An ultrasonic tomography sound velocity imaging method based on an implicit neural representation network

Abstract

The application belongs to the technical field of ultrasonic sound velocity image reconstruction, and particularly relates to an ultrasonic tomographic sound velocity imaging method based on an implicit neural representation network, which comprises the following steps: dividing a tomographic plane imaging area into grids, performing block division on all the grids, determining the two-dimensional coordinates of any grid in each grid block, and converting the two-dimensional coordinates into high-dimensional feature vectors; inputting all the high-dimensional feature vectors into a pre-trained implicit neural representation network, taking the output value as the sound velocity distribution value of the corresponding grid block, spatially arranging the sound velocity distribution values at the grid blocks, mapping the sound velocity distribution values at each grid block in the arrangement result to the actual sound velocity value range, and obtaining a sound velocity image of the tomographic plane imaging area; performing forward modeling on the sound velocity image to obtain simulated generated sound field data, comparing the simulated generated sound field data with actually observed sound field data, optimizing network parameters, and taking the final sound velocity image as a reconstruction result. The application can ensure the accuracy of ultrasonic tomographic sound velocity imaging without an accurate initial sound velocity model.

Description

Technical Field

[0001] This invention belongs to the field of ultrasonic velocity image reconstruction technology, and more specifically, relates to an ultrasonic tomographic velocity imaging method based on implicit neural representation networks. Background Technology

[0002] Ultrasound computed tomography (CT) is an emerging ultrasound imaging technology that is based on the theoretical development of CT while also possessing the advantages of ultrasound imaging, thus becoming a highly anticipated technological innovation. This technology uses an array of ultrasound transducers surrounding the subject to transmit and receive ultrasound signals, and then reconstructs and calculates the acquired data to obtain three modalities of sound velocity, attenuation, and reflection images of the target body's interior. Compared to traditional ultrasound imaging and CT, ultrasound computed tomography offers advantages such as being non-invasive, free of ionizing radiation, high-resolution, and multimodal, and has shown great potential in clinical applications such as musculoskeletal imaging, breast cancer screening, and cranial imaging.

[0003] Full waveform inversion is a high-resolution sound velocity image reconstruction algorithm widely used in ultrasound tomography. This method is based on optimization techniques constrained by the wave equation, establishing a relationship between tissue acoustic parameters and the received sound pressure signal. By iteratively updating the model, it minimizes the difference between the actual observation data and the predicted model, thereby recovering the acoustic parameters of the system's internal structure or properties and reconstructing the sound velocity image. Compared to other methods, full waveform inversion considers the full wave field information of the sound field, including rich wave phenomena (such as primary and multiple reflections, transmission, scattering, etc.), which more closely approximates the real situation of sound wave propagation. Therefore, the reconstructed image has better quality and higher resolution.

[0004] Although the full-waveform inversion algorithm can provide high-resolution imaging results, it is quite complex due to the need to solve nonlinear partial differential equations. Therefore, this method has high computational overhead and relatively high computational power requirements, resulting in a relatively long reconstruction time.

[0005] Meanwhile, from a mathematical perspective, full waveform inversion is an ill-conditioned, non-convex, nonlinear inverse problem. In practical solutions, it often encounters multiple solutions, and the final result tends to converge to a local optimum. Therefore, the initial sound velocity model provided in the application has a significant impact on the inversion results. This is a common problem faced by major domestic and international manufacturers of ultrasonic tomography equipment in sound velocity image reconstruction. In practical applications of ultrasonic tomography, especially at high frequencies, it is difficult to obtain an accurate initial sound velocity model. This not only significantly affects the solution results but also severely restricts the further development of full waveform inversion technology in this field. Summary of the Invention

[0006] To address the shortcomings and improvement needs of existing technologies, this invention provides an ultrasound tomography sound velocity imaging method based on implicit neural representation networks, aiming to ensure the accuracy of ultrasound tomography sound velocity imaging without requiring an accurate initial sound velocity model.

[0007] To achieve the above objectives, according to one aspect of the present invention, a method for ultrasound tomography sound velocity imaging based on implicit neural representation networks is provided, comprising:

[0008] S1. Divide the fault plane imaging region into a grid, and divide all grids into blocks to obtain multiple grid blocks. Determine the two-dimensional coordinates of any grid in each grid block, and convert each two-dimensional coordinate into a high-dimensional feature vector. The size of each grid block is n*n, where n represents the number of grids on any side, and n≥1.

[0009] S2. Input all the transformed high-dimensional feature vectors into the pre-trained implicit neural representation network, and use the output value as the sound velocity distribution value of the corresponding grid block. Arrange the sound velocity distribution values ​​of each grid block in space according to the distribution of the tomographic plane imaging region, and map the sound velocity distribution value of each grid block in the arrangement result to the actual sound velocity value range through a mapping function to obtain the sound velocity image of the tomographic plane imaging region.

[0010] S3. Perform forward modeling on the sound velocity image to obtain simulated sound field data. With the goal of minimizing the deviation between the sound field data and the actual observed sound field data, optimize the parameters of the implicit neural representation network, and repeat S2 until the preset termination condition is reached. Use the current sound velocity image as the final reconstructed ultrasound tomographic sound velocity image.

[0011] Furthermore, Fourier feature mapping is used to transform each two-dimensional coordinate into a high-dimensional feature vector.

[0012] Furthermore, the implicit neural representation network is a multilayer perceptron network.

[0013] Furthermore, by minimizing the loss function that includes data consistency and regularization terms, the deviation between the simulated sound field data and the actual observed sound field data is minimized.

[0014] Furthermore, n is greater than 1.

[0015] Furthermore, the pre-trained implicit neural representation network serves as the initial sound velocity model for network training, and it satisfies the following condition: it can output a uniform background sound velocity image.

[0016] The present invention also provides an electronic device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps of the method described above.

[0017] The present invention also provides a computer-readable storage medium comprising a stored computer program, wherein the computer program, when executed by a processor, controls the device on which the storage medium is located to perform the steps of the method described above.

[0018] The present invention also provides a computer program product, including a computer program or instructions, which, when executed by a processor, implement the steps of the method described above.

[0019] In summary, the above-described technical solutions conceived in this invention can achieve the following beneficial effects:

[0020] (1) This invention employs an implicit neural representation network (structure) to reconstruct sound velocity images. This method transforms the image reconstruction problem into the process of constructing a neural network that maps input coordinates to sound velocity values. Traditional image representation is usually a set of discrete pixel values, while implicit neural representation parameterizes the image as a continuous function that maps coordinates to the attribute value (i.e., sound velocity value) at that location. This approach enables efficient image storage and high-resolution reconstruction. Furthermore, the use of implicit neural representation networks can introduce regularization terms during network optimization, thereby alleviating the ill-conditioning of full waveform inversion and ensuring the accuracy of ultrasound tomographic sound velocity imaging even without requiring an accurate initial sound velocity model.

[0021] (2) Traditional implicit neural representation networks directly use the spatial coordinates of pixels in the image as the input of the multilayer perceptron. However, this processing method has a weak ability to represent complex signals. Therefore, in this method, the two-dimensional coordinates (x,y) are converted into high-dimensional features through Fourier feature mapping, so as to better learn the high-frequency information in the signal.

[0022] (3) In this invention, n is preferably greater than 1. In this case, the two-dimensional coordinate information of a certain grid in each grid block is mapped through the network and output as the sound velocity distribution information of the grid block. It is not necessary to input the two-dimensional coordinates of all grids in the grid block into the network for mapping, which improves the computational efficiency without sacrificing accuracy. Attached Figure Description

[0023] Figure 1 A flowchart of an ultrasound tomography sound velocity imaging method based on implicit neural representation network provided in an embodiment of the present invention;

[0024] Figure 2 A flowchart of a specific ultrasonic tomographic velocity imaging method provided in an embodiment of the present invention;

[0025] Figure 3 This is a schematic diagram of network input and output provided for an embodiment of the present invention;

[0026] Figure 4 The following are comparison images of sound velocity imaging provided in the embodiments of the present invention, wherein (a) is the ground truth image, (b) is the reconstruction result of the traditional full waveform inversion algorithm, (c) is the reconstruction result of the algorithm proposed in the present invention, (d) is the error diagram between the reconstruction result of the traditional method and the ground truth, and (e) is the error diagram between the reconstruction result of the present invention and the ground truth. Detailed Implementation

[0027] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0028] Example 1

[0029] A method for ultrasound tomography sound velocity imaging based on implicit neural representation networks, such as... Figure 1 As shown, it includes:

[0030] S1. Divide the fault plane imaging region into a grid, and divide all grids into blocks to obtain multiple grid blocks. Determine the two-dimensional coordinates of any grid in each grid block, and convert each two-dimensional coordinate into a high-dimensional feature vector. The size of each grid block is n*n, where n represents the number of grids on any side, and n≥1.

[0031] S2. Input all the transformed high-dimensional feature vectors into the implicit neural representation network, and use the output value as the sound velocity distribution value of the corresponding grid block. Arrange the sound velocity distribution values ​​of each grid block in space according to the distribution of the tomographic plane imaging region, and map the sound velocity distribution value of each grid block in the arrangement result to the actual sound velocity value range through a mapping function to obtain the sound velocity image of the tomographic plane imaging region.

[0032] S3. Perform forward modeling on the sound velocity image to obtain simulated sound field data. With the goal of minimizing the deviation between the sound field data and the actual observed sound field data, optimize the parameters of the implicit neural representation network, and repeat S2 until the preset termination condition is reached. Use the current sound velocity image as the final reconstructed ultrasound tomographic sound velocity image.

[0033] The full waveform inversion algorithm is based on the wave equation, the basic form of which is:

[0034]

[0035] Where f is the sound source term, u is the sound field data, and c is the sound speed, corresponding to the sound speed image to be reconstructed in this embodiment.

[0036] The full waveform inversion problem can be defined as an optimization problem satisfying the above wave equation:

[0037]

[0038] in, The image represents the reconstructed sound velocity, and u(c) represents the sound field data from the prediction model. obs This refers to the actual observed sound field data.

[0039] The optimization problem of full waveform inversion is essentially a nonconvex nonlinear problem constrained by partial differential equations. The algorithm is highly dependent on the initial model (i.e., the initial sound velocity image). Due to the influence of partial differential terms, this problem differs from other traditional medical imaging techniques (such as CT, MRI, and PET). Its nonconvex nonlinear characteristics make the solution process exceptionally complex and unstable. An inappropriate initial model selection may lead to local minima, resulting in sound velocity image reconstructions that do not conform to physiological characteristics. Furthermore, the nonconvexity of the problem intensifies with increasing ultrasound frequency, posing a significant challenge to the solution.

[0040] To address the aforementioned issues, this embodiment employs an implicit neural representation network (structure) to reconstruct sound velocity images. This method transforms the image reconstruction problem into a process of constructing a neural network that maps input coordinates to sound velocity values, and mitigates the ill-conditioning of full waveform inversion by incorporating a regularization term during the optimization process. Traditional image representations typically consist of a set of discrete pixel values, while implicit neural representations parameterize the image as a continuous function that maps coordinates to attribute values ​​(in this case, sound velocity values) at those locations. This approach enables efficient image storage and high-resolution reconstruction.

[0041] Based on this idea, this embodiment proposes using an implicit neural representation network as a generator to generate sound velocity images. This network receives image coordinate information as input and iteratively optimizes by comparing the sound field data calculated (forward modeling) from the sound velocity image output by the implicit neural representation network with the actual observed sound field data. Specifically, the network represents its output signal as a continuous function of two-dimensional coordinates (x, y). This function is represented as f. θ Preferably, the sound velocity image can be parameterized using a multilayer perceptron (MLP) with parameter θ. Represented as:

[0042]

[0043] Unlike traditional full-waveform inversion methods, this method does not directly optimize the sound velocity value, but rather optimizes the parameters within the generator network to effectively reconstruct the problem, thus achieving a parameterized transformation of the full-waveform inversion problem. Preferably, the following definition is used:

[0044]

[0045] Here, (x, y) represents the input spatial coordinates, φ(·) represents the Fourier feature map, and a high-dimensional feature vector φ(x, y) is obtained by performing a series of sine and cosine transformations on the two-dimensional coordinates as the network input to capture more complex features. θ is the network parameter to be optimized, and N θ This is a multilayer perceptron network structure. M is a mapping function that maps the network output to the actual range of sound velocity values. NR is a forward operator that converts the sound velocity distribution image into an ultrasonic signal, thereby enabling comparison with the actual measured signal. The mapping function is used to convert the network output N... θ (φ(x,y)) is mapped to the sound velocity value within a preset range in the region of interest. Assuming the sound velocity in this region is [c1,c2], the mapping function can be defined as follows:

[0046] M1(z)=(c2-c1)z+c1

[0047] M2(z)=(c2-c1) z +c1

[0048] M1 is a linear transformation suitable for tissues with relatively small changes in sound velocity, such as soft tissue regions (e.g., breast tissue); while M2 uses an exponential function for mapping, suitable for regions with significant changes in sound velocity, such as the brain or limbs containing bone (where sound velocity is much higher than the surrounding soft tissue). By applying these transformation operators, the network parameters can be made to converge more easily. In the above equation, z represents the sound velocity distribution value.

[0049] In summary, this invention presents an unsupervised algorithm for ultrasound tomography sound velocity imaging utilizing implicit neural representations. The desired sound velocity image is represented as a continuous function of spatial coordinates, and the original observation signal acquired by the ultrasound tomography system is used as a reference to reconstruct the sound velocity image. Given spatial coordinate values ​​are input, a fully connected neural network is used for parameterization, and the network generates a reconstructed sound velocity image. This image is then processed by a recurrent neural network operator to generate an ultrasound signal. The generated result is compared with the actual observed signal, and the network parameters are iteratively optimized by minimizing a loss function containing data consistency and regularization terms. The goal is to minimize the difference between the ultrasound signal calculated from the network-generated sound velocity image and the actual observed signal, thereby reconstructing a sound velocity image that most closely approximates the actual situation.

[0050] The specific implementation process can be found here. Figure 2 In this system, during signal acquisition (i.e., acoustic field data), the ultrasonic tomography system can consist of an array of ultrasonic transducers surrounding the subject. Data is acquired using a single-transmitter all-in-one mode, with each transmitting element sequentially emitting ultrasonic signals while all elements simultaneously receive the signals. The received signals can be represented by a three-dimensional matrix [N]. s N r [T] indicates that the three dimensions correspond to the transmitting array element, the receiving array element, and the time sampling point, respectively.

[0051] Furthermore, during the simulation, the physical parameters within the region of interest need to be appropriately discretized to obtain the coordinate distribution (image). Considering that the ultrasound tomography system has a fixed sampling frequency, it is equivalent to knowing that the time step Δt is the reciprocal of the sampling frequency. Therefore, the main focus is on the spatial discretization scale, i.e., the image size. To simplify the problem, a square grid is chosen for spatial discretization, meaning the same number of discrete points in both spatial dimensions. The number of discrete points is determined by the system's main transmission frequency, and is based on the stability and dispersion conditions of the finite difference method.

[0052]

[0053]

[0054] Where f represents the main frequency of the emitted sound source, L is the actual spatial size, and N represents the number of spatial discrete points, which also corresponds to the size of the image. In practical applications, under the condition of satisfying the above stability and dispersion conditions, the smallest possible value of N should be selected to reduce computational overhead and improve computational efficiency.

[0055] Furthermore, the main part of the reconstruction algorithm network (i.e., the implicit neural representation network) is a multilayer perceptron, also known as a fully connected neural network. Before utilizing the multilayer perceptron, the coordinate distribution needs to be transformed. Specifically, the two-dimensional coordinates (x, y) are converted into high-dimensional features through Fourier feature mapping. For example, a frequency matrix b that follows a normal distribution with a shape of (2, 200) is first randomly generated, where the two rows of the matrix correspond to the frequency vectors of the x and y coordinates, respectively. The elements in this frequency matrix are used as the frequencies of sine and cosine functions for feature mapping calculation to obtain the corresponding frequency features. Finally, each coordinate is converted into 400 corresponding features as the input layer of the network. Based on the above description, the Fourier feature mapping process can be represented by the following formula:

[0056]

[0057] Where j is the index of the input coordinates, i is the index of the frequency parameter pair, and k corresponds to the index of the Fourier feature, which determines whether to calculate sine or cosine features. The final input feature matrix has dimensions (n, 400), where n is the number of input coordinates, and each row corresponds to a Fourier feature obtained from the coordinate mapping.

[0058] To reduce computational load, this embodiment prioritizes designing the network output as 4×4 image patches. This reduces the number of input coordinates, requiring only one coordinate point in the center region of the image patch to generate the corresponding patch's value. Finally, the image patches are stitched together according to their positional relationships to form a complete sound velocity map. The specific process can be found in [link to documentation]. Figure 3 The mapped feature vectors are input into a multi-layer fully connected neural network, which learns the mapping relationship from these features to the sound speed distribution image through training.

[0059] The loss function, which includes a data consistency term and a regularization term, can be specifically defined as follows:

[0060]

[0061] Among them, Loss DC Loss represents a data consistency item. TV Let λ be the total variational regularization term, and let λ be the coefficient of the regularization term, which is determined experimentally.

[0062] The formula for the data consistency term is:

[0063]

[0064] This loss value is the L2 norm value between the simulated sound field data and the actual observed sound field data, used to measure the error between the two.

[0065] The formula for the total variational regularization term is:

[0066]

[0067] in, and These are the gradient values ​​of the image in the x and y directions, respectively. A total variational regularization term is added to improve the smoothness of the solution, thereby reducing artifacts and noise in the sound velocity image.

[0068] During training, a pre-training process is first performed to map the overall network architecture output to a uniform sound velocity image, where the constant sound velocity is the background sound velocity. This provides the network with a stable initial state, enabling it to converge to the correct solution more quickly. Subsequently, the generator network is trained based on the pre-trained network parameters. The input features are processed by the generator network N. θThe predicted sound velocity image is obtained after mapping function M, and this sound velocity image is input into the feedforward operator network N. R The sound field distribution signal corresponding to the sound velocity distribution is calculated. Then, based on the actual spatial location of the receiving sensor in the ultrasonic tomography system, signals from specific points are extracted from the calculated sound pressure distribution to obtain a set of simulated ultrasonic signal data (predicted sound field data). The loss between the calculated ultrasonic signal and the actual observed signal is used to progressively optimize the network parameters. In this process, a predefined loss function is used to quantify the difference between the two, and the gradient of the loss value with respect to the generator network parameters is calculated using the automatic differentiation technique of the deep learning framework. These gradients are then passed to an optimizer (such as Adam or L-BFGS) to update the network parameters. The network with updated parameters is able to generate a sound velocity image that more closely approximates the actual situation. This process continues iteratively until a predetermined maximum number of iterations is reached or the value of the loss function drops below a preset threshold, completing the training of the generator network.

[0069] according to Figure 4 As shown in the sound velocity imaging comparison images, the algorithm of this invention can reconstruct sound velocity images with higher accuracy. Numerical simulation results are used to illustrate this. Under the same initial sound velocity model conditions, the breast sound velocity image reconstructed by the algorithm of this invention is closer to the real image and can better determine the shape and location of the tumor, with smaller errors compared to the true value. It should be noted that the traditional full-waveform inversion algorithm and the algorithm of this invention use the same number of iterations.

[0070] Example 2

[0071] This application also relates to an electronic device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps of the method described above.

[0072] The electronic device can be a desktop computer, laptop, handheld computer, or cloud server, etc. The processor can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The memory can be used to store computer programs and / or modules. The processor performs various functions of the electronic device by running or executing the computer programs and / or modules stored in the memory, and by accessing data stored in the memory.

[0073] The relevant technical solutions are the same as in Embodiment 1, and will not be repeated here.

[0074] Example 3

[0075] This application also relates to a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method described above.

[0076] Specifically, the memory may include high-speed random access memory, as well as non-volatile memory, such as hard disks, RAM, plug-in hard disks, smart media cards (SMC), secure digital cards (SD), flash cards, at least one disk storage device, flash memory device, or other volatile solid-state storage devices.

[0077] The relevant technical solutions are the same as in Embodiment 1, and will not be repeated here.

[0078] Example 4

[0079] This application provides a computer program product or computer program that includes computer instructions stored in a computer-readable storage medium. A processor of a computer device reads the computer instructions from the computer-readable storage medium and executes the computer instructions, causing the computer device to perform the steps of the method described in the above embodiments of this application.

[0080] The relevant technical solutions are the same as in Embodiment 1, and will not be repeated here.

[0081] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for ultrasound tomography sound velocity imaging based on implicit neural representation networks, characterized in that, An implicit neural representation network is used as a generator to generate sound velocity images. The parameters within the generator network are optimized to effectively reconstruct the problem, achieving a parameterized transformation of the full waveform inversion problem. The method includes: S1. Divide the tomographic imaging region into a grid. The number of discrete grids is determined based on the stability and dispersion conditions of the finite difference method. Divide all grids into blocks, obtaining multiple grid blocks. Determine the two-dimensional coordinates of any grid within each block, and convert each two-dimensional coordinate into a high-dimensional feature vector. The size of each grid block is... , where n represents the number of grid cells on any side. ; S2. Input all the transformed high-dimensional feature vectors into the pre-trained implicit neural representation network, and use the output value as the sound velocity distribution value of the corresponding grid block. Arrange the sound velocity distribution values ​​of each grid block in space according to the distribution of the tomographic plane imaging region, and map the sound velocity distribution value of each grid block in the arrangement result to the actual sound velocity value range through a mapping function to obtain the sound velocity image of the tomographic plane imaging region. S3. Perform forward modeling on the sound velocity image to obtain simulated sound field data. With the goal of minimizing the deviation between the sound field data and the actual observed sound field data, optimize the parameters of the implicit neural representation network, re-execute S2 until the preset termination condition is reached, and use the current sound velocity image as the final reconstructed ultrasound tomography sound velocity image. Specifically, Fourier feature mapping is used to transform each two-dimensional coordinate into a high-dimensional feature vector; by minimizing the loss function that includes data consistency and regularization terms, the deviation between the simulated sound field data and the actual observed sound field data is minimized.

2. The ultrasonic tomographic velocity imaging method based on implicit neural representation networks according to claim 1, characterized in that, The implicit neural representation network is a multilayer perceptron network.

3. The ultrasonic tomographic velocity imaging method based on implicit neural representation networks according to claim 1, characterized in that, n is greater than 1.

4. The ultrasonic tomographic velocity imaging method based on implicit neural representation networks according to claim 1, characterized in that, The forward calculation operation is performed using a recurrent neural network.

5. A method for ultrasound tomography based on implicit neural representation networks according to any one of claims 1 to 4, characterized in that, The pre-trained implicit neural representation network serves as the initial sound velocity model for network training, and it satisfies the following condition: it can output a uniform image of known background sound velocity.

6. An electronic device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method as described in any one of claims 1 to 5.

7. A computer-readable storage medium, characterized in that, The computer-readable storage medium includes a stored computer program, wherein the computer program, when executed by a processor, controls the device on which the storage medium is located to perform the steps of the method as described in any one of claims 1 to 5.

8. A computer program product, comprising a computer program or instructions, characterized in that, When the computer program or instructions are executed by a processor, they implement the steps of the method as described in any one of claims 1 to 5.

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