Nonlinear Waveform Inversion (NLWI) System

Abstract

A system for recovering physical properties from a nonlinear medium includes a wave field modeler, a property adjuster, and a media property restorer. The wave field modeler models a wave field generated by a transmit pulse traveling in the nonlinear medium and generates a predicted transducer output from the modeled wave field. The wave field modeler is a neural network having a neural network representation of a nonlinear wave function of the physical properties of the wave field. The property adjuster optimizes a loss function between the predicted transducer output and the measured transducer output to generate an improved set of physical properties. The property adjuster operates a backpropagator using the neural network representation to activate the wave field modeler with the improved set of physical properties. The media property restorer outputs the current improved set of physical properties when the property adjuster finishes operating.

Description

[Technical field]

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS This application claims priority to U.S. Provisional Patent Application No. 63 / 339,473, filed May 8, 2022, and U.S. Provisional Patent Application No. 63 / 375,545, filed September 14, 2022, both of which are incorporated by reference herein.

[0002] Technical Field The present invention relates generally to nonlinear waveform inversion, and more particularly to the application of nonlinear waveform inversion to ultrasound. [Background technology]

[0003] Ultrasound imaging is widely used in medical applications due to its non-invasive and non-radioactive nature. Figures 1A-1G show the structure and operation of a typical ultrasound system 10. As shown in Figure 1A, ultrasound system 10 includes a transducer 11 and a medium 16 including tissue 17. Transducer 11 includes n transducers 11, each of which includes a transmitter portion 15 and a receiver portion 13. c The transducer array 12 comprises transducer elements 12. Figure 1A shows a time t0 before operation.

[0004] In ultrasound imaging, an image is produced by ionizing or transmitting 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 a pulse 21 exiting the transducer 11 at a starting time shown as t1. Figure 1C shows a pulse 22 exiting the transducer 11 at a later time t2, with pulse 21 continuing to travel away from the transducer 11. Figure 1D shows a pulse 23 exiting the transducer 11 at time t3, with pulse 22 and pulse 21 continuing to propagate away from the transducer 11.

[0005] The transmit pulses 21, 22, 23 propagate through the medium 16 and tissue 17, causing a series of reflections and refractions that create echoes that are detected by the same array. FIG. 1E shows a first reflected wave 24 (transmit pulses 21, 22, 23 omitted for clarity) traveling toward the transducer 11 at time t4. FIG. 1F shows a second reflected wave 25 following the wave 24 at time t5. FIG. 1G shows the wave 24 reaching the transceiver 11 at time t6. At time t6, the transceiver 11 acquires an ultrasound signal, after which a beamforming algorithm is used to properly align the signals from the different transducer elements and combine the data acquired from the multiple transmit schemes to generate an ultrasound image of the medium 16 and tissue 17.

[0006] A typical brightness mode (B-mode) image is generated by applying a corresponding time delay to the acquired signals and averaging across channels with adjusted weighting. However, B-mode images do not always provide sufficient contrast for certain anatomical structures and are difficult to interpret physically.

[0007] Imaging of physical properties of materials, such as speed of sound (SoS), density, acoustic attenuation, and elasticity, is known to have valuable differentiation capabilities and improve medical diagnosis. For example, SoS maps can distinguish benign and malignant breast tumors, identify muscle loss and fatty muscle degeneration (sarcopenia) in elderly people, and differentiate between healthy and diseased tissues, such as livers in humans and animals affected by non-alcoholic fatty liver disease (NAFLD). Acoustic attenuation maps can improve the diagnosis of non-healthy tissues. Finally, tissue density can indicate risk of breast cancer and quantify levels of fat and steatosis in the liver, which are important for monitoring NAFLD and non-alcoholic steatohepatitis (NASH).

[0008] Inverse ultrasound algorithms attempt to reconstruct the properties of a medium based on the acquired ultrasound signal. The standard method for solving inverse ultrasound problems is the Full Waveform Inversion (FWI) algorithm, a computational technique first developed in geophysics. FWI algorithms rely on physical wave propagation models and therefore account for a wider range of phenomena compared to B-mode images. To reconstruct the properties, the algorithm utilizes a computationally intensive iterative gradient-based approach.

[0009] Other inverse ultrasound methods use a differential path matrix to estimate the speed of sound in the medium. The differential path matrix links the SoS distribution to the acquired time delays at the transducer. However, the differential path matrix only estimates the SoS of the medium, as it relies on geometric considerations rather than a wave propagation model. As an alternative solution to the inverse ultrasound problem, machine learning approaches such as deep neural networks are used. Such approaches require a large amount of known medical data with known SoS maps to train the neural network, and the resulting models have low interpretability. Summary of the Invention

[0010] Therefore, according to a preferred embodiment of the present invention, there is provided a system for recovering physical properties from a nonlinear medium. The system comprises a wave field modeler, a property adjuster, and a media property restorer. The wave field modeler models a wave field generated by at least one transmit pulse as it travels through the nonlinear medium and generates a predicted transducer output from the modeled wave field. The wave field 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 wave field. The property adjuster optimizes a loss function between the predicted transducer output and the measured transducer output to generate an improved set of physical properties. The property adjuster operates a backpropagator using the neural network representation of the nonlinear wave function to activate the wave field modeler with the improved set of physical properties. The media property restorer outputs a current improved set of physical properties when the property adjuster finishes operating. The current improved set of physical properties is the restored physical properties of the nonlinear medium.

[0011] Furthermore, in accordance with a preferred embodiment of the present invention, the medium is two- or three-dimensional body tissue.

[0012] Furthermore, in accordance with a preferred embodiment of the present invention, the wave field is one of an acoustic wave field, an electromagnetic wave field, an elastic wave field, an optical acoustic wave field, and an acoustic optical wave field.

[0013] Furthermore, in accordance with a preferred embodiment of the present invention, the transmit pulse is one of a plane wave, a focused beam, and a diverging wave.

[0014] Furthermore, in accordance with a preferred embodiment of the present invention, the neural network of the wave field modeller accepts as input an improved set of physical parameters and comprises a nonlinear function to which the two most recent wave samples and one pulse sample are provided.

[0015] Furthermore, in accordance with a preferred embodiment of the present invention, the wave field modeller further comprises a constraint operator that constrains 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 a lumen array of elements.

[0016] Further in accordance with a preferred embodiment of the present invention, the property adjustment unit comprises a plurality of error calculators, a loss accumulator, and a nonlinear gradient calculator, each of which generates an error vector between the predicted and measured transducer outputs for an associated wavefield sample, the loss accumulator ...

[0017] Furthermore, in accordance with a preferred embodiment of the present invention, the neural network is one of a recurrent neural network or a deep neural network, and a layer of the recurrent neural network or the deep neural network represents the time dependence of a nonlinear wave function.

[0018] According to a preferred embodiment of the present invention, there is also provided a method of recovering physical properties from a nonlinear medium, the method including: modeling a wave field generated by at least one transmit pulse as it travels through 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 improved set using a backpropagator with the neural network representation of the nonlinear wave function; activating the modeling with the improved set of physical properties; and providing a current improved set of physical properties when the optimization has finished operating, the current improved set of physical properties being the recovered physical properties of the nonlinear medium.

[0019] Furthermore, in accordance with a preferred embodiment of the present invention, the modeling further 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 a lumen array of elements.

[0020] Further in accordance with a preferred embodiment of the present invention, the optimization includes generating an error vector between the predicted and measured transducer outputs for the associated wave field samples, accumulating the error vector, and returning the gradient of the wave field with respect to the set of physical properties by propagating the gradient through a neural network utilizing a nonlinear wave function.

[0021] The subject matter which is regarded as the invention is particularly pointed out and distinctly claimed in the concluding portion of the specification, but the invention, both as to organization and method of operation, together with objects, features, and advantages thereof, may best be understood by reference to the following detailed description taken in conjunction with the accompanying drawings, in which: [Brief description of the drawings]

[0022] [Figure 1A] FIG. 1 is a schematic diagram illustrating the operation of a prior art ultrasound imaging system; [Figure 1B] FIG. 1 is a schematic diagram illustrating the operation of a prior art ultrasound imaging system; [Figure 1C] FIG. 1 is a schematic diagram illustrating the operation of a prior art ultrasound imaging system; [Figure 1D] FIG. 1 is a schematic diagram illustrating the operation of a prior art ultrasound imaging system; [Figure 1E] FIG. 1 is a schematic diagram illustrating the operation of a prior art ultrasound imaging system; [Figure 1F] FIG. 1 is a schematic diagram illustrating the operation of a prior art ultrasound imaging system; [Figure 1G] FIG. 1 is a schematic diagram illustrating the operation of a prior art ultrasound imaging system; [Diagram 2] 1 is a schematic diagram of a Nonlinear Waveform Inversion System (NLWIS) constructed and operative in accordance with a preferred embodiment of the present invention; [Figure 3A] Schematic diagram of wave sample 28 at timestamp n generated by NLWIS in Fig. 2 [Figure 3B] Schematic diagram of multiple wave samples U(n), U(n-1) [Figure 4] Schematic diagram of the wavefield modeler useful in NLWIS in Fig. 2. [Diagram 5] Schematic diagram showing the implementation of the NLWIS system of Figure 2 using neural network tools. [Figure 6A] Plot of ground truth values ​​for the four properties [Figure 6B] Graph of the correct answers for the four characteristics [Figure 6C] Graph of the correct answers for the four characteristics [Figure 6D] Graph of the correct answers for the four characteristics [Figure 6E]A graph of the initial values ​​used as inputs to the NLWSI system of Figure 2 for the characteristics of Figure 6A. [Figure 6F] A graph of the initial values ​​used as inputs to the NLWSI system of FIG. 2 for the characteristics of FIG. 6B. [Figure 6G] A graph of the initial values ​​used as inputs to the NLWSI system of Figure 2 for the characteristics of Figure 6C. [Figure 6H] A graph of the initial values ​​used as inputs to the NLWSI system of FIG. 2 for the characteristics of FIG. 6D. [Figure 6I] 6A is a graphical representation of the reconstruction generated by the NLWSI system of FIG. 2 for the characteristics of FIG. [Figure 6J] A graphical representation of the reconstruction generated by the NLWSI system of FIG. 2 for the characteristics of FIG. 6B. [Figure 6K] A graphical representation of the reconstruction generated by the NLWSI system of Fig. 2 for the characteristics of Fig. 6C. [Figure 6L] A graphical representation of the reconstruction generated by the NLWSI system of FIG. 2 for the characteristics of FIG. 6D. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0023] It will be appreciated that for simplicity and clarity of illustration, elements shown in the figures have not necessarily been drawn to scale. For example, the dimensions of some elements may be exaggerated relative to other elements for clarity. Further, where considered appropriate, reference numerals may be repeated among the figures to indicate corresponding or analogous elements.

[0024] In the following detailed description, numerous specific details are set forth in order to provide a thorough understanding of the present invention. However, it will be understood by those skilled in the art that the present invention may be practiced without these specific details. In other instances, well-known methods, procedures, and components have not been described in detail so as not to obscure the present invention.

[0025] Applicant has recognized that inverse acoustic algorithms work well for linear media, but are inaccurate for ultrasound medical imaging, which is typically nonlinear. Furthermore, the Full Waveform Inversion (FWI) algorithm described above is computationally intensive and not useful for most applications.

[0026] The applicant has recognized that neural network platforms have been developed that make computationally complex calculations simpler to visualize and calculate, and that it is possible to use neural networks to represent wave equations rather than to learn a set of parameters. The applicant has recognized that neural network structures used in deep learning systems can be used to represent nonlinear time-based equations such as the wave propagation equation of FWI. In particular, a recurrent neural network (RNN) structure can be used to represent the time-based equations. Also, a deep neural network can be used whose layers represent the time dependency of the equations.

[0027] Furthermore, Applicant has recognized that such neural network systems also include derivative calculations as part of a "backpropagation" system for updating the neural network during training of the network (i.e., to learn the parameters of the neural network), and that different neural networks use different optimization algorithms in their backpropagation. Applicant has recognized that the backpropagation system of a neural network system can provide a very efficient implementation for the derivative calculations that form part of the iterative gradient calculations of the nonlinear waveform inversion.

[0028] Thus, applicants have recognized that a neural network platform may be utilized to solve inverse nonlinear physics problems, rather than providing an output given an unknown input, as is the standard use of neural networks. Thus, a nonlinear waveform inversion system implemented on a neural network platform may be used to restore the properties of a medium.

[0029] FIG. 2 is a schematic diagram of a nonlinear waveform inversion system (NLWIS) 40. The system 40 includes a Wave Field Modeler (WFM) 42, a Properties Adjuster (PA) 44, and a Medium Properties Recoverer (MPR) 46. The system 40 can recover and output a visual representation of a physical medium through which waves, such as ultrasound waves, flow. In an ultrasound implementation, the physical medium can be a portion of a human body, such as the abdomen. The physical medium can have multiple properties θ that can affect the flow of the waves, and the elements of θ can be multiple properties, and each property 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 described in more detail below.

[0030] A wave field modeler (WFM) 42 may calculate a wave field U generated in response to multiple transmit pulses F, such as pulses 21, 22, 23 of FIG. 1D, as they propagate through medium 16 and tissue 17. Using the calculated wave field U, wave field modeler 42 may calculate a detected wave P, such as reflected waves 24 and 25 of FIG. 1F, as detected by receiver 13. Because wave field U may depend on multiple properties θ, and property θ is an unknown variable to be determined, wave field modeler 42 may calculate a property estimate θ of property θ. k The characteristic adjustment unit 44 can use the characteristic estimation value θ k The characteristic estimate θ k+1 After updating to , we iteratively calculate the wave field U.

[0031] The medium characteristic restoration unit 46 adjusts the estimated value θ k+1 has converged or we can retrieve the property θ after a predefined maximum number of iterations k.

[0032] Because the system 40 is implemented on a neural network platform, it uses discrete wave samples U(n) and discrete transmit pulse samples F(n) at each timestamp n, as shown in Figures 3A and 3B. Figure 3A is a schematic diagram of a wave sample 28 at timestamp n. The wave sample 28 is a pressure value U of x*y. x、y For example, grid 27 may be a 4000×4000 grid, and wave field U may have 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 linear transmit section 15 may have, for example, 128 transmit pulses F(n) at each timestamp n. x 3B shows a number of wave samples U(n), U(n-1), etc., where each wave sample U(n) is two-dimensional.

[0033] The wavefield modeler 42 calculates the wavefield U for each iteration k using a nonlinear model NL(θ) derived from the lossy Westervelt equation described in the paper 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). kHowever, 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 modeller 42 may be its discrete version, as shown in Equation 1:

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[0034] In Equation 1 and Equation 2, vectors and matrices are represented by bold lowercase and uppercase letters, respectively (in this embodiment, not only in Equation 1 and Equation 2, but also in lowercase or uppercase θ, C, Q, D, F, U, P, B, M, p, and m represent vectors or matrices, respectively, in the order of appearance). The vectorization, convolution, transposition, and element-wise multiplication (Hadamard product) operators are vec(·), *, (·), respectively. T , and

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[0035] The wave field U at iteration k k To calculate θ, the wavefield modeler 42 may comprise a number of nonlinear modelers 50 (FIG. 2), each of which generates one of the samples n. Each modeler 50 uses the property estimate θ determined at the end of the previous iteration k−1. k may be used to implement the nonlinear function NL(θ) defined in Equations 1 and 2. Each nonlinear modeler 50 may accept as inputs the associated 2D pulse sample F(n) and U(n-1) and U(n-2) from each nonlinear modeler 50's two immediate predecessors that generated the 2D wave samples U(n-1) and U(n-2), respectively.

[0036] To predict each reflected signal P(n) received by each receiver 13 (FIG. 1A), the wave field modeler 42 may include a number of limiting operators 52 that may select a portion of the wave samples U(n) located at the location of the receiver 13 of the transducer 11. An example of a portion of the wave samples U(n) to use as the reflected signal P(n) is shown in FIG. 3A.

[0037] Of course, for the first wave sample U(1), wave samples U(n-2) and U(n-1) may not be available, in which case all elements of the starting wave sample U(0) may be set to zero, and the inputs to U(1) may be only the starting wave sample U(0) and the transmit sample pulse F(1).

[0038] According to a preferred embodiment of the present invention, as shown in Fig. 4, the wave field modeler 42 may be implemented as an untrained neural network, with each nonlinear modeler 50 and associated constraint operator 52 forming one layer of the neural network. In particular, since the computations of each layer are identical, the neural network may be a Recurrent Neural Network (RNN), which is a neural network in which nodes are connected over a time sequence such that the same operation is applied at each time step, and which can exhibit dynamic behavior. For the wave field modeler 42, the time step n of the wave equation may coincide with the time step n of the RNN.

[0039] Figure 4 shows the parameter estimates θ k 1 shows an RNN cell 60 having a nonlinear function NL(θ) that accepts as inputs, and is provided with wave samples U(n-1) and U(n-2) and a pulse sample F(n). The nonlinear function NL(θ) may generate a current wave sample U(n) to which a limiting operator R can be applied, thereby generating a predicted sample P(n). In the case of an RNN, the current wave sample U(n) may be provided to the next layer of the RNN cell 60, and the previous wave sample U(n-1) may be provided to the next layer of the RNN cell 60 to become the wave sample U(n-2).

[0040] Of course, the purpose of computing the nonlinear waveform inversion is to recover properties in the medium and to “discover” other bodies present in the medium. However, the wave field modeler 42 does not k To calculate the unknown parameter estimates, k In each iteration, for each sample n, the characteristic adjustment unit 44 calculates the parameter estimates θ using a loss function L based on a comparison of the predicted reflected waveform P(n) with its associated measured waveform M(n) measured by the transducer 15. k For example, the loss function L may be adjusted based on the predicted waveform, defined in Equation 3.

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[0041]

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[0042] Returning to FIG. 2, the characteristic adjustment unit 44 may use multiple error calculation units 61 and loss accumulation units 62 to determine the value of the loss function L at iteration k. In accordance with Equation 3, each error calculation unit 61 calculates an error vector Δ n = p(n) - m(n), and the loss accumulation unit 62 converts the output of the error calculation unit 61 into L 2 Losses can accumulate.

[0043] If the losses L are acceptably small, the wave field U k may be similar to a wave field in a physical medium, and the characteristic adjustment unit 44 adjusts the characteristic estimate θ k may be provided to the media characteristic reconstruction unit 46. If the loss L is not acceptably small, the calculated wave field U k does not represent the actual wave field in the physical medium, so the characteristic estimate θ used in the nonlinear function NL(θ) k does not generate a correct model of the wave field U. Therefore, the characteristic adjustment unit 44 adjusts the characteristic estimate θ k may be adjusted.

[0044] For this purpose, the characteristic adjustment unit 44 calculates a nonlinear gradient calculation unit 64 for minimizing the loss L, and calculates a characteristic estimate value θ k The characteristic estimate θ k+1 and a parameter update unit 66 for updating the parameter.

[0045] The characteristic adjustment unit 44 minimizes the loss L and adjusts the characteristic estimation value θ kTo update , a gradient-based operation such as gradient descent, the limited memory Broyden-Fletcher-Goldfarb-Shanno algorithm (L-BFGS), Adam, or AdaDelta operation may be performed. The characteristic adjustment unit 44 may perform the following operations.

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[0046] To calculate Equation 4, the nonlinear gradient calculator 64 calculates the derivative

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[0047] 5 illustrates an implementation of the system 40 using neural network tools. As can be seen, the wave field modeler 42 may be implemented or modeled using a neural network structure, specifically a recurrent neural network (RNN) structure 72 constructed using a nonlinear function NL(θ) as a recurrence relation. The nonlinear gradient calculator 64 may be implemented as a backpropagator, utilizing the recurrence relation NL(θ) to backpropagate the gradient through the RNN 72 to generate the wave field U for the physical property.k The gradient of (i.e.,

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[0048]

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[0049] Applicant has realised that by using a backpropagation system of RNN networks, the gradient of any wave equation, when expressed in the discrete representation of Equation 1, can be computed.

[0050] Of course, in the prior art, backpropagation tools in neural network platforms were used to train neural networks. The system 40 does not use neural network tools to learn and train neural networks. Instead, the system 40 uses an RNN to represent the objective function (i.e., the calculation of the wave field U), and then utilizes the representation as an RNN to facilitate the computation of gradients for the optimization process. As a result, the gradient computation may utilize advanced optimization algorithms (i.e., various backpropagation algorithms) used in neural networks and other deep learning systems.

[0051] In an alternative embodiment, the wave field modeler may be implemented in a non-recurrent neural network structure, such as a deep neural network, where the layers represent the time dependence of the equations, similar to the structure shown in Figure 2. In this embodiment, the relationship between successive layers is determined by the recurrence relation NL(θ). In the case of a non-recurrent neural network, the layers of the deep neural network correspond to the time steps n of the RNN.

[0052] It should also be appreciated that although the present invention focuses on ultrasound imaging and its nonlinear wave equations, NLWSI systems may operate on other types of physical waves and may thus be implemented to determine wave fields that may be acoustic, electromagnetic, elastic, optical, and acoustic optical wave fields.

[0053] It should also be appreciated that, similar to linear FWI algorithms, and unlike geometry-based methods for nonlinear property reconstruction, the system 40 may be activated with any type of pulse F, such as a plane wave, a diverging wave, or a focused beam, for example. The system may be implemented utilizing any transducer array shape imaged by a constrained operator, such as linear, convex, elliptical, and intrabore probes.

[0054] Applicants have recognized that a greater amount of information may be extracted from nonlinear waveform inversion compared to linear waveform inversion, including additional physical properties (such as nonlinearity of the medium). Improved contrast and resolution of the reconstructed properties may be obtained.

[0055] In an exemplary implementation, the results of which are shown in Figures 6A-6L, the properties of a 50 mm x 50 mm simulated medium with characteristics similar to human tissue are reconstructed from the ultrasound signal. 0The transducer array was a linear array of 80 ultrasonic elements emitting acoustic pulses F(n) generated by 16 transducer elements with a center frequency of 100 Hz to 4 MHz. The pulses were focused beams with a focusing depth of 5 mm and no steering angle, as described in more detail below. The transducer was moved along the array, firing 16 successive lateral insonifications of the focused beam.

[0056] Noise signals were added to the simulated signals. These additive noises were normally distributed with zero mean. The variance was chosen to achieve a signal-to-noise ratio (SNR) of 20, mimicking an in vivo ultrasound scan.

[0057] In this example, the loss is regularized L 2 It was a loss.

[0058]

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[0059] In Figures 6A-L, the simulated medium includes two types of tissues disposed in water 74. The tissue 70 on the left is adipose tissue, and the tissue 72 on the right is liver tissue. Figures 6A, 6B, 6C, and 6D show ground-truth values ​​for four properties: SoS, density, attenuation, and nonlinearity, respectively. Figures 6E, 6F, 6G, and 6H show the initial values ​​used as input to the inverse algorithm, and Figures 6I, 6J, 6K, and 6L show the reconstructions using system 40, respectively.

[0060] To initialize the system 40 (i.e., at iteration k=0), the medium is assumed to contain primarily water, and therefore the property estimates θ 0 were initialized with values ​​corresponding to water (e.g., the SoS map was initialized to the SoS of water (i.e., 1480 m / s), and the density map was initialized to the density of water (i.e., 1000 kg / m 3 ).

[0061] As shown below, each iteration determines the correct value of the parameters, θ GT To evaluate how close we are to the approximation, the normalized root mean square error (NRMSE) evaluation metric is used, giving a value in the range [0, 1].

[0062]

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[0063] Where:

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[0064] In the example of Figures 6A-L, estimation of the SoS and density parameters was completed first, before the attenuation and nonlinear parameters. As a result, the previously reconstructed density values ​​were used to create a mask indicating the location of the tissue within the medium, and that mask was used for the estimation of the attenuation and nonlinear parameters. To generate a density map, the density values ​​were reviewed to find regions in the reconstructed density map that had values ​​that were a predefined threshold away from the density of water. The attenuation and nonlinear parameter estimates were then updated only within the restricted region of the medium defined by the mask.

[0065] As can be seen from FIGS. 6A-6L, system 40 successfully reconstructed tissues 70 and 72 for each parameter, including the nonlinear parameters.

[0066] It will be appreciated that the above embodiments are exemplary and the variables may be two- or three-dimensional matrices of any size appropriate for the waveform to be inverted.

[0067] Unless otherwise expressly indicated, it will be understood and evident from the discussion above that throughout this specification discussions of terms such as "processing," "operation," "calculation," "determination," and the like refer to operations and / or processes of any type of general-purpose computer, such as a client / server system, mobile computing device, smart appliance, cloud computing unit, or similar electronic computing device, that manipulate data in the registers and / or memory of a computing system and / or transform data in the registers and / or memory of a computing system to data in the memory, registers, or other information storage, transmission, or display device of the computing system.

[0068] An embodiment of the present invention may include an apparatus for performing the operations herein. The apparatus may be specifically constructed for a desired purpose or may include a computing device or system, typically having at least one processor and at least one memory, selectively activated or reconfigured by a computer program stored in the computer. The resulting apparatus, when instructed by software, may transform a general-purpose computer into the inventive elements discussed herein. The instructions may define the device of the present invention when operating 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 optical disks, magnetic optical disks, read-only memory (ROM), volatile and non-volatile memory, random access memory (RAM), electrically programmable read-only memory (EPROM), electrically erasable and programmable read-only memory (EEPROM), magnetic or optical card, flash memory, disk-on-key, or any other type of medium suitable for storing electronic instructions and capable of coupling to a computer system bus. The computer-readable storage medium may be implemented in cloud storage.

[0069] Some general purpose computers may be equipped with at least one communication element enabling communication with a data network and / or a mobile communication network.

[0070] The processes and displays presented herein are not inherently related to any particular computer or other apparatus. Various general-purpose systems may be used with programs in accordance with the teachings herein, or it may prove convenient to construct a more specialized apparatus to perform the desired methods. The desired structure for a variety of these systems will appear from the description that follows. Additionally, embodiments of the present invention are not described with reference to any particular programming language. It will be appreciated that a variety of programming languages ​​may be used to implement the teachings of the present invention as described herein.

[0071] While certain features of the invention have been illustrated and described herein, many modifications, substitutions, changes, and equivalents will occur to those skilled in the art, and 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. 1. A system for recovering physical properties from a nonlinear medium, comprising: a wave field modeler for modeling a wave field generated by the at least one transmit pulse as it travels through the nonlinear medium and generating a predicted transducer output from the modeled wave field, the wave field 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 wave field; a property adjuster that optimizes a loss function between the predicted and measured transducer outputs to generate an improved set of physical properties, the property adjuster running a backpropagator using the neural network representation of the nonlinear wave function to activate the wave field modeler with the improved set of physical properties; a media characteristic restoration unit configured to output a current improved set of physical characteristics when the characteristic adjustment unit has finished operating, the current improved set of physical characteristics being the restored physical characteristics of the nonlinear medium; The system comprising:

2. The nonlinear medium is a two-dimensional or three-dimensional body tissue. The system of claim 1 .

3. The wave field is one of an acoustic wave field, an electromagnetic wave field, an elastic wave field, an optical acoustic wave field, and an optical acoustic wave field. The system of claim 1 .

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

5. the neural network of the wave field modeller comprises a non-linear function that accepts as input the improved set of physical parameters and is provided with two previous wave samples and one pulse sample. The system of claim 1 .

6. the wave field modeler further comprises a constraining operator that constrains an output of the neural network to one of a linear array of elements, a convex array of elements, an elliptical array of elements, and a lumen array of elements. The system of claim 5.

7. The characteristic adjustment unit is a plurality of error calculators each generating an error vector between the predicted transducer output and the measured transducer output for an associated wave field sample; a loss accumulation unit that accumulates the error vector; a nonlinear gradient calculator implemented by the backpropagator that returns a gradient of the wave field with respect to the set of physical properties by backpropagating a gradient through the neural network using the nonlinear wave function; Equipped with The system of claim 1 .

8. the neural network is one of a recurrent neural network or a deep neural network, and a layer of the recurrent neural network or the deep neural network represents the time dependence of the nonlinear wave function. The system of claim 1 .

9. 1. A method for recovering physical properties from a nonlinear medium, comprising: modeling a wave field generated by the at least one transmit pulse as it travels through the nonlinear medium, the modeling using a neural network having a nonlinear wave function representation of a set of physical properties of the wave field; generating a predicted transducer output from the modeled wave field; and optimizing a loss function between the predicted and measured transducer outputs to generate an improved set of physical properties, said improved set using backpropagation with the neural network representation of the nonlinear wave function; revitalizing the modeling with the improved set of physical properties; providing a current improved set of physical properties when the optimization has finished operating, the current improved set of physical properties being the restored physical properties of the nonlinear medium; and The method comprising:

10. The nonlinear medium is a two-dimensional or three-dimensional body tissue.

10. The method of claim 9.

11. The wave field is one of an acoustic wave field, an electromagnetic wave field, an elastic wave field, an optical acoustic wave field, and an optical acoustic wave field.

10. The method of claim 9.

12. the at least one transmit pulse is one of a plane wave, a focused beam, and a diverging wave.

10. The method of claim 9.

13. the neural network receiving as input the improved set of physical parameters and comprising a non-linear function to which two previous wave samples and one pulse sample are provided; 10. The method of claim 9.

14. the modeling further includes restricting an output of the neural network to one of a linear array of elements, a convex array of elements, an elliptical array of elements, and a lumen array of elements. The method of claim 13.

15. The optimization comprises: generating an error vector between the predicted transducer output and the measured transducer output for an associated wave field sample; accumulating said error vector; returning a gradient of the wave field with respect to the set of physical properties by backpropagating the gradient through the neural network using the nonlinear wave function; Including, 10. The method of claim 9.

16. the neural network is one of a recurrent neural network or a deep neural network, and a layer of the recurrent neural network or the deep neural network represents the time dependence of the nonlinear wave function.

10. The method of claim 9.

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