any method supported by available communication media. Such networking environments are common in offices, corporate computer networks, intranets, and the Internet.

[0124] Further, the processing unit may be configured to process data and / or send data to an external device, such as, for example, a display device, a server, a computer on which an artificial intelligence (AI) algorithm is executed, a dedicated workstation, or any other external device.

[0125] The following description summarizes the technical and scientific background of the present disclosure and illustrates the method of the present disclosure using several concrete examples and experiments. These exemplary embodiments do not limit the this disclosure, but primarily serve for a better understanding, including the benefits of this disclosure.

[0126] [Fig.3] schematically shows the principle of a method for decomposing the time reversal operator according to an example.

[0127] Part (a) of [Fig.3] schematically shows an incident wave, which is emitted by one of the transducers and propagates through the medium to the target (left diagram). Part (b) of [Fig.3] schematically shows that this wave is then reflected by the scatterers present in the studied medium, propagates again through the medium. The backscattered echoes are then recorded by the transducer array. This operation is repeated for each element of the array acting as a source of wave emission. The set of impulse responses between the transducers of the array is stored in the reflection matrix R thus acquired in the canonical basis. Part (c) of [Fig.3] schematically shows the spectrum of the singular values ​​of the matrix R. Parts (d) and (e) of [Fig.3] schematically show that each eigenvector U; associated with a significant singular value of R corresponds to the wavefront, which is to be re-emitted from the probe to selectively focus on the associated diffuser. The transmitted wave is then optimally focused on each target through the medium.

[0128] Generally, in ultrasound, an array of piezoelectric transducers is placed opposite the medium that one wishes to image (see part (a) of [Fig.3]). These elements can emit / receive ultrasonic waves independently over a wide spectral band. From a series of insonifications of the medium by all or part of this array, the echoes backscattered by the heterogeneities of the medium are recorded either by these same transducers or by other dedicated transducers. The signals thus recorded are then stored in a response matrix R (i.e. for example a reflection matrix). This matrix can be acquired for different types of incident waves.

[0129] A simple acquisition sequence consists of emitting each incident wave with one element at a time (see part (a) of Figure 3) and, for each emission, recording the field reflected by the medium on all the elements of the array (see part (b) of Figure 3). This canonical basis is used in the field of non-destructive testing, where it is called “full matrix capture”. A matrix acquired in this way can be written mathematically as R uu( / )=| / ?(u„ul um, / )|, where u is the position of the elements along the array, the indices 'in' and 'out' indicating emission and reception respectively. The response matrix can also be acquired using beamforming (emission and / or reception with all elements in concert with appropriate delays between each element) in order to synthesize, for example, focused beams as achieved in B-mode imaging or plane waves to increase the image rate In the latter case, for each plane wave whose direction is given by the unit vector o , the reflected field recorded by the transducers is stored in a response matrix noted ( ut 0. f ) ] ■ It is considered in the following, ultrasonic data acquired in the plane wave base at transmission and in the transducer base at reception. But the present disclosure is general and can be applied to any acquisition base.

[0130] From the response matrix, an ultrasound image can be formed by coherently adding the recorded echoes from each focal point rout, which then acts as a virtual detector within the medium. In practice, appropriate delays are applied to the recorded signals before their summation. The images obtained for each incident wave are then coherently added and give rise to a final image whose contrast is improved. This latter operation generates a posteriori a synthetic focus (i.e. a virtual source) on each focal point rin = rout. The composite image is thus equivalent to a confocal image which would be obtained by focusing the waves on the same point in both transmission and reception mode.

[0131] Matrix imaging consists of decoupling the focusing points rin and rout. A focused reflection matrix, R rr(ôt)=[rout, ôt)], can thus be synthesized by summing and applying delay times to the IQ signals of the recorded response matrix. For the reflection matrix recorded in the plane wave base, the double focusing operation is expressed mathematically as follows:

[0132] [Math.l] (Un' Uni' Sf) — u (^irp Uout' Un (®in' Un) Tout (^out' Uut)) vitruait with [Math.l] Tin And [Math.l] All the spatio-temporal delay laws to be applied at the input and output of the matrix R rr (ôt). These delay laws depend on our a priori knowledge of the sound speed distribution c(r) in the medium. For a homogeneous speed model (c(r)=c 0), [Math.l] [Math.l] ^Ollt are expressed as follows:

[0133] [Math.2] T in ( ®in' ^in ) ~ ®in^m IG) And [°134] Tmt (uout? rout) = 11 uout - rout 11 / cQ

[0135] With (Xin, Zin) and (xout, zout), the coordinates of the focal points and rou^.

[0136] This projection of the matrix R(t) into a focused basis can also be performed via matrix products in the frequency domain. For this, a first step consists of performing a time Fourier transform of the measured signals. A monochromatic reflection matrix R / / ) is obtained at each frequency / . For an initial acquisition of R in the plane wave basis, the projection of Ru0( / ) into the focused basis is performed via the following matrix product:

[0137] [Math.3] ___ -S A. ___

[0138] in which the matrices ry) j and Gm / / ) = [G(u, r, / ) ] are the transition matrices from the focused base to, respectively, the plane wave base and the transducer base. P.)r and Gur depend on our a priori knowledge of the sound speed distribution c(r) in the medium. For a homogeneous speed model, the coefficients of Pgr are given by:

[0139] [Math.4] P ( 0, r, f ) = exp ( ikr.Q ) with k=2^flc 0, the wave number. The coefficients of [Math.4] Gur correspond to the 2D or 3D Green functions of the wave equation in a homogeneous medium:

[0140] [Math 5],

[0141] Gw(ar)= G2D(u,r, / ) = -ÎHo(*lu-rl)

[0142] with H) the first-order Hankel function whose asymptotic expression is as follows: tt -i\ / 2"

[0143] [Math.6] r / „ r .... U, 1, J ) - 4^^

[0144] An inverse Fourier transform of Rrr( / ) can then be performed to obtain the focused reflection matrix R rr(ôt) in the time domain.

[0145] The present disclosure relates to the use of the matrix R rr(ôt) for the purpose of detecting and localizing targets (i.e. target objects) in heterogeneous environments.

[0146] Detection of targets buried in scattering media: The method for decomposition of the time reversal operator

[0147] The response matrix R can be used for target detection (i.e. target objects). Physically, this method allows selective focusing by iterative time reversal on each scatterer of a multi-target medium. Mathematically, it consists of an eigenvalue decomposition of the time reversal operator gg! in the frequency domain. In simple scattering regime and for point targets, each eigenspace of gg' is associated with a scatterer. A singular value decomposition (SVD) of R is performed to calculate the eigenspaces of gg':

[0148] [Math.7] R=Ux£xV

[0149] where E is a (diagonal) matrix whose diagonal coefficients o, are the singular values, V and U are unitary matrices whose column vectors, Vi and U; are the singular vectors at the input and output of R.

[0150] In simple scattering regime, each eigenspace is associated with a target. The corresponding singular value o, is proportional to the reflectivity of the target. If the matrix Ru() is considered, the phase conjugate of the eigenvector, U Uji„ corresponds to the wavefront to be emitted from the probe to focus on the associated scatterer (see parts (d) and (e) of figure 3). An image of the target is obtained by digitally repropagating the associated eigenvector:

[0151] [Math. 8]

[0152] If the method for decomposition of the time reversal operator is applied to the focused matrix Rff, the associated eigenvector Urj- provides the image of the diffuser. Compared to a conventional ultrasound image, the image obtained by this method suffers from poor axial resolution. Indeed, the analysis for decomposition of the time reversal operator is monochromatic. The axial resolution is therefore given by the depth of field of the probe and not by the temporal resolution of the ultrasound signals.

[0153] The strength of the method for decomposing the time reversal operator lies in the fact that the one-to-one association between eigenspaces and scatterers remains valid in the presence of aberrations. However, target detection is only possible if the target has a scattering power greater than the ambient ultrasonic speckle. Moreover, in the multiple scattering regime, the reflection matrix must first be filtered to eliminate a large part of the multiple scattering before the method for decomposing the time reversal operator can be applied to it. In all cases, the target can be detected if the penetration depth remains limited to a scattering mean free path k (average distance between two successive scattering events).

[0154] Finally, the one-to-one relationship between an eigenspace and a scatterer is only verified if the size of the target is smaller than a resolution cell of the imaging system. Otherwise, the rank of the matrix R is of the order of the number Q of resolution cells contained in the object. The image of the target is obtained by combining the first Q eigenspaces of rr'-

[0155] Localization and characterization of objects: The generalized polarization tensor

[0156] For electromagnetic waves, a mathematical method has been developed based on the monochromatic response matrix and the generalized polarization tensor (GPT) of the probed object (here, a dielectric inhomogeneity). When an antenna array surrounds the object, the GPT of the target can be accurately obtained from the matrix by solving a linear system of equations. Based on this, a fast algorithm is obtained that identifies a target from a dictionary of pre-computed GPT data. The location and shape of the object are characterized from an element of the dictionary after some rotation, scaling and translation. This dictionary matching procedure operates directly in the GPT data.

[0157] The present disclosure is based on the concept of detecting and characterizing targets from a dictionary of pre-calculated or pre-recorded data but directly on the broadband reflection matrix. Thus, there is no equation system to solve, which makes the method much simpler and more robust than the GPT approach. Furthermore, it does not require a network of transducers surrounding the medium under study. Finally, unlike the method for operator decomposition time reversal or the GPT approach, multispectral analysis advantageously allows for an axial resolution dictated by the bandwidth of the probe, and not by its depth of field. In addition, this allows optimal exploitation of the temporal (or spectral) response of the target for its detection in complex environments where its presence is generally hidden by strong multiscattering noise.

[0158] The method according to examples of the present disclosure

[0159] [Fig.3] schematically shows a diagram summarizing the different steps of the matrix projection method from a calibration measurement of a reflection matrix R 0(r 0) according to examples of the present disclosure. Obtain a dictionary of reference matrices

[0160] The first step consists in constituting a dictionary of reference matrices F(r, {qj}) depending on the position r of the target that one seeks to detect and on a set of parameters qj which designate for example its size, its shape, its orientation, its composition, local intensive parameters of the surrounding environment, such as temperature, pressure, temperature, composition, mechanical properties and / or the concentration of a compound of the surrounding environment, etc. In practice, this dictionary can be constituted using a calibration step consisting in experimentally measuring the reflection matrix R 0(r, {qi}) associated with the target for a set of positions r of the latter and a set of values ​​of the parameters qj. It can also be generated numerically using a model of wave propagation from the probe to the object and a model of wave diffusion by the latter.Finally, the two approaches can be combined by experimentally measuring the reflection matrix R 0(r 0,q) for a position r 0 of the target and then deducing the value of F for each position r in the field of view (see [Fig.4]). The same method or an artificial intelligence model can be used to determine the dependence of F(r, {q J) on other parameters qj characterizing the target.

[0161] Once this dictionary of reference matrices has been created, the second step consists of acquiring the reflection matrix R of the medium that we are seeking to characterize. The matrix filter then consists of producing a normalized scalar product between the measured matrix and the set of reference matrices F(r,q) in order to estimate the probability P(r,q) that the object is at position r and in state q. This scalar product can be produced in the time domain,

[0162] [Math.9] p ( r ) „ ^^9^4^

[0163]

[0164]

[0165]

[0166]

[0167]

[0168]

[0169]

[0170]

[0171]

[0172]

[0173] or, in the frequency domain, [Math. 10] with Tr {A}, the trace of the matrix A, and !| 11 — { AA" If the projector F (i.e., for example, the dictionary of reference matrices) is taken equal to the matrix R 0, the equations [Math 9] and [Math 10] correspond to a suitable and optimal filter for the object sought from the matrix R. The result P( r, q ) of the matrix projection method then corresponds to the coherent sum of the correlation coefficients between the elements of the matrices R 0 and R integrated on the bandwidth of ultrasonic signals. The RR^ operator differs from the operator of time reversal RR' is considered by the method for decomposition of the time reversal operator. It is a reflection of the 'Scattering Invariant Mode' (SIM) operator yy^ introduced by reference Pai et.al. in a configuration in transmission, cf. Pai, P., Bosch, J., Kühmayer, M. et al. Scattering invariant modes of light in complex media. Nat. Photonics 15, 431-434 (2021). The matrix T represents the response matrix between two transducer arrays placed on either side of the medium and the matrix To is the reference matrix that would be obtained if the medium were homogeneous. Depending on the configuration studied and the quality of the calibration measurement, the F projector can take more elaborate forms: (z) by filtering the matrix R 0 in order to make the matrix filter more target specific sought in relation to the surrounding environment; (zz) by whitening its frequency spectrum; (iii) by modifying the nature of the matrix filter. For example, the projector F can be constructed from an estimator r 1 of the inverse matrix of Rq. Taking^,; the equations [Math 9] and [Math 10] correspond to a F -Kq inverse filtering operation of the matrix R. For illustration purposes, several examples of matrices F will be considered subsequently. Above, the matrix projection method has been defined mathematically (Eqs. [Math 9] and [Math 10]). In the following, its advantages will be illustrated in the context of two examples for target detection and localization as well as for quantitative ultrasound imaging of biological tissues. Detection and localization of targets buried in a scattering medium

[0174] [Fig.5] schematically shows a proof of concept according to a first experiment comprising matrix imaging of steel spheres in highly scattering granular media according to examples of the present disclosure. Part (a) of [Fig.5] schematically shows an experimental setup: A matrix probe measures the reflection matrix R associated with the medium of interest, two steel spheres buried in a particularly scattering granular medium. Parts (b), (c) of [Fig.5] schematically show an ultrasound image of the two spheres, respectively, in the absence and presence of the granular medium. Part (d) of [Fig.5] schematically shows a position likelihood map for each intruder resulting from the matched matrix filter.

[0175] For the first experiment, the experimental setup consists of a 2D matrix probe placed in front of a strongly scattering granular suspension consisting of a random stack of 315 pm diameter glass beads immersed in water. A frequency filter was applied to reduce the bandwidth over a range where the Fonde transport properties can be considered relatively constant. From coherent pulse transmission measurements, the longitudinal phase velocity is estimated to be 1.6 mm / ps and the diffusion free path k is of the order of 1 mm in the studied bandwidth, ^corresponds to the average distance between two successive scattering events experienced by the wave. The objects to be imaged are two steel spheres of 8 mm and 10 mm diameter whose center is buried at z~7ls and 96 below the surface of the medium (see part (a) of figure 5).These imaging conditions are therefore particularly disadvantageous because the simply scattered wave is attenuated exponentially by the scattering of the granular medium by a factor exp(-zjls)- Part (c) of [Fig.5] shows the confocal image of the entire medium. The presence of the two targets is not revealed due to a largely predominant multiple scattering background. Very advantageously, the matrix projection method described above allows the construction of a likelihood map for each target (see part (a) of [Fig.5]) and their exact positions are found without ambiguity.

[0176] Figure 6 schematically shows a device and method for obtaining an experimentally measured reference matrix Rq in the context of the first experiment according to examples of the present disclosure. The device and method can be used for the detection and localization of targets buried in a scattering medium according to the present disclosure. This experiment uses a reference matrix Rq measured for a position of the steel sphere (¢ = 8 mm). Part (a) of Figure 6 schematically shows an experimental device used for recording Rq. Part (b) of Figure 6 schematically shows a image made in B-mode (B- "brightness" scan of the ultrasound image). Part (c) of Figure 6 schematically shows the time dependence of the confocal signal at the level of the sphere cap. Part (d) of Figure 6 schematically shows the resonance of the body and surface waves explaining the long temporal tail of the signal visible in parts (b) and (c). Part (e) of Figure 6 schematically shows the Rq matrix in the focused base at the depth z=27 mm of the ultrasound image [horizontal line on part (b)]. Part (f) of [Fig.6] schematically shows surface waves explaining the off-diagonal signal in part (e).

[0177] This advantageous result described in the context of Figure 5 was obtained by measuring in a first calibration step the reflection matrix associated with each of the balls for a given position (see part (a) of Figure 6). These matrices can therefore form a dictionary of reference matrices. Thanks to a process described below, one can virtually move the object in the field of vision and determine the spatial evolution of Rq(L ¢). The complex spatio-temporal signature of the balls is illustrated by [Fig.6] which illustrates the case of the 8 mm steel sphere in water. Its confocal signal has a long reverberation time (see part (c) of [Fig.6]) due to the Mie (volume waves) (see part (d) of [Fig.6]) and Rayleigh (surface) (see part (f) of [Fig.6]) resonances that such a ball can generate.The reflection matrix also exhibits a complex spatial signature highlighted by strong off-diagonal energy in the focused base (see part (e) of [Fig.6]). In particular, to highlight the specificity of the target's spatio-temporal signature compared to the signature of surrounding objects, a temporal filter can be applied to the reflection matrix to keep only the echoes recorded at long times, corresponding to surface and volume waves propagating on and in the target.

[0178] This complexity of the spatio-temporal signature of each bead can be quantified by the numbers of spatial and temporal degrees of freedom, N s and N t, contained in this signature. N s is equal to the effective rank of the matrix R 0, or approximately the number of transverse resolution cells occupied by the target. N t is equal to the product of the target's reverberation time by the frequency bandwidth. In the present case, the large size of the targets (Nx -20) associated with their long temporal tail (Nt ~20) gives rise to a high number of spatio-temporal degrees of freedom. By compressing the signal associated with each target to a single point, the matrix projection developed here enhances the scattering ratio shnple-to-multiple by a factor (M = Nsx Nt -400). This considerable gain makes it possible to compensate for the exponential attenuation of waves simply scattered in the granular medium t[exp( -z / ls) ~2-5 x 102] 1 - A detection of each target and their localization are obtained as if the granular medium had been suddenly made homogeneous (cf. part (d) of [Fig.5]).

[0179] Detection and localization of a lesion marker embedded in the ultrasound speckle

[0180] [Fig.7] schematically illustrates a method for detecting and localizing a lesion marker in the ultrasound speckle according to a second experiment conducted according to examples of the present disclosure. Part (a) of [Fig.7] schematically shows a 3D spherical lesion marker m in an experimental device. Part (b) of [Fig.7] schematically shows the ultrasound image obtained in B mode. Part (c) of [Fig.7] schematically shows a position likelihood map c for the marker resulting from the adapted matrix filter.

[0181] A second experiment was carried out consisting of detecting and locating a lesion marker used for marking biopsy sites and suspicious lesions in breast tissues. For this experiment, the marker is positioned in a foam immersed in water. This foam generates a typical ultrasonic speckle, for example of breast tissues. The presence of the marker is difficult to detect on the conventional ultrasound image acquired with the 2D probe (see [Fig.7]). On the other hand, the present disclosure implemented via matrix projector exploits the matrix signature of the marker to detect it with excellent contrast and locate it with a precision well below the diffraction limit. Imaging of fibrous tissue anisotropy

[0182] [Fig.8] schematically shows an example of matrix imaging of a calf, in which the reference matrix dictionary is constituted entirely synthetically according to the present disclosure.

[0183] Part (a) of Figure 8 schematically shows an ultrasound image of the calf in dB (co= 1580 m / s). Part (b) of Figure 8 schematically shows a numerically simulated experimental configuration (homogeneous sound speed model c0) to establish a dictionary of matrices Ro(r, {a, lc} ) associated with a mirror of orientation a and size^-. Part (c) of Figure 8 schematically shows the orientation and local size of the fibers, ( r ) and ^opt) fp estimated by the matrix matched filter for the transverse positions x={-10;0;10] mm. Part (d) of [Fig.8] schematically shows a mapping of the fiber orientation superimposed on the ultrasound image of the calf.

[0184] Beyond the detection and localization of targets, the adapted matrix filter can be used for quantitative imaging of tissues in ultrasound echography. For example, a mapping of the anisotropy of the tissues can be carried out. fibrous media that typically make up muscles. This measurement is particularly relevant for the diagnosis of neuromuscular diseases or diseases affecting the myocardium. In elastography, fibrous media also generate shear wave velocity anisotropy. A detailed knowledge of this anisotropy is therefore required to correctly map tissue stiffness from shear wave propagation films.

[0185] This third experiment was carried out on a calf, the fibers of which are partly visible on the ultrasound image shown in part (a) of [Fig.8]. The reflection matrix R is recorded using a linear array of transducers (N = 256 elements spaced 0.2 mm apart, center frequency 7.5 MHz and bandwidth [2.5;9.5] MHz). The illumination base consists of 101 plane waves whose angle of incidence varies from -25° to 25°. For each insonification, the reflected field is recorded by all the transducers.

[0186] To quantitatively image the fibrous tissues, the adapted matrix filter was applied to the matrix R, considering here, as a reference object, a mirror of constant reflectivity whose parameters qj are here the orientation a relative to the probe and the characteristic size L (see part (b) of figure 8). A dictionary of reference matrices F(r, (a, lc} ) associated with this object is constructed using a numerical calculation described below.

[0187] The adapted matrix filter makes it possible to calculate a likelihood index P(r, {a, lc}) with respect to the parameters a and k at each point r of the image (see Eq. 10). The maximum value of this quantity gives the orientation c?W)(r) and the characteristic size of the diffusers at each point of the image:

[0188] [Math. 11] {( r ) ^ 4°^ ( I ) ) = argmax [ P ( r, {a, lc} ) ] aJc

[0189] The size and orientation of the fibers thus determined are represented for different transverse positions in part (c) of [Fig.8]. A detection threshold was applied a priori by representing only the result of the matrix filter whose associated likelihood index is greater than 103. The fiber orientation map is also superimposed on the ultrasound image in part (d) of [Fig.8]. A very good agreement is found between the visual appearance of the fibers on the ultrasound image and their orientation determined by the adapted matrix filter.

[0190] Note that this approach can be considered as a generalization of specular beamforming developed e.g. by Rodriguez-Morales et al., cf. A. Rodriguez-Molares, A. Fatemi, L. Lpvstakken and H. Torp, "Specular Beamforming," in IEEE Transactions on Ultrasonics, Ferroelectrics, and Erequency Control, vol. 64, no. 9, pp. 1285-1297, Sept. 2017, doi: 10.1109 / TUFFC.2017.2709038.

[0191] This latter approach corresponds in fact to a filter adapted for a mirror of infinite size. Specular beamforming is therefore suitable for detecting and locating large objects in ultrasound. On the other hand, optimizing the characteristic size of the diffuser allows for a filter more adapted to fibrous media. This is also an important parameter for locally adapting the formation of channels to the different types of fibers encountered and obtaining a better quality ultrasound image. The image formed is, for example, the maximum of the observable P measured for each pixel. Apart from this, other objects can be simulated synthetically, for example, a needle inserted into the tissue.

[0192] A link exists between the matched matrix filter and the analysis of the reflection matrix in the plane wave base developed in the context of non-destructive testing for the purpose of characterizing anisotropic media. However, this approach does not allow the anisotropy of the fibers to be resolved laterally; only the axial evolution of the anisotropy can be determined. The technique of spatial correlation of the backscattered field only allows the fiber orientation to be determined in a plane parallel to the probe.

[0193] Matrix projection of ultrasound data is a very general method that can be applied to the imaging of a large number of environmental parameters. Here, parameters considered are, for example, the size and orientation of scatterers, but the shape or composition of the latter can also be parameters that can be mapped with this method. A necessary condition, however, remains the constitution of a sufficiently complete and precise dictionary of the structures being studied. To this end, in the following section, the different ways of proceeding are described to constitute such a dictionary.

[0194] Constitution of the dictionary of reference matrices

[0195] There are different ways to numerically generate a dictionary of reference matrices F(r,q). A first approach consists in measuring, during a first calibration step, the reflection matrix R 0(r 0,q) associated with the target alone, for a position of the latter, then in generating a dictionary of reference matrices F(r,q) for each point r of the field of vision. An alternative strategy consists in analytically calculating the set of reference matrices F(r,q).

[0196] Digital emulation of a dictionary from an experimental measurement

[0197] Part (a) of Figure 6 shows the experimental setup for the calibration measurement of R 0 carried out as part of the experiment for detecting targets buried in a scattering medium. The matrix network of 1024 transducers located at z=0 is used to independently probe each target placed at a position ro and immersed in water. The associated reference matrix, ty is recorded in the time domain between the input plane wave base ( ü ) and the output transducer base (Uout). It thus contains all the uin signals measured by each of the transducers identified by their Uout coordinates for a set of plane wave illuminations propagating in the direction o . Note that this choice of illumination and reception bases can be arbitrary and that the reference matrix could very well be measured using another sequence of illuminations, in the focused base for example. In addition, intermediate steps can be considered, such as temporal filtering of the measured reference matrix, whitening of the spectrum, etc.

[0198] Once this reference matrix is ​​measured, a Fourier transform is applied to it in the time domain. Thus the reference matrix, “(0). ”, "-U0 \ ■'■O' J ) in the frequency domain is obtained. Then a translation of the target can be numerically simulated to a new position r in the medium. This operation can be performed in different bases, for example the focused basis. A first step consists of projecting ^(o), ,. into this basis (Eq. [Math 3]) and then generating Ku8tr0' J ) a new matrix "(oL for a new target position r from the ku0KL J 1 coefficients of -«(0) ✓ „. , such that: Krr V r? J )

[0199] [Math. 12] W r) = ^o(rin - Ar, rout-Ai, r0) with [Math. 12] Ar = rr()

[0200] Depending on the acquisition base of the matrix, one may also be required to work in the transducer base to limit the calculation time and / or the use of memory. A matrix ^(0), „, can be generated for each virtual position Kuu(r, J ) r of the target from its measurement in ro by decomposing the displacement Ar according to its transverse projections Ap and axial Az. The transverse displacement is done by a translation in the base of the transducers:

[0201] [Math. 13] «o ( Uout, {p, z0} ) = Ro ( ui(1 - Ap, uout - Ap, {p0, z0} )

[0202] with P and Pq the transverse coordinates of the points r and r 0.

[0203] The axial displacement, on the other hand, requires a propagation of the data from the z 0 plane to the z plane at the input and output of the matrix jJo): ■Kuu

[0204] [Math. 14] ~ (0) ■? ~ (0) A TT (r) — Gup (z) x Gup (Zq) x Ruu ({p, z0}) x Gup (zQ) Gu / > (z)

[0205] where the symbol T denotes the matrix transposition operation.

[0206] [Fig.9] schematically shows the virtual translation of the position of the target object according to examples of the present disclosure. The upper part (“Case of a large opening”) of [Fig.9] schematically shows that by carrying out this translation in the base of the transducers or in the focused base, it is possible to virtually move the object as long as the support of the field associated with the target is contained in the opening of the transducer array. The lower part (“Case of a restricted opening”) of [Fig.9] schematically shows that for a lateral position of the target approaching the ends of the transducer array, a lateral translation of the ultrasonic signals is no longer adequate.

[0207] The reflection matrix R 0(r) can also be generated from the matrix R 0(ro) from the Fourier basis. The first step is therefore to project the experimentally acquired matrix R 0(ro) into the plane wave basis at both input and output. For a matrix R 0(r 0) recorded using a plane wave illumination sequence, only an output projection into the Fourier basis is required:

[0208] [Math. 15] (ro) - X Ru0( ro)

[0209] In the case of a matrix acquired in the canonical basis (transducers), the projection must be carried out at the input and output of the matrix: It should be noted that the canonical basis is only an illustrative example.

[0210] [Math. 16] ^(0) xt* fJO) • x ^■09 ( ro) ~ X ^10 ( ro)

[0211] Once the matrix Æ0(r0 ) is projected into the plane wave base, its virtual displacement to the position r can be carried out in the following manner:

[0212] [Math 17], [02131 [02141 = P( 9^ 9ir Ar)

[0215] This equation consists of applying input and output phase ramps to the data projected into the plane wave base. Depending on the position r of the object, not all plane waves emitted from the probe reach it, in the same way such that the backscattered echoes reaching the transducers can only come from a limited opening (see [Fig. 10]).

[0216] [Fig. 10] schematically shows the transmission and reception of a plane wave associated with an angle of incidence from which the data is to be filtered in the matrix R 0 according to examples of the present disclosure. The left part of [Fig. 10] schematically shows a plane wave associated with an angle of incidence from which the data is to be filtered in the matrix R 0. The right part of [Fig. 10] schematically shows that at reception, the plane waves associated with the arrows pointing towards the transducer array and the other arrows pointing outside the transducer array are to be respectively kept and filtered in the measured matrix R 0.

[0217] Any signal corresponding to extreme angles, which can be determined based on the geometries of the probe and the position of the object, is therefore of little interest and can be assimilated to noise, which should therefore be filtered in an implementation option.

[0218] Whatever the focused basis, that of the transducers or in the Fourier basis, equations 12, 13 and 14 are based on an assumption of invariance by translation of the focusing process (see [Fig.9]). This last assumption is only verified if the whole of the field associated with the target is well measured by the network of transducers:

[0219] [Math. 18] ^x2 + y2 < y - ztan / i

[0220] with the opening angle of the probe imposed by its directivity and A its width.

[0221] The choice of the basis in which the virtual translation must be carried out is dictated by considerations of time and computational costs. In quasi-real-time mode, for example, one could choose to carry out all the operations from the acquisition basis of the reflection matrices R 0 and R in order to limit the number of matrix operations to be carried out. Reference matrix optimization

[0222] Specificity of the reference matrix with respect to the surrounding environment

[0223] Figure 11 schematically shows position likelihood maps for each target resulting from the matrix projection defined by Eq. 10 according to examples of the present disclosure. Part (a) of Figure 11 schematically shows a matched filter with F(r, 0) = R^(r, ¢) • Part (b) of Figure 11 schematically shows a matched filter after suppression of the specular echo of the targets with F(r, ¢) = Rs(r, ¢) [cf. Eq. 19]. Part (c) of Figure 11 schematically shows a matched filter with F(r, 0) = Rs(r, ¢) [cf. Eq. 20]. Part (d) of Figure 11 schematically shows an inverse filter with F(r, ¢)=^(1,0) [cf. Eq. 22]. Note that the frequency filter applied to the ultrasonic data is here broadband (Hann window, [0;6] MHz).

[0224] In the case of the experiment of detecting targets in a granular medium, one step consists of filtering beforehand the specular echo of the targets in Ro(r: 0). Without this prior filtering, the image obtained is dominated by the interface echo of the granular medium (see part (a) of [Fig.l 1]). Indeed, the specular echo is not specific to the target and will also enhance the interface echo of the granular medium which dominates the signals recorded in the matrix R.

[0225] There is therefore an interest in constructing reference matrices F(r, 0) from the echoes most specific to each target. In this illustrative example, these are the echoes of multiple reflections within them and the echoes of surface waves previously highlighted by [Fig.6]. In practice, this operation can be carried out by a time windowing of the measured ultrasonic signals (see part (b) of [Fig.6]):

[0226] [Math. 19] where H is the Heaviside function, t is the arrival time of the direct echo of the target and ô t=Af 7 is the time resolution of the measured ultrasonic signals. The specific reference matrix R s is then virtually translated and used to construct a suitable image [Math. 19] P(r, of the sought targets [cf. Eq. 9 with [Math. 19] F = Rg ]. The result is in this example presented in part (c) of figure 11. We note advantageously that the interface echo of the granular medium is much less intense, the two targets are detected with good contrast and the position of their center found with excellent precision. Frequency spectrum whitening

[0227] A second step consists of whitening the frequency spectrum of the matrix Rs, such that:

[0228] [Math.20] Rs(r, ¢, f) =Rs(r. ^,f) / ||Ès(r, ¢, / ) ||“

[0229] Considering this family of normalized matrices Rs as the reference dictionary F in equation 10, a new map P(r, 0) is obtained on the part (c) of [Fig.l 1]. The frequency whitening operation makes it possible to make the most of the temporal degrees of freedom highlighted by part (c) of [Fig.6] and improve the contrast between the targets and the noise associated with the surrounding environment. Reverse filter

[0230] The previous examples were limited to a matched filter of the matrix R whereas an inverse filter should theoretically be able to maximize the contrast of the two targets. The matrix inversion process is ill-conditioned and extremely sensitive to noise. A regularization method can be used to optimize the inversion process. To this end, the singular value decomposition of Rs must be calculated beforehand:

[0231] [Math.21] 8.( / )=^,( / )^( / )^( / )

[0232] The spectrum of singular values ​​is shown in [Fig. 12] for both targets. A large number of singular values ​​exceed the noise level.

[0233] Figure 12 schematically shows a spectrum of the singular values ​​of the matrices Rs associated with the spheres according to examples of the present disclosure, for example spheres of diameter ¢=8 mm and ¢ = 10 mm at the frequency / = 2.5 MHz after time windowing to retain only the echoes of multiple reflections and surface waves specific to the target.

[0234] The set of eigenspaces associated with these singular values ​​forms the signal subspace associated with the target. The rank Q of this subspace increases as the number of resolution cells contained in the target. An estimator aL of the matrix Rs( / ) inverse of RX / ) can be calculated by inverting the first Q singular values ​​of the signal subspace of Rs and canceling that of the noise subspace:

[0235] [Math.22] 83( / )=^^( / )^( / )^( / )

[0236] The resulting dictionary, py 4^ryy can then be used to construct an image of the probability of target presence [cf. Eq. 10]. The result is shown in part (d) of [Fig. 11] for Q = 20. Admittedly, the resolution of the echoes associated with each target is finer than for the matched filter in part (c) of [Fig.l 1]. Nevertheless, this improvement in resolution comes at the cost of significant false alarms upstream of the targets and of cross-talk (i.e. interference of a first signal with a second) between them. These artifacts are related to the sensitivity of the inversion process to experimental noise.

[0237] To improve the robustness of the method, in a variant, a Tikhonov-type regularization can be applied. The matrix F(rC), f ) is expressed in this case:

[0238] [Math.23] The ir ;• with [Math.23] b , the estimated noise level on the singular value spectrum. Digital generation of a dictionary

[0239] The dictionary of reference matrices can also be constituted in a completely synthetic manner, i.e. obtained by calculations and simulation, without experimental measurement. To illustrate, the example of muscle anisotropy imaging can be taken as an example. The results shown in Figure 8 were obtained by numerically calculating the reference matrix F( r0 ) from the following matrix product:

[0240] [Math.24] Ruu ( r0 ) — Peu x Per xr ( r, et, lc ) x P0r x P0B where [Math.24] r(r, oc, Zc) represents the reflectivity matrix of a plane tilt mirror [Math.24] a and size [Math.24] THE [cf. part (b) of figure 8] centered at r in real space. [Math.24] r(r,a,Zc) is a diagonal matrix whose coefficients [Math.24] y(r) correspond to the reflectivity of the mirror whose response is simulated. In practice, it is advantageous if the real space is sampled with a grid pitch much smaller than the diffraction limit ( [Math.24] ~x / 5 ). The grid defined in real space is not the same as that of the focused base whose spatial sampling is of the order of [Math.24] 2 / 2

[0241] The results shown in Figure 8 were obtained from the equation 10 considering for reference matrices F(r, a, 4) 'cs simulated matrices R0(r, oc, lc). Note that, in the case of a plane mirror, the number of non-zero singular values ​​of Ro (r, cc, lc) is equal to the number of resolution cells contained in the object and that these eigenvalues ​​are all degenerate. The inverse filter [F(ra, l ) = ^(r œ, Z ) ] would therefore give a strictly identical result.

[0242] All of these embodiments and other examples as described above are given solely by way of non-limiting example, and may be combined and / or modified within the scope of the present disclosure.

Claims

Claims

1. A method for characterizing a target object in a medium, the method comprising: obtaining a reference matrix F(q) associated with the target object, obtaining a reflection matrix R of the medium, and projecting the reflection matrix R onto the reference matrix F(q) to estimate a probability P(q) that the object is in a state q.

2. The method of claim 1, wherein the target object comprises at least one of: a predefined element of the medium, such as a tissue of the medium, and an external object inserted into the medium, such as a medical device.

3. The method of claim 1 or 2, wherein the state q of the target object comprises at least one of: the position of the object in the medium, the orientation of the object in the medium, the shape and / or structure of the object, the size of the object, the composition of the object, and local parameters of the surrounding medium, such as temperature, pressure, composition, mechanical properties and / or the concentration of a compound of the surrounding medium.

4. Method according to one of the preceding claims, wherein, obtaining the reflection matrix comprises obtaining reflection matrices measured at different times t, wherein each of the reflection matrices is projected onto the reference matrix to measure the dynamics of the state of the object.

5. Method according to one of the preceding claims, in which, obtaining a reference matrix F(q) consists of obtaining a dictionary of reference matrices F(q) associated with the target object, and the projection of the reflection matrix R corresponds to projecting the reflection matrix R onto the set of reference matrices F(q) to estimate a probability P(q) that the object is in a state q.

6. A method according to any preceding claim, wherein the projection of the reflection matrix R comprises applying a matrix filter to the reflection matrix R.

7. Method according to the preceding claim, in which the matrix filter comprises a normalized scalar product between the reflection matrix R and the set of reference matrices F(q), or the matrix filter comprises an artificial intelligence model.

8. Method according to one of the preceding claims, in which the reference matrices F(q) of the dictionary depend on a state q of the target object, the state optionally comprising at least one parameter among: position, orientation, shape and / or structure, size, composition.

9. Method according to one of the preceding claims, in which obtaining the reference matrix F(q) comprises: a measurement of a first reference matrix corresponding to a reflection matrix R 0(q 0) for a first value q 0 of the state q of the target object, and / or a measurement of a first set of reference matrices associated with several states q of the target object.

10. Method according to one of the preceding claims, wherein obtaining a reference matrix F(q) comprises: digitally generating a second reference matrix for a second state q of the target object from a first reference matrix measured for a state q of the target object.

11. Method according to the preceding claim, in which, the second reference matrix is ​​digitally simulated from the first reference matrix by a translation of the target object to a new state q being the position of the object, optionally in a focused basis, the basis of the transducers, or the basis of plane waves.

12. The method of claim 9 or 10, wherein the dictionary of reference matrices comprises the first and second reference matrices.

13. The method of claim 10, wherein the dictionary of reference matrices is optimized using at least one of the following methods: adapting the matrix filter based on the first reference matrix to make the matrix filter more specific to the target object being searched for relative to the surrounding medium; optimizing the frequency spectrum of the dictionary to improve the contrast between the target object and noise associated with the medium; and construction of the dictionary from an estimator R^' of the inverse matrix of the first reference matrix.

14. Method according to one of the preceding claims, in which the first reference matrix F(q) and / or the reflection matrix R is obtained by an ultrasound imaging method.

15. Method according to one of the preceding claims, wherein obtaining the first reference matrix and / or the reflection matrix comprises: - a step of generating a series of incident waves (USin) in a medium, by means of an array (10) of transducers (11), said series of incident waves being an emission base (i); and - a step of generating an experimental reflection matrix R ui(t) defined between the emission base (i) at the input and a reception base (u) at the output;- a step of determining a focused reflection matrix R rr = [R(r in , r out, ôt)] in a focused base, the focused reflection matrix R rr comprises responses R(r in , r out, ôt)] of the medium between a virtual input transducer (TVin) of spatial position r in and a virtual output transducer (TVout) of spatial position r out, the responses of the virtual output transducer (TVout) being taken at a time instant shifted by an additional delay ôt relative to a time instant of the responses of the virtual input transducer (TVin), in which the waves optionally comprise ultrasonic waves.;

16. Method according to one of the preceding claims, in which obtaining a reference matrix F(q) comprises constituting a dictionary of reference matrices in a fully synthetic manner by numerically simulating: a first reference matrix of a virtual reflector for a predefined state qo, and a second reference matrix for a second state q of the target object, optionally as a function of the first reference matrix Ro(q).

17. A method for recognizing and / or finding a target object in an environment, the method comprising a method according to one of the preceding claims.

18. A method for generating a map of a medium comprising a target object, comprising: a method according to one of the preceding claims, and generating the map based on the estimated state of the target object.

19. Method according to the preceding claim, in which the mapping of the medium consists of an image of the medium and an identification of the target object superimposed thereon, in which the identification of the target object is carried out by a method according to one of the preceding claims.

Images