Nonlinear waveform inversion system

Abstract

A system for recovering physical properties from a non-linear medium includes a wavefield modeler, a property tuner, and a medium property restorer. A wavefield modeler processes a wavefield generated by a transmit pulse traveling in a non-linear medium, and generates a predicted transducer output from the modeled wavefield. The wavefield modeler is a neural network of a neural network representation of a non-linear wave function having physical properties of the wavefield. The attribute tuner optimizes a loss function between the predicted transducer output and the measured transducer output and generates an improved set of physical attributes. The attribute tuner operates the back-propagator using the neural network representation and activates the wavefield modeler with an improved set of physical attributes. Once the attribute adjuster completes the operation, the media attribute restorer outputs the currently improved set of physical attributes.

Description

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims priority to U.S. Provisional Patent Application No. 63 / 339,473 filed on May 8, 2022, and No. 63 / 375,545 filed on September 14, 2022, both of which are incorporated herein by reference. Technical Field

[0003] The present invention relates generally to nonlinear waveform inversion and, more particularly, to its application to ultrasound. Background Art

[0004] Ultrasound imaging is widely used in medical applications due to its non-invasive and non-radiative properties. Referring to FIGS. 1A to 1G , the structure and operation of a typical ultrasound system 10 are shown. As shown in FIG. 1A , the ultrasound system 10 has a transducer 11 and a medium 16 containing tissue 17. The transducer 11 has a transducer array 12, which is composed of a plurality of n c The transducer elements each contain a transmitter 15 and a receiver 13. Fig. 1A is shown at time t0 prior to operation.

[0005] In ultrasound imaging, images are generated by ionizing or emitting one or a series of acoustic pulses from an array of transducer elements 12, as shown in Figures 1B, 1C, and 1D. Figure 1B shows pulse 21 leaving transducer 11 at a starting time, shown as t1. Figure 1C shows pulse 22 leaving transducer 11 at a later time, shown as t2, and pulse 21 continues to travel away from transducer 11. Figure 1D shows pulse 23 leaving transducer 11 at time t3, and pulses 22 and 21 continue to propagate away from transducer 11.

[0006] The transmit pulses 21, 22, and 23 propagate through the medium 16 and tissue 17, resulting in a series of reflections and refractions that produce echoes that are then detected by the same array. FIG. 1E shows a first reflected wave 24 at time t4 (the transmit pulses 21, 22, and 23 have been omitted for clarity) traveling toward the transducer 11. FIG. 1F shows a second reflected wave 25 following the wave 24 at time t5. FIG. 1G shows the wave 24 arriving at the transceiver 11 at time t6. At time t6, the transceiver 11 acquires an ultrasound signal, after which the signals from the different transducer elements are properly aligned using a beamforming algorithm, and the data acquired from the multiple transmission schemes are combined to generate an ultrasound image of the medium 16 and tissue 17.

[0007] Typical brightness mode (B-mode) images are generated by applying corresponding time delays to the acquired signals and averaging over channels with tailored weights. However, B-mode images do not necessarily provide sufficient contrast for certain anatomical structures and have poor physical interpretation.

[0008] Imaging of physical properties of known materials, such as speed of sound (SoS), density, acoustic attenuation, and elasticity, has valuable differentiation capabilities and improves medical diagnostics. For example, SoS maps can discern between benign and malignant breast tumors, identify muscle loss and fatty muscle degeneration (sarcopenia) in the elderly, and differentiate between healthy and diseased tissues affected by non-alcoholic fatty liver disease (NAFLD), such as human and animal liver. Acoustic attenuation maps can improve the diagnosis of non-healthy tissue. Finally, tissue density can indicate breast cancer risk, and the levels of fat and steatosis in the liver can be quantified, which is critical for monitoring NAFLD and non-alcoholic steatohepatitis (NASH).

[0009] Inverse ultrasound algorithms attempt to reconstruct the properties of the medium based on the acquired ultrasound signals. The standard method used to solve the inverse ultrasound problem is the full waveform inversion (FWI) algorithm, a computational technique originally developed in geophysics. It relies on a physical wave propagation model and therefore explains a wider range of phenomena than B-mode images. To reconstruct the properties, the algorithm utilizes a computationally expensive, iterative gradient-based method.

[0010] Other inverse ultrasound methods use a differential path matrix to estimate the sound velocity of the medium. The differential path matrix links the SoS distribution to the obtained time delays at the transducer. However, the differential path matrix only estimates the SoS of the medium because it depends on geometric considerations rather than on a wave propagation model. Alternative solutions to the inverse ultrasound problem use machine learning methods, such as deep neural networks. This approach requires a large amount of known medical data with known SoS maps in order to train the neural network, and the obtained model has poor interpretability. Summary of the invention

[0011] Therefore, according to a preferred embodiment of the present invention, a system for recovering physical properties from a nonlinear medium is provided. The system includes a wavefield modeler, a property adjuster, and a medium property restorer. The wavefield modeler models a wavefield generated by at least one transmit pulse when the at least one transmit pulse travels in a nonlinear medium, and generates a predicted transducer output according to the modeled wavefield. The wavefield modeler is implemented as a neural network having a neural network representation of a nonlinear wave function of a set of physical properties of the wavefield. The property adjuster optimizes a loss function between the predicted transducer output and the measured transducer output, and generates an improved set of physical properties. The property adjuster operates a back propagator using the neural network representation of the wave function, and activates the wavefield modeler with the improved set of physical properties. Once the property adjuster completes the operation, the medium property restorer outputs a current improved set of physical properties. The current improved set of physical properties is the restored physical properties of the nonlinear medium.

[0012] Furthermore, according to a preferred embodiment of the present invention, the medium is a two-dimensional or three-dimensional body tissue.

[0013] Furthermore, according to a preferred embodiment of the present invention, the wave field is one of the following: an acoustic wave, an electromagnetic wave, an elastic wave, a photoacoustic wave, and an acousto-optic wave.

[0014] Furthermore, according to a preferred embodiment of the present invention, the transmit pulse is one of: a plane wave, a focused beam, and a diverging wave.

[0015] Furthermore, according to a preferred embodiment of the present invention, the neural network of the wavefield modeler comprises a non-linear function receiving as input the improved set of physical parameters and being provided with two previous wave samples and pulse samples.

[0016] Furthermore, according to a preferred embodiment of the present invention, the wavefield modeler further comprises a restriction operator for restricting the output of the neural network to one of the following: a linear array of elements, a convex array of elements, an elliptical array of elements, and an intracavity array of elements.

[0017] Furthermore, according to a preferred embodiment of the present invention, the property adjuster includes a plurality of error calculators, a loss accumulator, and a nonlinear gradient calculator. Each of the plurality of error calculators generates an error vector between a predicted transducer output and a measured transducer output for an associated wavefield sample. The loss accumulator accumulates the error vectors, and the nonlinear gradient calculator implemented by the backpropagator backpropagates the gradient through the neural network using a nonlinear wave function, thereby returning a gradient of the wavefield relative to the set of physical properties.

[0018] Furthermore, according to a preferred embodiment of the present invention, the neural network is a recursive neural network or a deep neural network, each layer of which expresses the time dependency of a nonlinear wave function.

[0019] According to a preferred embodiment of the present invention, a method for recovering physical properties from a nonlinear medium is also provided. The method includes: modeling a wave field generated by at least one transmit pulse when the at least one transmit pulse travels in the nonlinear medium, the modeling using a neural network having a neural network representation of a nonlinear wave function of a set of physical properties of the wave field; generating a predicted transducer output from the modeled wave field; optimizing a loss function between the predicted transducer output and the measured transducer output to generate an improved set of physical properties, the generation using back propagation of the neural network representation with the wave function; activating the modeling with the improved set of physical properties; and providing a currently improved set of physical properties once the optimization operation is completed, wherein the currently improved set of physical properties is the recovered physical properties of the nonlinear medium.

[0020] Furthermore, in accordance with a preferred embodiment of the present invention, the modeling further comprises restricting the output of the neural network to one of: a linear array of elements, a convex array of elements, an elliptical array of elements, and an intracavitary array of elements.

[0021] Still further in accordance with a preferred embodiment of the present invention, the optimizing includes generating an error vector between a predicted transducer output and a measured transducer output for an associated wavefield sample, accumulating the error vectors, and back-propagating the gradient through a neural network using a nonlinear wave function to return a gradient of the wavefield with respect to the set of physical properties. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] The subject matter contemplated by the invention is particularly pointed out and distinctly claimed in the concluding portions of the specification. However, the organization and method of operation of the invention, together with objects, features, and advantages thereof, may best be understood by reference to the following detailed description when read with the accompanying drawings, in which:

[0023] 1A, 1B, 1C, 1D, 1E, 1F and 1G are schematic diagrams of the operation of a prior art ultrasound imaging system;

[0024] Figure 2 is a schematic diagram of a nonlinear waveform inversion system (NLWIS) constructed and operative in accordance with a preferred embodiment of the present invention;

[0025] Figure 3A Is Figure 2 Schematic diagram of wave sample 28 at time stamp n generated by NLWIS;

[0026] Figure 3B It is a schematic diagram of multiple wave samples U(n) and U(n-1);

[0027] Figure 4 is Figure 2 Schematic diagram of useful wavefield modelers in NLWIS;

[0028] Figure 5 Using neural network tools Figure 2 A schematic diagram of an implementation scheme of the NLWIS system;

[0029] Fig. 6A , Figure 6B , Figure 6C and Fig.6D They are graphical representations of the actual values ​​of the four attributes;

[0030] Fig. 6E , Fig. 6F , Figure 6G and Figure 6H are used as Figure 2 The NLWSI system is for Fig. 6A , Figure 6B , Figure 6C and Fig.6D The properties of are used as a graphical representation of the initial values ​​of the input; and

[0031] Fig.6I , Figure 6J , Figure 6K and Figure 6L They are respectively Figure 2 The NLWSI system is targeted at Fig. 6A , Figure 6B , Figure 6C and Fig.6D The properties of the generated reconstruction are graphically represented.

[0032] It should be understood that for simplicity and clarity of illustration, the elements shown in the drawings are not necessarily drawn to scale. For example, for clarity, the size of some elements may be enlarged relative to other elements. In addition, where appropriate, reference numerals may be repeated in the drawings to indicate corresponding or similar elements. DETAILED DESCRIPTION

[0033] In the following detailed description, many specific details are set forth in order to provide a thorough understanding of the present invention. However, it will be appreciated by those skilled in the art that the present invention may be practiced without these specific details. In other cases, well-known methods, processes and components are not described in detail to avoid obscuring the present invention.

[0034] Applicants have recognized that inverse acoustic algorithms work well with linear media, but are inaccurate for ultrasound medical imaging, which is typically nonlinear. Furthermore, the full waveform inversion (FWI) algorithms described above are computationally heavy, making them useless for most applications.

[0035] Applicants have recognized that neural network platforms have been developed that make computationally complex calculations easier to visualize and calculate, and that neural networks can be used to express wave equations rather than learning sets of parameters. Applicants have recognized that neural network structures used in deep learning systems can be used to express nonlinear time-based equations, such as the wave propagation equations of FWI. Specifically, recursive neural network (RNN) structures can be used to express time-based equations. Alternatively, deep neural networks can also be used, where the layers express the time dependency of the equation.

[0036] Furthermore, Applicants have appreciated that such neural network systems also include differential computations as part of their "back-propagation" systems for updating the neural network during training of the network (i.e., for learning the parameters of the neural network), and that different neural networks use different optimization algorithms in their back-propagation. Applicants have appreciated that the back-propagation system of a neural network system can provide a very efficient implementation for differential computations that form part of the iterative gradient computations of nonlinear waveform inversion.

[0037] Thus, Applicants have realized that a neural network platform can be used to solve inverse nonlinear physics problems, rather than providing an output given an unknown input, as is standardly done with neural networks. Thus, a nonlinear waveform inversion system implemented on a neural network platform can be used to recover properties of a medium.

[0038] Reference now Figure 2 , Figure 2 4 is a schematic diagram of a nonlinear waveform inversion system (NLWIS) 40. The system 40 includes a wave field modeler (WFM) 42, a property adjuster (PA) 44, and a medium property restorer (MPR) 46. The system 40 can restore and output a visual representation of a physical medium in which waves such as ultrasound waves flow. In an ultrasound embodiment, the physical medium can be a part of a human body, such as an abdomen. The physical medium can have multiple properties θ that may affect the flow of waves, where the elements of θ can be multiple properties, each of which can be two-dimensional or three-dimensional. For example, the elements of θ can be discrete sound speed C, density Q, attenuation D, and nonlinearity B throughout the physical medium, as will be explained in more detail below.

[0039] A wavefield modeler (WFM) 42 may calculate a wavefield U generated in response to a plurality of transmit pulses F (such as pulses 21, 22, and 23 of FIG. 1D ) as they propagate through medium 16 and tissue 17. Wavefield modeler 42 may use the calculated wavefield U to calculate detected waves P, such as reflected waves 24 and 25 of FIG. 1 , when detected by receiver 13. Since wavefield U may depend on a plurality of attributes θ, and since attribute θ is an unknown variable to be found, wavefield modeler 42 may estimate θ using the attributes of attribute θ. k, and the attribute estimate θ may be updated in the attribute adjuster 44 k To attribute estimate θ k+1 Then repeat the calculation of wave field U.

[0040] Once the attribute adjuster 44 may instruct the estimation of θ k+1 Having perhaps converged or after a predefined, maximum number of iterations k, the medium property restorer 46 may then retrieve the property θ.

[0041] Since the system 40 is implemented on a neural network platform, the system 40 uses discrete wave samples U(n) and discrete transmit pulse samples F(n) at each timestamp n, as now referred to Figure 3A and 3B shown. Figure 3A is a schematic diagram of a wave sample 28 at a time stamp n. The wave sample 28 comprises a two-dimensional grid 27 containing x*y pressure values ​​U x,y For example, the grid 27 may be a 4000 x 4000 grid, and the wave field U may include N grids 27, one for each timestamp n, where in this example, N may also be 4000. Similarly, each transmit pulse sample F(n) generated by the linear transmitter 15 may have, for example, 128 transmit pulses F at each timestamp n. x Linear grid. Figure 3B A plurality of wave samples U(n), U(n-1), etc. are shown, where each wave sample U(n) is 2-dimensional.

[0042] The wavefield modeler 42 may calculate the wavefield U for each iteration k using the nonlinear model NL(θ) derived from the lossy Westervelt equation. k , described in the following articles, by G. Yao et al. ("An effective absorbing layer for the boundary condition in acoustic seismic wave simulation", Journal of Geophysics and Engineering, vol. 15, no. 2, pp. 495-511, 2018) and the book by MF Hamilton and DT Blackstock ("Nonlinear acoustics", Academic Press., p. 55, 1998). However, the lossy Westervelt equation is a continuous equation. According to a preferred embodiment of the present invention, the nonlinear acoustic model implemented by the wave field modeler 42 can be a discrete version thereof, as provided in Equation 1:

[0043]

[0044] in, is a discrete gradient filter, is a discrete Laplace filter, is one of the matrices, and G1, G2, G3, and G4 are variables constructed from the two-dimensional attributes C, Q, D, and B, as defined in Equation 2:

[0045]

[0046] where Δ t is the time interval, and U(n-1) and U(n-2) are the previous two wave samples of the current iteration k, and the values ​​of attributes C, Q, D, and B determined in iteration k-1 are used.

[0047] Note that in Equations 1 and 2, bold lowercase and uppercase are used for vectors and matrices, respectively. The vectorization, convolution, transposition, and element-wise multiplication (Hadamard product) operators are written as vec(·), *, (·), respectively. T and ⊙. Matrix division and exponentiation are performed element-by-element.

[0048] To calculate the wavefield U for iteration k k The wave field modeler 42 may include a plurality of nonlinear modelers 50 ( Figure 2 ), each nonlinear modeler produces one of the samples n. Each modeler 50 can estimate θ using the attributes determined at the end of the previous iteration k-1. k The value of θ can be used to implement the nonlinear function NL(θ) as defined in Equations 1 and 2. Each nonlinear modeler 50 receives as input its associated 2D pulse sample F(n) and 2D wave samples U(n-1) and U(n-2) from the two previous nonlinear modelers 50 from which U(n-1) and U(n-2) were generated, respectively.

[0049] To predict each reflection signal P(n) received by receiver 13 ( FIG. 1A ), wavefield modeler 42 may include a plurality of restriction operators 52 that select portions of wave samples U(n) located at locations of receivers 13 of transducer 11 . Figure 3A An example of a portion of a wave sample U(n) used as a reflection signal P(n) is shown in FIG.

[0050] It should be understood that wave samples U(n-2) and U(n-1) may not be available for the first wave sample U(1). In this case, all elements of the starting wave sample U(0) may be set to zero, and the input to U(1) may be only the starting wave sample U(0) and the transmitted sample pulse F(1).

[0051] According to the preferred embodiment of the present invention and as now referred to Figure 4 As shown, the wavefield modeler 42 can be implemented as an untrained neural network, where each nonlinear modeler 50 and its associated restriction operator 52 can form a layer of the neural network. In particular, since the calculations of each layer are the same, the neural network can be a recurrent neural network (RNN), which is a neural network in which nodes are connected in a time series so that the same operation is applied at each time step, allowing it to exhibit dynamic behavior. For the wavefield modeler 42, the time step n of the wave equation can be consistent with the time step n.

[0052] Figure 4 An RNN unit 60 is shown having a parameter estimate θ for the current iteration received. k The nonlinear function NL(θ) is taken as input, and the RNN unit 60 provides which wave samples U(n-1) and U(n-2) and the pulse sample F(n). The nonlinear function NL(θ) can produce the current wave sample U(n) to which the restriction operator R can be applied, thereby producing the predicted sample P(n). For the RNN, the current wave sample U(n) can be provided to the next layer of the RNN unit 60, and the previous wave sample U(n-1) can be provided to the next layer of the RNN unit 60 as its U(n-2).

[0053] It should be understood that the goal of computing a nonlinear waveform inversion is to recover the property values ​​in the medium and to "discover" any other entities present in the medium. However, the wavefield modeler 42 estimates θ using the unknown parameters k , in order to calculate the wave field U k At each iteration, the property adjuster 44 may use the loss function L to adjust the parameter estimate θ based on a comparison of the predicted reflection waveform P(n) with its associated measured waveform M(n) measured by the transducer 15 for each sample n. k For example, the loss function L may be the L2 loss between the vectorization of the predicted waveform p=vec(P) and the vectorization of the measured waveform m=vec(M) defined by Equation 3:

[0054]

[0055] Return to reference Figure 2 , the attribute adjuster 44 may use multiple error calculators 61 and loss accumulators 62 to determine the value of the loss function L for iteration k. Each error calculator 61 may generate an error vector Δ for its sample n. n =p(n)−m(n), and the loss accumulator 62 can accumulate the output of the error calculator 61 as the L2 loss according to Equation 3.

[0056] If the loss L is acceptably small, then the wave field U k can be similar to a wave field in a physical medium, and the property adjuster 44 can provide a property estimate θ to the medium property restorer 46. k Otherwise, the calculated wave field U k does not represent the actual wavefield in the physical medium, and therefore the property estimate θ used in the nonlinear function NL(θ) k does not produce a correct model of the wavefield U. Therefore, the attribute adjuster 44 may adjust the attribute estimate θ k .

[0057] To this end, the attribute adjuster 44 may include a nonlinear gradient calculator 64 to minimize the loss L, and a parameter updater 66 for updating the attribute estimate θ based on the output of the nonlinear gradient calculator 64. k To attribute estimate θ k+1 .

[0058] The attribute adjuster 44 may perform a gradient-based operation such as gradient descent, L-BFGS (Limited Memory Broyden-Fletcher-Goldfarb-Shannon algorithm), Adam, or AdaDelta operation to minimize the loss L and update the attribute estimate θ k The attribute adjuster 44 may perform the following operations:

[0059]

[0060] where α is the learning rate, which is set to be less than 1, and is the loss L with respect to the attribute estimate θ k The attribute adjuster 44 can use the updated attribute estimate θ k+1 to activate the wavefield modeler 44 for the next iteration k+1. The wavefield modeler 44 may start from the same pulse samples F(n) but with an updated parameter vector θ k+1 A new value of the predicted reflected signal P(n) is generated.

[0061] To calculate Equation 4, the nonlinear gradient calculator 64 may determine the derivative According to a preferred embodiment of the present invention, the nonlinear gradient calculator 64 may be implemented via a back-propagation portion of a neural network system that performs differentiation on the functions implemented by the neural network.

[0062] Reference now Figure 5, which shows an implementation of the system 40 using a neural network tool. It can be seen that the wavefield modeler 42 can be implemented or modeled using a neural network structure and specifically a recursive neural network (RNN) structure 72 constructed using a nonlinear function NL(θ) as its recursive relationship. The nonlinear gradient calculator 64 can be implemented as a backpropagator, which can use the recursive relationship NL(θ) to backpropagate the gradient through the RNN 72 to return the wavefield U k With respect to physical properties (i.e. ). Based on these gradients, the parameter updater 66, which can calculate the derivative of the loss function of Equation 4, can calculate and can be calculated from it, as provided in Equation 5:

[0063]

[0064] Applicants have realized that by using the back-propagation system of an RNN network, the gradient of any wave equation can be calculated when expressed in the discrete representation of Equation 1.

[0065] It should be understood that in the prior art, back propagation tools in neural network platforms are used for training neural networks. System 40 does not use neural network tools to learn and train neural networks. Instead, system 40 uses RNN to express its objective function (i.e., the calculation of wavefield U), and then uses this expression as RNN to facilitate the calculation of gradients for the optimization process. As a result, the gradient calculation can utilize advanced optimization algorithms for neural networks and other deep learning systems (i.e., various back propagation algorithms).

[0066] In an alternative embodiment, the wavefield modeler may be implemented with a non-recursive neural network structure (such as a deep neural network) in which the layers express the temporal dependencies of the equations, similar to Figure 2 In this embodiment, the relationship between consecutive layers is determined by the recursive relationship NL(θ). For non-recursive neural networks, the layers of the deep neural network are consistent with the time step n of the RNN.

[0067] It should also be understood that although the present invention focuses on ultrasound imaging and its nonlinear wave equations, the NLWSI system can operate on other types of physical waves. Thus, it can be implemented to determine wave fields that can be acoustic waves, electromagnetic waves, elastic waves, photoacoustic waves, or acousto-optic waves.

[0068] It should also be understood that, similar to the linear FWI algorithm and in contrast to the geometry-based approach for the recovery of nonlinear properties, the system 40 can be activated with any type of pulse F, such as a plane wave, a diverging wave, or a focused beam. The system can also be implemented with any transducer array geometry captured by the limiting operator, such as linear, convex, elliptical, and intracavity probes.

[0069] Applicants have appreciated that an increased amount of information, including additional physical properties (such as medium nonlinearities), can be extracted from nonlinear waveform inversion compared to linear waveform inversion. Improved contrast and resolution of the reconstructed properties can be obtained.

[0070] In an exemplary embodiment, the results are shown in the present referenced Figures 6A-6L The properties of a 50 mm x 50 mm simulated medium with properties similar to those of human tissue are reconstructed from ultrasound signals as shown in FIG. The transducer array is a linear transducer array of 80 ultrasound elements, which emits acoustic pulses F(n) generated by 16 transducer elements, with a center frequency of f0 = 4 MHz. The pulses are focused beams with a focus depth of 5 mm and no steering angle, as discussed in more detail below. The transducer performs 16 consecutive lateral incidences of the focused beam, moving along the array.

[0071] Noise signals are added to the simulated signal. These additive noises are usually distributed with zero mean. The variance is chosen so that the obtained signal-to-noise ratio (SNR) is 20, mimicking an in vivo US scan.

[0072] In this example, the loss is the regularized L2 loss:

[0073]

[0074] Among them, n θ is the number of parameters, is the prediction signal, and is the measured signal, where n t is the number of time samples. In addition, D S is the Sobel regularization operator that enforces soft edges, and Controls the regularization level. At each iteration, the estimate is updated using the Adam optimizer.

[0075] exist Figure 6A-6L , the simulation medium contains two types of tissues placed in water 74, where the left tissue 70 is fat and the right tissue 72 is liver. Fig. 6A , Figure 6B , Figure 6C and Fig.6D Actual values ​​are provided for four attributes - SoS, density, attenuation and nonlinearity respectively. Fig. 6E , Fig. 6F , Figure 6G and Figure 6H The and used as the inverse algorithm are shown respectively. Fig.6I , Figure 6J , Figure 6K and Figure 6LThe initial values ​​of the inputs are shown and the reconstruction using system 40 is shown.

[0076] To initialize, the system 40 (ie, at iteration k=0), assumes that the medium contains primarily water, and therefore, initializes the property estimates θ with values ​​corresponding to water. 0 (For example, the SoS map is initialized to the SoS of water (ie 1480 m / s), and the density map is initialized to the density of water (ie 1000 kg / m3)).

[0077] The NRMSE (normalized root mean square error) evaluation metric is used to assess how close each iteration is to the actual value of the parameter θ GT , thus providing values ​​in the range [0,1] as follows:

[0078]

[0079] where θ k is the reconstruction attribute at iteration k, and θ GTmax and θ GTmin are predefined upper and lower bounds, respectively, for the estimated attribute value.

[0080] exist Figure 6A-6L In the example of , the estimation of SoS and density parameters is done first before the attenuation and nonlinear parameters. As a result, the previously reconstructed density values ​​are used to create a mask indicating the location of tissue inside the medium, and the mask is used to estimate the attenuation and nonlinear parameters. To generate a density map, the density values ​​are checked to find those areas in the reconstructed density map that have values ​​far from a predefined threshold of density for water. The estimates of damping and nonlinear parameters are then updated only in restricted areas of the medium defined by the mask.

[0081] As from Figure 6A-6L As can be seen, system 40 successfully reconstructs tissues 70 and 72 for each parameter, including non-linear parameters.

[0082] It should be understood that the embodiments provided above are exemplary and that the variables may be 2- or 3-dimensional matrices of any size suitable for the waveform being inverted.

[0083] Unless otherwise specifically noted, as is apparent from the foregoing discussion, it should be understood that throughout the specification, discussions utilizing terms such as "processing," "computing," "calculating," "determining," etc. refer to the actions and / or processes of any type of general purpose computer, such as a client / server system, a mobile computing device, an intelligent appliance, a cloud computing unit, or a similar electronic computing device that manipulates and / or transforms data within registers and / or memory of a computing system into other data within the computing system's memory, registers, or other such information storage, transmission, or display device.

[0084] Embodiments of the present invention may include a device for performing the operations herein. The device may be specially constructed for the desired purpose, or it may include a computing device or system generally having at least one processor and at least one memory, which is selectively activated or reconfigured by a computer program stored in a computer. When indicated by software, the resulting device can convert a general-purpose computer into an inventive element as discussed herein. Instructions may define the inventive device that operates with a desired computer platform. Such a computer program may be stored in a computer-readable storage medium, such as, but not limited to, any type of disk, including an optical disk, a magneto-optical disk, a read-only memory (ROM), a volatile and non-volatile memory, a random access memory (RAM), an electrically programmable read-only memory (EPROM), an electrically erasable programmable read-only memory (EEPROM), a magnetic card or an optical card, a flash memory, a disk on a disk, or any other type of medium suitable for storing electronic instructions and capable of being coupled to a computer system bus. Computer-readable storage media may also be implemented in cloud storage.

[0085] Some general purpose computers may include at least one communication element for enabling communication with a data network and / or a mobile communication network.

[0086] The processes and displays presented herein are not inherently related to any particular computer or other device. According to the teachings herein, various general purpose systems can be used together with the program, or it may prove convenient to construct a more specialized device to perform the desired method. The desired structure of various these systems will emerge from the following description. In addition, embodiments of the present invention are described without reference to any particular programming language. It should be understood that various programming languages ​​can be used to implement the teachings of the present invention as described herein.

[0087] Although certain features of the present invention have been shown and described herein, many modifications, substitutions, changes and equivalents will now occur to those skilled in the art. It is therefore to be understood that the appended claims are intended to cover all such modifications and changes that fall within the true spirit of the invention.

Claims

1. A system for recovering physical properties from a nonlinear medium, the system comprising: a wavefield modeler for modeling a wavefield generated by the at least one transmit pulse as it travels in the nonlinear medium and generating a predicted transducer output based on the modeled wavefield, the wavefield modeler being implemented as a neural network having a neural network representation of a nonlinear wave function of a set of physical properties of the wavefield; a property adjuster for optimizing a loss function between the predicted transducer output and the measured transducer output and generating an improved set of physical properties, the property adjuster operating a back propagator using the neural network representation of a wave function, the property adjuster for activating the wavefield modeler with the improved set of physical properties; as well as A medium property restorer is configured to output a currently improved set of physical properties once the property adjuster completes its operation, wherein the currently improved set of physical properties are restored physical properties of the nonlinear medium.

2. The system according to claim 1, wherein: The medium is a two-dimensional or three-dimensional body tissue.

3. The system according to claim 1, wherein: The wave field is one of the following: an acoustic wave, an electromagnetic wave, an elastic wave, a photoacoustic wave, and an acousto-optic wave.

4. The system according to claim 1, wherein: The at least one transmit pulse is one of: a plane wave, a focused beam, and a diverging wave.

5. The system according to claim 1, wherein: The neural network of the wavefield modeler comprises a non-linear function receiving as input the modified set of physical parameters and being provided with two previous wave samples and a pulse sample.

6. The system according to claim 5, wherein: The wavefield modeler also includes a restriction operator for restricting the output of the neural network to one of: a linear array of elements, a convex array of elements, an elliptical array of elements, and an intracavity array of elements.

7. The system according to claim 1, wherein: The attribute adjuster comprises: a plurality of error calculators, each error calculator of the plurality of error calculators for generating an error vector between the predicted transducer output and the measured transducer output for an associated wavefield sample; a loss accumulator, the loss accumulator being configured to accumulate the error vector; and A nonlinear gradient calculator implemented by the back propagator for back-propagating gradients through the neural network using the nonlinear wave function to return a gradient of the wave field relative to the set of physical properties.

8. The system according to claim 1, wherein: The neural network is one of: a recurrent neural network and a deep neural network, whose layers express the time dependency of the nonlinear wave function.

9. A method for recovering physical properties from a nonlinear medium, the method comprising: modeling a wavefield generated by the at least one transmit pulse as it travels in the nonlinear medium, the modeling using a neural network having a neural network representation of a nonlinear wave function of a set of physical properties of the wavefield; generating a predicted transducer output based on the modeled wavefield; optimizing a loss function between the predicted transducer output and the measured transducer output to generate an improved set of physical properties, the generating using back propagation using the neural network representation of the wave function; activating said modeling using said improved set of physical properties; as well as Once the optimization is finished operating, a current improved set of physical properties is provided, wherein the current improved set of physical properties are restored physical properties of the nonlinear medium.

10. The method according to claim 9, wherein: The medium is a two-dimensional or three-dimensional body tissue.

11. The method according to claim 9, wherein: The wave field is one of the following: an acoustic wave, an electromagnetic wave, an elastic wave, a photoacoustic wave, and an acousto-optic wave.

12. The method according to claim 9, wherein: The at least one transmit pulse is one of: a plane wave, a focused beam, and a diverging wave.

13. The method according to claim 9, wherein: The neural network comprises a non-linear function receiving as input the modified set of physical parameters and being provided with two previous wave samples and a pulse sample.

14. The method according to claim 13, wherein: The modeling also includes restricting the output of the neural network to one of: a linear array of elements, a convex array of elements, an elliptical array of elements, and an intracavitary array of elements.

15. The method according to claim 9, wherein: The optimization includes: generating an error vector between the predicted transducer output and the measured transducer output for associated wavefield samples; Accumulating the error vector; and Gradients are back-propagated through the neural network using the nonlinear wave function to return gradients of the wavefield with respect to the set of physical properties.

16. The method according to claim 9, wherein: The neural network is one of: a recurrent neural network and a deep neural network, whose layers express the time dependency of the nonlinear wave function.

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