A method and system for ultrasonic velocity reconstruction based on FNO-GNN

Abstract

This invention discloses an ultrasonic velocity reconstruction method and system based on FNO-GNN. A rectangular phantom module containing low, medium, and high sound velocity regions is fabricated. Multiple phantoms with elliptical internal structures are formed using tissue-equivalent materials with different proportions. RF echo data of the phantoms is acquired in water using a linear array probe, and the sound velocity of each region is independently calibrated. The acquired RF echo data is input into a trained FNO-GNN sound velocity reconstruction network to obtain a reconstructed sound velocity image of the phantom's cross-section. This invention can more effectively improve the sound velocity reconstruction capability in complex tissue scenarios.

Description

Technical Field

[0001] This invention belongs to the field of medical ultrasound imaging and tissue parameter quantification, specifically relating to an ultrasound velocity reconstruction method and system based on FNO-GNN. Background Technology

[0002] Speed ​​of sound (SoS) is one of the key physical quantities characterizing the acoustic properties of soft tissue. Significant differences exist between different tissue types, therefore, high-precision sound velocity imaging is helpful for functions such as tissue classification, lesion detection, and beam focusing correction. Existing ultrasound sound velocity reconstruction methods mainly include time-of-flight (ToF) based tomographic imaging methods and iterative reconstruction methods based on full-wave inversion (FWI).

[0003] Time-of-Flight (ToF) methods are typically based on the ray approximation, measuring arrival times from multiple incident angles or transmission / reception paths and solving the corresponding inverse tomographic problem. However, in cases of complex tissue structures and significant scattering and multipath effects, the ray model struggles to accurately describe the wave propagation path, leading to substantial reconstruction errors. While Frequency-Induced Width (FWI) methods iteratively update the sound velocity distribution directly within the wave equation framework, theoretically achieving high-resolution reconstructions, they require extensive forward and adjoint simulations, resulting in extremely high computational costs. Furthermore, they are highly sensitive to initial model, noise, and measurement errors, limiting their application in routine clinical systems.

[0004] Inspired by the success of deep learning in medical image reconstruction and inverse problem solving, existing research has attempted to use structures such as convolutional neural networks (CNNs) and U-Nets to map time-of-flight maps, B-mode images, or stacked RF data to sound velocity distributions, thereby significantly reducing reconstruction time and automatically learning regularized priors. However, existing learning-based methods still have shortcomings in the following aspects: First, many studies rely on specific anatomical sites and fixed ultrasound acquisition protocols, lacking the ability to systematically evaluate the model's generalization ability to geometry, contrast, and noise conditions in controlled geometric scenarios. Second, traditional CNNs are mainly based on local convolution operations, making it difficult to explicitly encode the physics of long-range wave propagation and the geometric topology of the transmitter-receiver array. Third, the transfer path from pure simulation data to physical phantoms and even real tissue data is still insufficient, resulting in limited verification of the model's sim-to-real generalization performance.

[0005] Therefore, there is an urgent need for a learning-based sound velocity reconstruction method that constructs a large-scale full-wave simulation dataset on a controllable geometric phantom and explicitly integrates wave propagation operators with array geometric priors. This method should be combined with physical phantom experiments to form a complete verification chain from numerical simulation to physical samples, thereby improving the reliability and practical value of the method. Summary of the Invention

[0006] The purpose of this invention is to provide an ultrasonic velocity reconstruction method and system based on FNO-GNN, so as to overcome the shortcomings of existing ultrasonic velocity reconstruction methods in terms of insufficient long-range dependency modeling, insufficient utilization of array element topology relationships, and limited reconstruction accuracy in complex boundary regions.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: An ultrasonic velocity reconstruction method based on FNO-GNN includes the following steps: A rectangular phantom module containing low, medium, and high sound velocity regions was fabricated. Multiple phantoms with elliptical internal structures were formed by using tissue equivalent materials with different ratios. RF echo data of the phantoms were collected in water using a linear array probe, and the sound velocity of the materials in each region was independently calibrated. The collected RF echo data is input into the trained FNO-GNN sound velocity reconstruction network to obtain the sound velocity reconstruction image of the phantom cross section; The FNO-GNN sound speed reconstruction network includes a Fourier neural operator backbone branch and a sensor graph neural network branch. The Fourier neural operator backbone branch and the sensor graph neural network branch are fused at the feature level to output the sound speed reconstruction result. The training of the FNO-GNN sound speed reconstruction network adopts a multi-index loss function, which includes L1 reconstruction loss, gradient constraint loss and smoothing regularization loss, and is formed by weighted summation.

[0008] Furthermore, the method for constructing the FNO-GNN sound speed reconstruction network includes the following steps: A geometric soft tissue phantom was constructed and full-wave simulation was performed to obtain multi-channel RF echo data corresponding to each sound velocity distribution. The RF echo data and sound velocity distribution obtained from the simulation are preprocessed to obtain the preprocessed RF echo data tensor and label image; The FNO-GNN sound velocity reconstruction network is constructed based on the preprocessed RF echo data tensor.

[0009] Furthermore, the construction of the geometric soft tissue phantom and the performance of full-wave simulation to obtain multi-channel RF echo data corresponding to each sound velocity distribution are specifically as follows: Based on a 2D 512×512 pixel geometric phantom image, multiple non-overlapping elliptical soft tissue masses are randomly generated in a water background. Different ranges of sound velocity and density values ​​are assigned to different color regions to obtain sound velocity distributions. The above process is repeated to obtain several sound velocity distributions. Using the k-Wave toolbox, under given probe parameters, mesh generation, time step, and excitation pulse conditions, full-wave acoustic field simulation is performed to obtain multi-channel RF echo data corresponding to each sound velocity distribution.

[0010] Furthermore, the preprocessing of the simulated RF echo data to obtain the preprocessed RF echo data tensor is specifically as follows: The RF echo data is uniformly interpolated to T_align sampling points in the time dimension and aligned to the number of array elements S_align in the channel dimension. The amplitude is normalized to obtain the preprocessed RF echo data tensor. The sound velocity distribution is resampled to a fixed output resolution H_out×W_out and linearly normalized according to the global sound velocity range to obtain the label image. Here, T_align represents the number of sampling points after time alignment, S_align represents the number of array elements after channel alignment, and H_out and W_out represent the height and width of the output sound velocity image, respectively.

[0011] Furthermore, the Fourier neural operator backbone includes a one-dimensional convolution or 1×1 convolution layer and several spectral convolution modules. The Fourier neural operator backbone takes a preprocessed RF echo data tensor as input. The preprocessed RF echo data tensor is unified to T_align sampling points in the time dimension and to the number of channels S_align in the array element dimension, arranged into a two-dimensional data plane of size 1×T_align×S_align. First, the input is mapped to a feature representation with C feature channels through a one-dimensional convolution or 1×1 convolution layer, and then several spectral convolution modules are concatenated; where C represents the number of feature channels of the backbone.

[0012] Furthermore, each spectral convolution module performs the following process: 1) Perform a two-dimensional fast Fourier transform on the feature tensors entering the spectral convolution module in the time-element plane to obtain the frequency domain representation; 2) Learnable linear transformation weights are applied to a finite number of Fourier modes in the frequency domain representation of low and mid frequencies to model long-range correlations and obtain low-frequency and mid-frequency data. 3) The low-frequency and mid-frequency data are restored to the spatial domain through two-dimensional inverse fast Fourier transform, and then added to a 1×1 convolution branch to form a residual connection. After passing through a nonlinear activation function, the frequency domain features are obtained.

[0013] Furthermore, the sensor graph neural network branch takes the spatial coordinates of the array elements as input, treating each array element as a node in the graph; the one-dimensional or two-dimensional coordinates of the array elements in the probe coordinate system are mapped to d-dimensional initial node features after linear transformation and nonlinear activation; a k-nearest neighbor graph is constructed based on the array element index or actual geometric distance as an adjacency relationship, and several layers of graph convolution or message passing operations are performed on each node to obtain the node embedding vector corresponding to each array element; where d represents the initial node feature dimension and k represents the number of nearest neighbor nodes; The node embeddings output by the graph neural network branch are arranged into a matrix of size d_out×S_align according to the element dimension, and are copied or broadcast in the time dimension to T_align sampling points, making it a spatial feature of size d_out×T_align×S_align; then the spatial feature is concatenated with the frequency domain feature of the Fourier neural operator backbone in the channel dimension to form a fused feature, where d_out represents the node embedding dimension of the graph neural network branch output.

[0014] Furthermore, the FNO-GNN sound speed reconstruction network also includes a two-dimensional decoding sub-network. After feature fusion, through several layers of two-dimensional convolution, activation functions, and upsampling or interpolation operations, the fused features are mapped from the T_align×S_align plane to a preset output resolution H_out×W_out. At the end, a 1×1 convolution is used to compress the number of channels to 1 channel, resulting in a normalized sound speed image. Finally, the normalized sound speed image is restricted to the [0,1] interval by a sigmoid or similar monotonic nonlinear function, and then linear inverse normalization is performed according to the global lower limit c_lo and upper limit c_hi to restore the sound speed distribution in physical units of m / s; where c_lo represents the lower limit of sound speed and c_hi represents the upper limit of sound speed.

[0015] Furthermore, the multi-index loss function is expressed as follows: L = λ1L1 + λ2L grad + λ3L smooth In the formula, L represents the multi-index loss function; L1 represents the L1 reconstruction loss; L grad L represents the gradient constraint loss; smooth λ1, λ2, and λ3 represent the weight coefficients corresponding to the L1 reconstruction loss, gradient constraint loss, and smoothing regularization loss, respectively. The L1 reconstruction loss is expressed as:

[0016] In the formula, H and W represent the height and width of the output sound velocity image, respectively; i and j represent the row index and column index in the image, respectively; This represents the physical sound velocity value at coordinate (i,j) of the predicted sound velocity map; This represents the physical speed of sound at coordinates (i,j) on the label's sound velocity map. Define the first-order difference operators in the horizontal and vertical directions as follows:

[0017]

[0018] In the formula, z represents the two-dimensional image whose difference is to be calculated; This represents the first-order difference operator in the horizontal direction; This represents the first-order difference operator in the vertical direction; The gradient constraint loss is then expressed as:

[0019] In the formula, and These represent the horizontal and vertical gradients of the predicted sound velocity map at coordinates (i,j), respectively. and These represent the horizontal and vertical gradients of the label's sound velocity map at coordinates (i,j), respectively. The smoothing regularization loss is expressed as:

[0020] In the formula, L smooth This is used to constrain the local variation amplitude of the predicted sound velocity map, in order to suppress local high-frequency oscillations and stripe artifacts, making the predicted sound velocity map more spatially smooth and continuous.

[0021] An ultrasonic velocity reconstruction system based on FNO-GNN includes: The first module is used to prepare rectangular phantom modules containing low, medium and high sound velocity regions. Multiple phantoms with elliptical internal structures are formed by using tissue equivalent materials with different ratios. RF echo data of the phantoms are collected in water using a linear array probe, and the sound velocity of the materials in each region is calibrated independently. The second module is used to input the acquired RF echo data into the trained FNO-GNN sound velocity reconstruction network to obtain the sound velocity reconstruction image of the phantom cross-section. The FNO-GNN sound speed reconstruction network includes a Fourier neural operator backbone branch and a sensor graph neural network branch. The Fourier neural operator backbone branch and the sensor graph neural network branch are fused at the feature level to output the sound speed reconstruction result. The training of the FNO-GNN sound speed reconstruction network adopts a multi-index loss function, which includes L1 reconstruction loss, gradient constraint loss and smoothing regularization loss, and is formed by weighted summation.

[0022] Compared with the prior art, the present invention has the following beneficial technical effects: This invention introduces both a Fourier neural operator backbone branch and a sensor graph neural network branch into the sound velocity reconstruction network. The former is used to model the long-range correlation of RF data in the time-element plane, while the latter is used to encode the topological relationship between elements. This balances global propagation priors and local element associations, and compared with network structures that rely solely on local convolutions, it can more effectively improve the sound velocity reconstruction capability in complex organizational scenarios.

[0023] This invention employs a multi-index loss function consisting of L1 reconstruction loss, gradient constraint loss, and smoothing regularization loss. While ensuring the overall numerical approximation capability, it enhances the constraint on boundary changes and local structures, and suppresses local oscillations and artifacts in the reconstruction results, thereby improving the boundary preservation capability and spatial continuity of the reconstructed image.

[0024] This invention was validated on an independent test set generated by full-wave simulation. Experimental results show that the method achieved MAE_all of 16.13 m / s, MAE_roi of 23.78 m / s, MAE_bg of 6.37 m / s, MAE_inner of 18.32 m / s, and MAE_boundary of 121.00 m / s on the test set, indicating that this invention can stably achieve end-to-end reconstruction of RF data into a two-dimensional sound velocity distribution image. Attached Figure Description

[0025] The accompanying drawings are provided to further understand the invention and constitute a part of this invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0026] Figure 1 is a schematic diagram of the overall structure of the ultrasonic velocity reconstruction system of the present invention; Figure 2a is a schematic diagram of the numerical geometry soft tissue phantom of the present invention; Figure 2b is a schematic diagram of the sound velocity distribution corresponding to the geometric soft tissue phantom; Figure 3 is a schematic diagram of the sound velocity reconstruction network structure based on FNO-GNN of the present invention; Figure 4 is a schematic flowchart of the ultrasonic velocity reconstruction method of the present invention; Figure 5a is a statistical chart of the main quantitative indicators of the test set of this invention; Figure 5b is a statistical graph of the mean absolute error of the region of interest in the test set of this invention; Figure 5c is a statistical graph of the mean absolute error between the background region and the interior region of the test set of the present invention; Figure 5d is a statistical graph of the mean absolute error of the boundary region of the test set of the present invention; Figure 6 is a comparison of the true sound velocity, prediction results, and error of a typical test sample of the present invention. Figure 7 is a comparison of the true sound velocity, prediction results, and error of the difficult test sample of the present invention. Detailed Implementation

[0027] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0028] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0029] Example 1 like Figure 1 , Figures 2a-2b ,as well as Figure 3 and Figure 4This embodiment provides an ultrasound velocity reconstruction method based on FNO-GNN. A rectangular phantom module containing low, medium, and high sound velocity regions is prepared. Each rectangular phantom module can be further cut into several elliptical structures to simulate different soft tissue masses. By changing the ratio of tissue-equivalent materials (e.g., hydrogel, gelatin, agar, glycerol mixture, and silica gel), material blocks within a predetermined sound velocity range are obtained, and RF echo data are acquired in a water bath using a linear array probe. Subsequently, the sound velocity of each material is independently calibrated. The acquired phantom RF echo data is input into an FNO-GNN sound velocity reconstruction network trained with numerical phantoms to obtain a sound velocity reconstruction image of the phantom cross-section. This image is then compared with the calibrated sound velocity to verify the effectiveness and sim-to-real generalization ability of the method.

[0030] The FNO-GNN sound speed reconstruction network includes a Fourier neural operator backbone branch and a sensor graph neural network branch. The Fourier neural operator backbone branch and the sensor graph neural network branch are fused at the feature level to output the sound speed reconstruction result. Furthermore, the training of the FNO-GNN sound speed reconstruction network adopts a multi-index loss function, which includes L1 reconstruction loss, gradient constraint loss and smoothing regularization loss, and is formed by weighted summation.

[0031] The construction method of the FNO-GNN sound speed reconstruction network includes the following steps: First, a two-dimensional geometric soft tissue phantom is constructed. Preferably, within a two-dimensional 512×512 pixel geometric field of view, using water as the background medium, multiple non-overlapping elliptical soft tissue blocks are randomly generated, and corresponding sound velocity and density value ranges are assigned to different regions to obtain sound velocity and density distributions. Then, under given probe array element number, center frequency, mesh division, time step, and excitation pulse conditions, the above medium model is simulated using the k-Wave toolbox to obtain multi-channel RF echo data corresponding to each sound velocity distribution.

[0032] The RF echo data is interpolated to T_align sampling points in the time dimension and aligned to the number of array elements S_align in the channel dimension, while amplitude normalization is performed to obtain preprocessed RF echo data. The sound velocity distribution is resampled to a fixed output resolution H_out×W_out and linearly normalized according to the global sound velocity range to obtain the label image. Here, T_align represents the number of sampling points after time alignment, S_align represents the number of array element channels, and H_out and W_out represent the height and width of the output sound velocity image, respectively.

[0033] The FNO-GNN sound velocity reconstruction network comprises a Fourier neural operator backbone branch and a sensor graph neural network branch. The Fourier neural operator backbone branch takes an RF echo data tensor of size 1×T_align×S_align as input. After mapping the input to a feature channel of width C through an input mapping layer, several spectral convolutional modules are concatenated. Each spectral convolutional module first performs a two-dimensional fast Fourier transform on the feature tensor to obtain a frequency domain representation. Learnable linear transformation weights are applied to a finite number of Fourier modes in the low and mid-frequency domains of the frequency domain representation to model long-range correlations, obtaining low-frequency and mid-frequency data. The low-frequency and mid-frequency data are then returned to the spatial domain through a two-dimensional inverse fast Fourier transform and added to a 1×1 convolutional branch to form a residual connection. Finally, after passing through a nonlinear activation function, the frequency domain features are obtained.

[0034] The sensor graph neural network branch takes the element position coordinates as input, treating each element as a node in the graph. Preferably, the element coordinates are mapped to d-dimensional initial node features after linear transformation and nonlinear activation, and a k-nearest neighbor graph is constructed based on the element index or actual geometric distance. Several layers of graph convolution or message passing operations are performed on each node to obtain the node embeddings corresponding to each element. The node embeddings output by the graph neural network branch are then arranged into a matrix of size d_out × S_align according to the element dimension, and copied or broadcast in the time dimension to T_align sampling points to obtain spatial features of size d_out × T_align × S_align. Subsequently, the spatial features are concatenated with the frequency domain features output by the Fourier neural operator backbone branch in the channel dimension to obtain fused features.

[0035] The FNO-GNN sound velocity reconstruction network also includes a two-dimensional decoding sub-network. After feature fusion, the two-dimensional decoding sub-network maps the fused features from a T_align×S_align plane to a preset output resolution H_out×W_out, where H_out and W_out represent the height and width of the output sound velocity image, respectively. At the end, a 1×1 convolution is used to compress the number of channels to 1, resulting in a normalized sound velocity image. Finally, the normalized sound velocity image is constrained to the [0,1] interval using a sigmoid monotonic nonlinear function, and then linearly denormalized according to the global lower limit c_lo and upper limit c_hi to restore the sound velocity distribution in physical units of m / s. Here, c_lo represents the lower limit of the sound velocity, and c_hi represents the upper limit of the sound velocity.

[0036] Furthermore, the training method of the FNO-GNN sound speed reconstruction network is explained. During the training phase, a multi-index loss function is used to optimize the network. This multi-index loss function includes L1 reconstruction loss, gradient constraint loss, and smoothing regularization loss, expressed as follows: L = λ1L1 + λ2L grad + λ3L smooth .

[0037] In the formula, L represents the multi-index loss function; L1 represents the L1 reconstruction loss; L grad L represents the gradient constraint loss; smooth λ1 represents the smoothing regularization loss; λ2 and λ3 represent the weighting coefficients of the three loss terms, respectively.

[0038] L1 reconstruction loss is expressed as:

[0039] In the formula, H and W represent the height and width of the output sound velocity image, respectively; i and j represent the row index and column index in the pixel coordinates, respectively; This represents the physical sound velocity value at coordinate (i,j) of the predicted sound velocity map; This represents the physical sound velocity value at coordinate (i,j) on the label sound velocity map.

[0040] Define the first-order difference operators in the horizontal and vertical directions as follows:

[0041]

[0042] In the formula, z represents the two-dimensional image whose difference is to be calculated; This represents the first-order difference operator in the horizontal direction; This represents the first-order difference operator in the vertical direction.

[0043] The gradient constraint loss is expressed as:

[0044] In the formula, and These represent the horizontal and vertical gradients of the predicted sound velocity map at coordinates (i,j), respectively. and These represent the horizontal and vertical gradients of the label sound velocity map at coordinates (i,j), respectively. The gradient-constrained loss is used to enhance the model's sensitivity to boundary changes and differences in local structure.

[0045] The smoothing regularization loss is expressed as:

[0046] In the formula, L smooth It is used to suppress local high-frequency oscillations and stripe artifacts in the predicted sound velocity map, making the predicted sound velocity map more spatially smooth and continuous.

[0047] Example 2 This embodiment illustrates the simulation verification results. Based on full-wave simulation, a total of 10448 pairs of RF-velocity of sound samples were constructed, including 7314 training sets, 1045 validation sets, and 2089 test sets. The RF inputs were uniformly formatted as 1×2048×128 tensors, and the output velocity of sound maps were uniformly resampled to 1×256×256. The AdamW optimizer was used during the training phase, with a learning rate set to 2×10⁻⁶. -4 The weight decay is set to 1×10. -4 The batch size is 8, and the total number of training rounds is 180.

[0048] As shown in Figure 5a to Figure 5d As shown, on the independent test set, the method of this invention achieved MAE_all of 16.13 m / s, MAE_roi of 23.78 m / s, MAE_bg of 6.37 m / s, MAE_inner of 18.32 m / s, and MAE_boundary of 121.00 m / s. MAE_all represents the mean absolute error over the entire sound velocity image; MAE_roi represents the mean absolute error within the region of interest; MAE_bg represents the mean absolute error within the background region; MAE_inner represents the mean absolute error within the inner region of the target region; and MAE_boundary represents the mean absolute error within the boundary band of the target region. All these indicators are in m / s, and a smaller value indicates a higher consistency between the reconstructed sound velocity and the true value. Therefore, the method of this invention can reconstruct the numerical distribution and overall structure of the main region relatively stably. The background region error is low, while the boundary band error is relatively high, indicating that the boundary region and high-gradient transition region remain the main challenges in sound velocity reconstruction.

[0049] As shown in Figure 6, for typical test samples, the method of the present invention can accurately recover the position, main outline and overall hierarchical relationship of the main hypersonic region. The error is mainly concentrated at the local boundary position, indicating that the method of the present invention has a good ability to recover the main structure.

[0050] As shown in Figure 7, for difficult test samples, the method of the present invention can still identify the approximate location of the high-velocity region, but large errors still occur in complex contours, internal concave structures, and boundary transition regions, indicating that complex geometric structures and strong contrast boundaries are important factors affecting the reconstruction accuracy.

[0051] Example 3 An ultrasonic velocity reconstruction system based on FNO-GNN, reference Figure 1 ,include: The first module is used to prepare rectangular phantom modules containing low, medium and high sound velocity regions. Multiple phantoms with elliptical internal structures are formed by using tissue equivalent materials with different ratios. RF echo data of the phantoms are collected in water using a linear array probe, and the sound velocity of the materials in each region is calibrated independently. The second module is used to input the acquired RF echo data into the trained FNO-GNN sound velocity reconstruction network to obtain the sound velocity reconstruction image of the phantom cross-section. The FNO-GNN sound speed reconstruction network includes a Fourier neural operator backbone branch and a sensor graph neural network branch. The Fourier neural operator backbone branch and the sensor graph neural network branch are fused at the feature level to output the sound speed reconstruction result. The training of the FNO-GNN sound speed reconstruction network adopts a multi-index loss function, which includes L1 reconstruction loss, gradient constraint loss and smoothing regularization loss, and is formed by weighted summation.

[0052] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0053] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0054] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0055] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0056] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit its scope of protection. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that after reading the present invention, they can still make various changes, modifications or equivalent substitutions to the specific implementation of the invention, but these changes, modifications or equivalent substitutions are all within the scope of protection of the pending claims of the invention.

Claims

1. A method for reconstructing ultrasonic velocity based on FNO-GNN, characterized in that, Includes the following steps: A rectangular phantom module containing low, medium, and high sound velocity regions was fabricated. Multiple phantoms with elliptical internal structures were formed by using tissue equivalent materials with different ratios. RF echo data of the phantoms were collected in water using a linear array probe, and the sound velocity of the materials in each region was independently calibrated. The collected RF echo data is input into the trained FNO-GNN sound velocity reconstruction network to obtain the sound velocity reconstruction image of the phantom cross section; The FNO-GNN sound speed reconstruction network includes a Fourier neural operator backbone branch and a sensor graph neural network branch. The Fourier neural operator backbone branch and the sensor graph neural network branch are fused at the feature level to output the sound speed reconstruction result. The training of the FNO-GNN sound velocity reconstruction network adopts a multi-index loss function, which includes L1 reconstruction loss, gradient constraint loss and smoothing regularization loss, and is formed by weighted summation.

2. The ultrasonic velocity reconstruction method based on FNO-GNN according to claim 1, characterized in that, The method for constructing the FNO-GNN sound velocity reconstruction network includes the following steps: A geometric soft tissue phantom was constructed and full-wave simulation was performed to obtain multi-channel RF echo data corresponding to each sound velocity distribution. The RF echo data and sound velocity distribution obtained from the simulation are preprocessed to obtain the preprocessed RF echo data tensor and label image; The FNO-GNN sound velocity reconstruction network is constructed based on the preprocessed RF echo data tensor.

3. The ultrasonic velocity reconstruction method based on FNO-GNN according to claim 2, characterized in that, The process of constructing a geometric soft tissue phantom and performing full-wave simulation yields multi-channel RF echo data corresponding to each sound velocity distribution, specifically as follows: Based on a 2D 512×512 pixel geometric phantom image, multiple non-overlapping elliptical soft tissue masses are randomly generated in a water background. Different ranges of sound velocity and density values ​​are assigned to different color regions to obtain sound velocity distributions. The above process is repeated to obtain several sound velocity distributions. Using the k-Wave toolbox, under given probe parameters, mesh generation, time step, and excitation pulse conditions, full-wave acoustic field simulation is performed to obtain multi-channel RF echo data corresponding to each sound velocity distribution.

4. The ultrasonic velocity reconstruction method based on FNO-GNN according to claim 2, characterized in that, The preprocessing of the simulated RF echo data to obtain the preprocessed RF echo data tensor is specifically as follows: The RF echo data is uniformly interpolated to T_align sampling points in the time dimension and aligned to the number of array elements S_align in the channel dimension. The amplitude is normalized to obtain the preprocessed RF echo data tensor. The sound velocity distribution is resampled to a fixed output resolution H_out×W_out and linearly normalized according to the global sound velocity range to obtain the label image. Here, T_align represents the number of sampling points after time alignment, S_align represents the number of array elements after channel alignment, and H_out and W_out represent the height and width of the output sound velocity image, respectively.

5. The ultrasonic velocity reconstruction method based on FNO-GNN according to claim 2, characterized in that, The Fourier neural operator backbone includes a one-dimensional convolution or 1×1 convolution layer and several spectral convolution modules. The Fourier neural operator backbone takes a preprocessed RF echo data tensor as input. The preprocessed RF echo data tensor is unified to T_align sampling points in the time dimension and to the number of channels S_align in the element dimension, arranged into a two-dimensional data plane of size 1×T_align×S_align. First, the input is mapped to a feature representation with C feature channels through a one-dimensional convolution or 1×1 convolution layer, and then several spectral convolution modules are concatenated; where C represents the number of feature channels of the backbone.

6. The ultrasonic velocity reconstruction method based on FNO-GNN according to claim 5, characterized in that, Each spectral convolution module performs the following process: 1) Perform a two-dimensional fast Fourier transform on the feature tensors entering the spectral convolution module in the time-element plane to obtain the frequency domain representation; 2) Learnable linear transformation weights are applied to a finite number of Fourier modes in the frequency domain representation of low and mid frequencies to model long-range correlations and obtain low-frequency and mid-frequency data. 3) The low-frequency and mid-frequency data are restored to the spatial domain through two-dimensional inverse fast Fourier transform, and then added to a 1×1 convolution branch to form a residual connection. After passing through a nonlinear activation function, the frequency domain features are obtained.

7. The ultrasonic velocity reconstruction method based on FNO-GNN according to claim 5, characterized in that, The sensor graph neural network branch takes the spatial coordinates of the array elements as input, and regards each array element as a node in the graph; the one-dimensional or two-dimensional coordinates of the array elements in the probe coordinate system are mapped to d-dimensional initial node features after linear transformation and nonlinear activation; A k-nearest neighbor graph is constructed based on the element index or the actual geometric distance as the adjacency relationship. Several layers of graph convolution or message passing operations are performed on each node to obtain the node embedding vector corresponding to each element; where d represents the initial node feature dimension and k represents the number of nearest neighbor nodes. The node embeddings output by the graph neural network branch are arranged into a matrix of size d_out×S_align according to the element dimension, and are copied or broadcast in the time dimension to T_align sampling points, making it a spatial feature of size d_out×T_align×S_align; then the spatial feature is concatenated with the frequency domain feature of the Fourier neural operator backbone in the channel dimension to form a fused feature, where d_out represents the node embedding dimension of the graph neural network branch output.

8. The ultrasonic velocity reconstruction method based on FNO-GNN according to claim 7, characterized in that, The FNO-GNN sound speed reconstruction network also includes a two-dimensional decoding sub-network. After feature fusion, the fused features are mapped from the T_align×S_align plane to a preset output resolution H_out×W_out through several layers of two-dimensional convolution, activation functions, and upsampling or interpolation operations. At the end, a 1×1 convolution is used to compress the number of channels to 1 channel to obtain a normalized sound speed image. Finally, the normalized sound speed image is restricted to the [0,1] interval by a sigmoid or similar monotonic nonlinear function, and then linear inverse normalization is performed according to the global lower limit c_lo and upper limit c_hi to restore the sound speed distribution in physical units of m / s. Here, c_lo represents the lower limit of sound speed and c_hi represents the upper limit of sound speed.

9. The ultrasonic velocity reconstruction method based on FNO-GNN according to claim 1, characterized in that, The multi-index loss function is expressed as follows: L = λ1L1+ λ2L grad + λ3L smooth In the formula, L represents the multi-index loss function; L1 represents the L1 reconstruction loss; L grad L represents the gradient constraint loss; smooth λ1, λ2, and λ3 represent the weight coefficients corresponding to the L1 reconstruction loss, gradient constraint loss, and smoothing regularization loss, respectively. The L1 reconstruction loss is expressed as: In the formula, H and W represent the height and width of the output sound velocity image, respectively; i and j represent the row index and column index in the image, respectively; This represents the physical sound velocity value at coordinate (i,j) of the predicted sound velocity map; This represents the physical speed of sound at coordinates (i,j) on the label's sound velocity map. Define the first-order difference operators in the horizontal and vertical directions as follows: In the formula, z represents the two-dimensional image whose difference is to be calculated; This represents the first-order difference operator in the horizontal direction; This represents the first-order difference operator in the vertical direction; The gradient constraint loss is then expressed as: In the formula, and These represent the horizontal and vertical gradients of the predicted sound velocity map at coordinates (i,j), respectively. and These represent the horizontal and vertical gradients of the label's sound velocity map at coordinates (i,j), respectively. The smoothing regularization loss is expressed as: In the formula, L smooth This is used to constrain the local variation amplitude of the predicted sound velocity map, in order to suppress local high-frequency oscillations and stripe artifacts, making the predicted sound velocity map more spatially smooth and continuous.

10. An ultrasonic velocity reconstruction system based on FNO-GNN, characterized in that, include: The first module is used to prepare rectangular phantom modules containing low, medium and high sound velocity regions. Multiple phantoms with elliptical internal structures are formed by using tissue equivalent materials with different ratios. RF echo data of the phantoms are collected in water using a linear array probe, and the sound velocity of the materials in each region is calibrated independently. The second module is used to input the acquired RF echo data into the trained FNO-GNN sound velocity reconstruction network to obtain the sound velocity reconstruction image of the phantom cross-section. The FNO-GNN sound speed reconstruction network includes a Fourier neural operator backbone branch and a sensor graph neural network branch. The Fourier neural operator backbone branch and the sensor graph neural network branch are fused at the feature level to output the sound speed reconstruction result. The training of the FNO-GNN sound velocity reconstruction network adopts a multi-index loss function, which includes L1 reconstruction loss, gradient constraint loss and smoothing regularization loss, and is formed by weighted summation.

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