Classifications

• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
  • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
  • G01S7/52—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S15/00
  • G01S7/52017—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S15/00 particularly adapted to short-range imaging
  • G01S7/52023—Details of receivers
  • G01S7/52036—Details of receivers using analysis of echo signal for target characterisation
• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
  • G01S15/00—Systems using the reflection or reradiation of acoustic waves, e.g. sonar systems
  • G01S15/88—Sonar systems specially adapted for specific applications
  • G01S15/89—Sonar systems specially adapted for specific applications for mapping or imaging
  • G01S15/8906—Short-range imaging systems; Acoustic microscope systems using pulse-echo techniques
  • G01S15/8977—Short-range imaging systems; Acoustic microscope systems using pulse-echo techniques using special techniques for image reconstruction, e.g. FFT, geometrical transformations, spatial deconvolution, time deconvolution
• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
  • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
  • G01S7/52—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S15/00
  • G01S7/52017—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S15/00 particularly adapted to short-range imaging
  • G01S7/52046—Techniques for image enhancement involving transmitter or receiver

Definitions

• the present invention relates to the general technical field of the analysis of a medium by wave propagation, and in particular sound or ultrasonic waves, or electromagnetic waves.
• the present invention relates to a method and a device for analyzing a target object, or a diffuse medium such as a biological, human or animal tissue.
• This analysis may consist of:
• scattering is a phenomenon by which a wave UE is deflected and redistributed in various directions Ui, U2, P, Echi by an interaction with a “scattering object” Obi contained in a medium.
• Receive signals consist of two components:
• the diffusion of the wave induces its deviation and its redistribution in various directions, so that certain parts P of the deviated wave can interact with other Ob2 scattering objects contained in the medium before be received by the receiver R.
• the parts Echi of the deflected wave which are picked up by the receiver R before interacting with other scattering objects Ob2 constitute the simple scattering component.
• the parts Ech2 of the deflected wave which are picked up by the receiver R after having interacted with several receiver objects Obi , Ob2 constitute the multiple scattering component.
• the description is limited to 2 scattering objects but can of course be generalized to a larger number of scatterers.
• the solutions for analyzing a medium generally use the simple diffusion component of the reception signals (at each given instant of reception of an echo, the measurement of the time elapsed between the transmission and the reception of its associated simple diffusion component is representative of the position of the scattering object).
• document WO 2010/001027 has proposed a method making it possible to separate the single and multiple components of the reception signals thanks to a technique of filtering an inter-element impulse response matrix by projection or by decomposition into singular values.
• This method is based on the following steps: i) recording inter-element responses for each transmitter/receiver pair of a set of transmitters/receivers, ii) determining a time-windowed inter-element response matrix K from inter-element responses, each element/coefficient Kij of the temporally windowed inter-element response matrix K corresponding to the signal received by a receiver n°j following the transmission of a wave by the transmitter n°i, iii ) processing of the temporally windowed inter-element response matrix K, the processing step consisting in separating: o the multiple scattering component, o from the single scattering component, in the temporally windowed inter-element response matrix K at function of the coherence of the coefficients of the temporally windowed interelement response matrix K on each antidiagonal of said temporally windowed interelement response matrix K. 2.
• the principle of recording an interelement response of a transmitter/receiver pair of a set of Ei-En/Ri-Rn transmitters/receivers is as follows.
• An incident wave Inc corresponding to an impulse signal is sent from each transmitter (Ei in FIGS. 2a to 2c, E2 in FIG. 2d, etc.) during a transmission step, and the wave reflected Ref by the medium following the emission of this incident wave Inc, is recorded by each receiver (Ri in FIG. 2a, R2 in FIG. 2b, Rn in FIG. 2c, etc.) during a measurement step.
• each transmitter E1 (respectively E2, respectively En) of the set of transmitter Ei-E n can be activated successively, the set of receivers Ri-R n being activated simultaneously in reception for the simultaneous acquisition of a set of pairs ( E1, Ri), (E1, R2), (E1, Rn) (respectively (E2, Ri), (E2, R2), (E2, Rn), respectively (En, Ri), (En, R2), ( En, Rn)) associated with the emission of an incident wave by the activated emitter E1 (respectively E2, respectively En).
• the principle of construction of a row "/" of a temporally windowed interelement response matrix K consists of: - for transmitter n°i, to emit an ultrasonic wave (emitter Ei in the case of FIGS. 2a to 2c),
• time-dependent reception signals into a time window of duration At and centered around a time t (which can for example correspond to a time of flight of the ultrasonic wave to reach a depth d interest in the environment).
• the construction of the "i+1" row of the inter-element matrix can then be initiated by activating transmitter n°i+1 of the set of transmitters/receivers (E2 in the case of figure 2d) to transmitting an ultrasonic wave, by activating all receivers n°j of the set of transmitters/receivers to respectively receive an acoustic echo and convert it into an associated time-dependent reception signal, and by windowing the reception signals.
• the shape of the inter-element matrix is not completely antidiagonal, as illustrated in figure 3 where one observes a more complex behavior than a simple constancy on the antidiagonals.
• the antidiagonals indeed appear to be curved, which can be taken into account in the model but complicates it significantly. These approximations degrade the separation quality of the single and multiple scattering components.
• the set of emitters/receivers and the medium must remain stationary with respect to each other in order to guarantee that the reception signals acquired by all the receptors are representative of the same environment (that is to say of an environment that has not evolved, in particular in terms of position).
• a set of transmitters/receivers conventionally comprises 128 elements or more.
• the position of the middle must therefore remain invariant during the implementation of the 128 successive transmissions and the 128 associated receptions.
• a final drawback of the method described in WO 2010/001027 relates to the low signal-to-noise ratio as well as the low penetration of the transmission made with an element. This can significantly limit the depth exploitable by such a method.
• Document XP255911387 also discloses a method for quantifying single and multiple scattering ratios of ultrasonic signals by observing the characteristics of an impulse response matrix between virtual transducers located inside the middle.
• the method according to XP255911387 is similar to the method according to WO 2010/001027 in that it deals with inter-element matrices, but differs therefrom in that the elements of XP255911387 are virtual and located in the medium, at a studied depth. It therefore has the same drawbacks as document WO 2010/001027.
• An object of the present invention is to propose a method and a device for analyzing a medium making it possible to remedy at least one of the aforementioned drawbacks.
• the invention proposes a method for analyzing a medium from a network of (virtual) transducers, said method comprising:
• reception plane waves or spirals
• reception plane waves or spirals
• the signals resulting from these reception plane waves (or spirals) comprising: o a simple scattering component, representative of wave paths resulting from a single reflection of the plane wave (or spiral ) emission on a diffuser of the diffusing medium, o a component of multiple diffusion, representative of wave paths resulting from several successive reflections of the plane wave (or spiral) of emission on diffusers of the diffusing medium before reach the transducers of the transducer array,
• the processing phase comprises a step of separating the single diffusion component and the multiple diffusion component, in said reception signals.
• the separation step can include a sub-step of filtering at least one windowed inter-angle matrix representative of the emission and reception angles of the emission and reception waves (plane or spiral): o each row of the windowed inter-angle matrix being representative of the emission angle of a wave (plane or spiral) of emission, and o each column of the windowed inter-angle matrix being representative of a reception angle d a reception wave (plane or spiral);
• the invention also relates to a method for analyzing a medium from a network of transducers, noteworthy in that the method comprises the following phases:
• each reception signal comprising: o a component simple scattering, representative of wave paths resulting from a single reflection of the emission plane wave on a scatterer of the scattering medium, o a multiple scattering component, representative of wave paths resulting from several successive reflections of the emission plane wave on scatterers of the scattering medium before reaching the transducers of the array of transducers,
• the processing phase comprising a step of separating the single and multiple scattering components in the reception signals, the said separation step including the following sub-steps: o determination of at least one windowed inter-angle matrix in which each line is representative of the angle of emission of a plane wave of emission and each column is representative of the angle of reception of a plane wave of reception, o filtering at least one windowed inter-angle matrix to separate the single-scatter component and the multi-scatter component in each receive signal.
• each column is representative of a reception angle of a plane wave received.
• Such an inter-angle matrix has rectilinear antidiagonals (as will be described in more detail below), unlike the antidiagonals of an inter-element matrix (as described in WO 2010/001027 or in XP25591 1387) which are curved.
• This linearity of the antidiagonals of the inter-angle matrix makes it possible to improve the quality of separation of the single and multiple diffusion components of the reception signals.
• various examples of the phase for processing this inter-angle matrix will be described, it being understood by those skilled in the art that the phase for processing the inter-angle matrix can be of any type known to them.
• each generation step can comprise the sub-step consisting in: o activating in transmission transducers of the network according to a respective activation delay law, so that each transducer transmits an elementary ultrasonic wave at a respective instant as a function of said activation delay law, said elementary ultrasonic waves combining to form the wave (plane or spiral) of emission having the desired angle of emission, the angle of emission of the wave (plane or spiral) transmission dependent on the activation delay law used;
• each reception step can include the sub-steps consisting in: o activating network transducers in reception according to a respective activation delay law, so that each transducer records an elementary received signal corresponding to a portion of the wave reception (planar or spiral) having a desired reception angle, the desired reception angle depending on the activation delay law used, o combining the elementary signals received to form a reception signal corresponding to the wave (planar or reception spiral) having the desired reception angle;
• each reception step can include the sub-steps consisting in: o simultaneously activating the transducers in reception, each transducer recording a signal picked up representative of several waves reverberated by the medium, o combining the signals picked up according to different temporal delay laws to form reception signals representative of reception waves (plane or spiral), said sub-step consisting in combining the signals, comprising, for each reception signal representative of a wave reception (planar or spiral) having a desired reception angle, the following phases:
• each temporal delay law used being associated with a respective desired reception angle
• the separation step can also comprise the following sub-steps: o determination of a plurality of windowed inter-angle matrices, each windowed inter-angle matrix corresponding to a temporal matrix defining, over a temporal window close to a time T and duration At, pairs of angles of emission and reception of waves (plane or spiral) of emission and reception, o then for each windowed inter-angle matrix:
• the sub-steps of estimating the resulting first and second inter-angle matrices may comprise the filtering of the windowed inter-angle matrix considered as a function of the coherence of the coefficients on each ascending diagonal of said considered windowed inter-angle matrix;
• the filtering of the windowed inter-angle matrix considered can include: o the rotation of the inter-angle matrix by an angle of 45° to obtain at least one rotated matrix, o the decomposition into at least one singular value of each matrix rotated to obtain a decomposed matrix, o subtracting the decomposed matrix from said rotated matrix to obtain a subtracted matrix, o inversely rotating the decomposed matrix by an angle of -45° to obtain the first representative resulting inter-angle matrix from the single scattering component, o the inverse rotation of the matrix subtracted by an angle of ⁇ 45° to obtain the resulting second inter-angle matrix representative of the multiple scattering component;
• the array of transducers may comprise a plurality of transducers extending along at least one line so as to have a substantially planar shape: o the wave generated during the generation step consisting of a plane wave, o the signals combined during the reception step being representative of reception plane waves, o each activation delay law consisting of a linear delay law applied to the transducers extending along at least a line ; - in another alternative embodiment, the array of transducers may comprise a plurality of transducers extending along at least one radius of curvature so as to have a convex shape: o the wave generated during the generation step consisting of a spiral wave, o the signals combined during the reception step being representative of reception spiral waves, o each activation delay law consisting of a linear delay law applied to the transducers extending along at least one radius of curvature.
• FIG. 1 is a schematic representation illustrating the principle of wave diffusion
• FIGS. 2a to 2d are schematic representations illustrating the principle of determining an inter-element matrix
• FIG. 4 is a schematic representation of an ultrasound imaging device including an acquisition probe and one (or more) calculation unit(s),
• FIG. 5 is a schematic representation illustrating the principle of emission of a plane wave from a network of transducers
• FIG. 6a to 6d are schematic representations illustrating the principle of determining an inter-angle matrix
• FIG. 7 illustrates a real part of a windowed inter-angle matrix
• FIG. 8 is a schematic representation of the steps of a separation method by singular value decomposition
• FIG. 9a to 9d schematically illustrate a technique for rotating a matrix by two-dimensional interpolation
• FIG. 10 schematically illustrates a technique for rotating a matrix by selection of coefficients
• FIG. 11 is a schematic representation of plane and spiral waves emitted by arrays of plane and curved transducers.
• the invention will be described with reference to the field of imaging the human body by ultrasound. It is obvious to those skilled in the art that the method and the device for analyzing a medium according to the invention can be used for other applications, such as SONAR, RADAR applications, or other applications not medical (seismography, study of materials such as concrete or polycrystalline materials, etc.).
• FIG. 4 an example of a device has been illustrated in which the method for analyzing a medium described below can be implemented.
• This device includes:
• control and processing unit Uc for: o controlling the network of Ti-T n transducers and o processing the signals acquired by the network of Ti-T n transducers.
• the Ti-Tn transducer array comprises a set of “n” ultrasonic transducers (“n” being an integer greater than or equal to one) arranged linearly.
• n being an integer greater than or equal to one
• the Ti-T n transducers of the network can be arranged in a curve, or in concentric circles, or in a matrix.
• the network of Ti-T n transducers makes it possible to emit ultrasonic excitation waves towards a medium to be analyzed (organ, biological tissue, etc.), and to receive acoustic echoes (ie ultrasonic waves reflected by the medium to be analyzed) .
• Each Ti-T n transducer consists for example of a plate of piezoelectric material of rectangular shape coated on its front and rear faces with electrodes and covered on the front face with lenses and acoustic impedance matching layers. Such transducers are known to those skilled in the art and will not be described in more detail below.
• all the Ti-Tn transducers of the network are used both in transmission and in reception. In other embodiments, separate transducers may be used for transmission and reception.
• the control and processing unit Uc is connected to the array of Ti-T n transducers.
• control and processing unit Uc allows:
• the control and processing unit Uc can be composed of one or more distinct physical entities, possibly remote from the network of transducers Ti-T n .
• control and processing unit Uc comprises for example:
• controller(s) 11 such as a Smartphone, a personal assistant (or "PDA”, acronym for the English expression “Personal Digital Assistant”), or any type of mobile terminal known to the person skilled in the art;
• PDA Personal Digital Assistant
• one (or more) computer(s) 12 such as a computer(s), a microcomputer(s), a workstation(s), and/or other devices known to those skilled in the art including processor(s), microcontroller(s), programmable logic controller(s), application specific integrated circuit(s), and/or or other programmable circuits,
• one (or more) storage unit(s) 13 comprising one (or more) memory(s) which can be a ROM/RAM memory, a USB key, a memory of a central server.
• the storage unit 13 In addition to the storage of data associated with the analysis of a medium, the storage unit 13 also makes it possible to store programming code instructions intended to execute the steps of the analysis method described below.
• a spiral wave Os emitted by a network of curved transducers Te is independent of the shape of the network of transducers.
• an array of planar transducers can be configured to emit a spiral wave (using an adapted delay law).
• a curved transducer array can be configured to emit a plane wave (using a suitable delay law).
• a network of virtual transducers T is defined as a set of points in the middle arranged on a line or according to an arc of a circle.
• the characteristics of the plane or spiral wavefronts are chosen (in particular the angle of emission or reception) with respect to this network of virtual transducers.
• the delay laws applied to the network of real transducers are deduced therefrom. In the framework of the wavefront approximation, everything happens as if the waves were emitted by the network of virtual transducers.
• any type of plane or spiral wave can be emitted by defining an array of corresponding virtual transducers.
• the spiral wave Os the equivalent of the plane wave OP in polar referential.
• the plane wave OP corresponds to a limit case of the spiral wave where the origin of the reference moves away to infinity from the probe.
• reception angle is understood to mean the angle between:
• plane or spiral waves OP, OS can be generated independently of the geometry of the probe used. It will be noted that in the case where the network of virtual transducers corresponds to the real network of transducers (plane waves in linear probes or spiral waves in curved probes), the transmission (respectively the reception) of such waves is facilitated by the similarity between the geometry of the probe and the shape of the wavefront. It is also more advantageous from the point of view of the directivity of the elements.
• the inter-angle matrix defines pairs of plane or spiral wave emission and reception angles.
• each coefficient of the inter-angle matrix corresponds to a reception angle (by all the transducers Ti-T n of the network) of a plane or spiral reflected wave following the reverberation in the medium of a wave plane or spiral emission of an emission angle.
• the Ti-T n transducers of the array are activated together (in transmission) so that the Eh-EIn elementary waves generated by each of the Ti-T n transducers combine to form a plane wave d emission having a desired emission angle.
• This resulting plane ultrasonic wave 14 can be emitted according to different emission angles (ie different directions) by varying the instants of activation (t, t+At, t+2At, ... t+nAt) of each transducer Ti -T n of the network.
• the Ti-T n transducers are activated together to generate the plane wave, ie the Ti-T n transducers are all activated in transmission for each reception.
• the first solution consists in applying a law of delay in the activation (in reception) of the transducers Ti-T n of the network.
• the Ti-T n transducers of the network are activated together (in reception), the reception plane wave corresponding to the sum of the reception signals acquired by the network Ti-T n transducers:
• the inventors have developed a second solution in which the Ti-T n transducers simultaneously acquire the signals representative of the receiving plane waves, independently of their orientation (ie independently of the directions of movement of their wavefronts).
• each transducer is activated simultaneously in reception to record signals picked up representative of the reverberation by the middle of the plane wave of emission.
• the signals picked up by the transducers Ti-T n are then summed according to a temporal delay law depending on the desired reception angle for the reception plane wave. For example, to receive a reception plane wave having a reception angle a from the captured signals ⁇ Si(t) ⁇ o ⁇ j ⁇ n _i measured by the transducers Ti-Tn, the following summation operation is performed:
• - "p" represents the pitch of the probe (i.e. difference between two adjacent transducers of the array of transducers).
• the processing of the block of captured signals makes it possible to “reorient” the responses recorded by the various Ti-Tn transducers to obtain the reception waves at the various desired reception angles. N plane waves are thus generated in reception from a single transmission.
• the principle of construction of a coefficient Kij of a row “/” of a temporally windowed inter-angle matrix K(T) comprises the following steps:
• the receive signal representative of the receive plane wave having the desired receive angle is time dependent.
• This signal is truncated (windowed) into successive time windows FT (potentially partially superimposed) - of duration At - each associated with a respective windowed inter-angle matrix.
• the corresponding truncated receive signal is multiplied by a windowing function and stored in the coefficient Kij of the associated windowed inter-angle matrix K(T).
• each windowed inter-angle matrix K(T) is completed by receiving plane waves of reception Orec2, Orec3 each having a reception angle distinct from the other plane waves of reception and by truncating the reception signals representative of the reception plane waves Orec2, Orec3 into successive time windows FT.
• each line "/" is representative of the emission angle of an emitted plane wave
• each column "j" is representative of a reception angle of a plane wave received.
• the considered windowed inter-angle matrices K(T) are acquired with emission and reception angles spaced apart by a constant pitch.
• the information contained in a windowed inter-element matrix is different from the information contained in a windowed inter-angle matrix.
• a windowed inter-element matrix corresponds to the temporal responses of the receivers of a transmitter/receiver set following a succession of transmissions by transmitters of the transmitter/receiver set. So :
• each row of a windowed inter-element matrix corresponds to a respective transmitter of the transmitter/receiver set
• each column of a windowed inter-element matrix corresponds to a respective receiver of the transmitter/receiver set.
• a windowed inter-angle matrix corresponds to the angles of reception of the plane waves of reception following a succession of plane waves emitted at different angles of emission. So :
• each line of a windowed inter-angle matrix is representative of the emission angle of an emitted plane wave
• - each column of a windowed inter-angle matrix is representative of a reception angle of a plane wave received.
• each windowed inter-angle matrix K(T) this separation of the simple and multiple components is carried out according to the coherence of the coefficients Kij on each antidiagonal of said considered windowed inter-angle matrix K(T).
• antidiagonal means an alignment of coefficients Kij of the matrix such that the sum “i+j” is constant (“/” corresponding to a row of the matrix, and “j” to a column of the matrix).
• the simply scattered waves present a particular coherence according to the antidiagonals of the windowed inter-angle matrix K(T), whereas the multiplely scattered waves do not present a privileged direction of coherence in the windowed inter-angle matrix K(T).
• a filtering of the antidiagonals according to the coherence of the Kij coefficients allows a separation of the single and multiple scattering components.
• the first separation method comprises, for each windowed inter-angle matrix considered, the following steps:
• the rotation step “by interpolation” makes it possible to generate a rotated matrix K PjV (T). This technique can be used in the case of a sufficiently resolved inter-angle matrix.
• each coefficient of the rotated matrix K P iv(T) is determined by interpolation of the coefficients of the windowed inter-angle matrix K(T) neighboring the coefficient considered in the rotated matrix K PjV (T).
• the value of the coefficient K P ivn of the rotated matrix K P iv(T) is determined by interpolation of the four values K12 K13, K14 , K23 of the windowed inter-angle matrix K(T), as illustrated in figure 9b .
• the value of the central coefficient K P iv2i of the rotated matrix K P iv(T) is determined by interpolation of the four values K12 K13, K22 , K23 of the windowed inter-angle matrix K(T), as illustrated in Figure 9c.
• the value of the central coefficient K P iv3i of the rotated matrix K P iv(T) is determined by interpolation of the four values K21, K22, K31, K32 of the windowed inter-angle matrix K(T), as illustrated in figure 9d , And so on.
• the elementary matrices Kén (T), Kéi2(T) are square matrices made up of subsets of the windowed inter-angle matrix K(T):
• - Kén (T) is a first square matrix of dimensions smaller than the windowed inter-angle matrix K(T), the rows of the first elementary matrix Kén (T) corresponding to the first diagonals of the windowed inter-angle matrix K(T) ; for example, in the case of a 5x5 windowed inter-angle matrix K(T), the first elementary matrix Kén(T) is a 3x3 square matrix each column of which corresponds to a diagonal of respective odd rank of the windowed inter-angle matrix K (T);
• - Kéi2(T) is a second square matrix of dimensions smaller than the windowed inter-angle matrix K(T), the rows of the second elementary matrix Kéi2(T) corresponding to the second diagonals of the windowed inter-angle matrix K( T); for example, in the case of a 5x5 windowed inter-angle matrix K(T), the second elementary matrix Kéi2(T) is a 2x2 square matrix each column of which corresponds to a diagonal of respective even rank of the windowed inter-angle matrix K (T).
• the filtering step separates:
• aberration means any phenomenon which is not expected in a simple diffusion model, that is to say a model where the received signals are exclusively composed of directly reflected signals. through the middle. Aberrations therefore include, among others, system thermal noise and multiple scattering.
• a matrix M (M being able to correspond to the rotated matrix K P iv(T) or to one of the elementary matrices Kén (T), Kéi2(T)) can be considered as being the sum of two terms M s and M M denoting respectively the contribution due to the simple scattering component and the contribution due to the aberration component:
• K P iv(T) K P iv s (T) + K P iv M (T),
• Kén(T) Kéii s (T) + Kén M (T),
• Kéi2(T) Kéi2 s (T) + Kéi2 M (T).
• Simple diffusion being characterized, after rotation of the data, by a great coherence along the columns of the elementary matrices, the decomposition into singular values brings out this contribution in the signal space (the simple diffusion contribution will be associated with the highest singular values ) while the contribution of the outlier will be associated with the weaker singular values.
• the singular value of rank 1 may be sufficient to separate the signal space (associated with single scattering) from the aberration space (associated with multiple scattering). In other embodiments, several singular values (carrying the trace of the contribution associated with the simple scattering component) can be calculated to separate the signal space from the aberration space.
• each filtered matrix Parked (Gfiltered which can correspond to K P iv s (T), K P iv M (T), Kéii s (T), Kéu M (T), Kéi2 s (T), or to Kéi2 M (T)) is rotated to obtain a Gtoured matrix by applying the following rule:
• a Gturned x , y (T) a Gfiltered (x- y -i)/2+M,(x+ y -i)/2.
• the Hankel space is a vector subspace of the space of square matrices which is defined in that all the matrices of the Hankel space have their anti diagonals constant.
• This second method of projection onto Hankel space is advantageously carried out on the windowed inter-angle matrix K(T) not rotated, that is to say that this method does not require performing a rotation of the inter-angle matrix -angles windowed K(T) and uses all the coefficients of this matrix, where a rotation reduces the number of available coefficients.
• the second method of Hankel separation consists in separating the windowed inter-angle matrix K(T) into a Hankel matrix H(T) and a residual matrix R(T).
• a Hankel matrix is a square matrix whose values are constant along the antidiagonal (i.e. ascending diagonals), i.e. a matrix whose indices verify the relation:
• the Hankel matrix H(T) thus obtained is representative of the simple diffusion component.
• the remainder “K(T)-H(T)” is representative of the multiple scattering component.
• Hankel's second method has the advantage of limiting the number of calculations performed (and therefore the amount of hardware resources required) to separate the single and multiple scattering components contained in the windowed inter-angle matrix K(T). Indeed, it is not necessary to carry out the operations of rotation and reverse rotation, contrary to the first method of separation by decomposition into singular values.
• aberrations all phenomena that are not expected in a simple diffusion model, that is to say a model where the signals received are exclusively composed of signals directly reflected by the medium.
• the aberrations therefore include, among others, the thermal noise of the system and multiple scattering (i.e. signal obtained corresponding to the echoes of waves reflected by several elements of the environment before returning to the probe).
• a first step comprising: o a sub-step of emission of wave beams obtained by applying a delay law to the elements of the array of transducers; these beams approximate a base of progressive plane waves in emission, either propagating towards the imaged medium; we will therefore speak, in the following, of plane wave or plane wave in emission to characterize the ultrasonic wavefront propagating in the imaged medium; o a reception sub-step, on the elements, of the signals representative of the reverberation of the ultrasonic waves by the insonified medium, o a processing sub-step making it possible to break down the signals received on the elements on a basis of progressive plane waves in reception , either propagating towards the array of transducers,
• This part describes the method used to emit and receive plane waves using an ultrasonic probe composed of a set of ultrasonic transducers. These transducers are typically arranged uniformly along a straight line, defining a linear probe, or an arc of a circle, defining a curved probe.
• the signals received by elements are delayed and summed, with a delay depending on the angle of the plane wave of reception desired.
• This processing step thus allows access to a set of signals ⁇ Saj,pk(t) ⁇ i sjsN to lsjsN/3 , corresponding to Na angles synthesized in transmission and Np angles synthesized in reception.
• Second step quantification of aberrations
• the quantification of aberrations requires separating the signal from the single scattering by the middle of the rest (multiple scattering, noise). This separation is possible in the angular domain by exploiting the strong redundancy of the signals coming from simple diffusion.
• this vector is a constant vector since it is systematically the same reflections which are observed.
• a number Na of transmissions is carried out, and a number Np of angular receptions is calculated for each transmission.
• N a xNp we obtain an inter-angle matrix of dimension N a xNp. If the angles emitted and the angles received are identical and regular (spaced by a constant pitch), we obtain a matrix of size N a xN a whose coefficient kij corresponds to the signal received for an emission at angle ai and a reception d angle aj.
• the singular value decomposition method uses the fact that a matrix with constant columns is a rank 1 matrix. To use this property, several steps are necessary: i) First, the inter-angle matrix, expressed in the time or frequency domain, is rotated by 45° so that the antidiagonals become columns; several techniques are possible for this step a. Two-dimensional interpolation of elements; this method is valid for a sufficiently resolved inter-angle matrix, b.
• This matrix H (T) corresponds to simple diffusion, and the remainder K - H to aberrations.
• the norm of these matrices is indicative of the amount of single scatter and the amount of multiple scatter, hence also the ratio of multiple scatter to single scatter.
• the invention was described with reference to an array of Ti—T n transducers having a linear geometry. It is obvious to those skilled in the art that the array of Ti—T n transducers can have other shapes such as a curved or matrix shape. In the case of a matrix probe, therefore two-dimensional, the above method is generalized by defining plane waves or two-dimensional spirals. These plane or spiral waves are nothing other than the combination of a plane or spiral wave along one axis with a plane or spiral wave along the other axis, thus giving delay laws defined in Cartesian, cylindrical or polar.
• virtual transducer network means a set of points defining a geometric shape chosen according to delay laws applied to the real transducer network so that said points of the set emit an edge plane or spiral wave.

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• 2021
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