Data reconstruction method based on radon domain sparse representation and related device

Abstract

The present disclosure provides a data reconstruction method based on Radon domain sparse representation and related equipment, relating to the technical field of communication. The method comprises: obtaining low-resolution Radon coefficients; inputting the low-resolution Radon coefficients into a neural network of an encoding-decoding structure to obtain first high-resolution Radon coefficients; and increasing the sparsity of the first high-resolution Radon coefficients through an adaptive soft threshold function cascaded at the back end of the neural network to obtain second high-resolution Radon coefficients. The method can reduce the data size, operation time, and operation cost of time-domain inversion of reduced-time variable Radon transform, and improve the stability and resolution of reconstructed data.

Description

Technical Field

[0001] This disclosure relates to the field of communication technology, and in particular to a data reconstruction method, apparatus, computer-readable storage medium, and electronic device based on the sparse representation of the Ladon domain. Background Technology

[0002] With the rapid development of modern technology, the types and amounts of data generated in networks have increased dramatically, increasing the difficulty of data processing for network operators. Furthermore, low-resolution data is insufficient for training high-accuracy algorithm models. High-resolution data, on the other hand, has a high pixel density, provides clear and rich detail, and contains many high-frequency components, meeting the needs of researchers for post-processing and practical applications. Data super-resolution reconstruction is the process of generating high-resolution data of the same scene from low-resolution data, and is widely used in data preprocessing and extracting feature information from knowledge graphs. The process of obtaining physical parameters from observation data is called inversion. Inversion problems are usually ill-posed; only by constraining the inversion can a relatively accurate and stable solution be obtained. Sparse inversion has proven to be an important tool for low-resolution data processing. Low-resolution data can be represented by a few coefficients in an appropriate transform domain, and sparse data in the transform domain is highly beneficial for operations such as denoising, separation, and high-resolution reconstruction. Radon inversion, as one of the important methods of data image processing, provides a guarantee for super-resolution reconstruction of data images.

[0003] In terms of its applications, the Radon transform faces two major problems:

[0004] Firstly, the computational efficiency is low. Inversion using a large amount of complex data involves the construction of large operator matrices and eigenvectors, which is time-consuming and costly. Secondly, the resolution is difficult to meet the requirements. Poor quality of real data and low pixel density will lead to low-resolution inversion results, which can only be compensated for by improving the algorithm.

[0005] It should be noted that the information disclosed in the background section above is only used to enhance the understanding of the background of this disclosure, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0006] The purpose of this disclosure is to provide a data reconstruction method, apparatus, computer-readable storage medium, and electronic device based on the sparse representation of the Radon domain, so as to at least solve the technical problems in the related art such as the excessively large size of the time-domain inversion matrix of the time-varying Radon transform, the long operation time, the high cost, and the instability and low resolution of the convolution operator inversion.

[0007] Other features and advantages of this disclosure will become apparent from the following detailed description, or may be learned in part from practice of this disclosure.

[0008] The technical solution disclosed herein is as follows:

[0009] According to one aspect of this disclosure, a data reconstruction method based on sparse representation of the Radon domain is provided. The method includes: obtaining low-resolution Radon coefficients; inputting the low-resolution Radon coefficients into a neural network with an encoder-decoder structure to obtain a first high-resolution Radon coefficient; and increasing the sparsity of the first high-resolution Radon coefficient through an adaptive soft thresholding function cascaded after the neural network to obtain a second high-resolution Radon coefficient.

[0010] In some embodiments of this disclosure, the step of inputting low-resolution Radon coefficients into a neural network with an encoder-decoder structure to obtain first high-resolution Radon coefficients includes: downsampling the low-resolution Radon coefficients through an encoder convolutional layer in the neural network to obtain encoded data; and upsampling the encoded data through a decoder convolutional layer in the neural network to obtain decoded data, and fusing the encoded data obtained during the downsampling process to obtain the first high-resolution Radon coefficients.

[0011] In some embodiments of this disclosure, the step of obtaining low-resolution Radon coefficients includes, prior to: sequentially inputting a training dataset into the neural network and the adaptive soft thresholding function to obtain predicted transform domain coefficients; calculating a loss value for the predicted transform domain coefficients; and updating the adaptive soft thresholding function based on the loss value using gradient.

[0012] In some embodiments of this disclosure, a training dataset is constructed using conjugate solutions and corresponding least squares solutions, wherein the conjugate solutions serve as model inputs and the least squares solutions serve as labels.

[0013] In some embodiments of this disclosure, the loss function for calculating the loss value of the predicted transform domain coefficients is expressed as formula (3).

[0014] In some embodiments of this disclosure, the adaptive soft threshold function AdST is expressed as Equation (4).

[0015] In some embodiments of this disclosure, the gradient update of the adaptive soft threshold function based on the loss value is calculated using formulas (5) and (6).

[0016] According to another aspect of this disclosure, a data reconstruction apparatus based on sparse representation of a Radon domain is provided. The apparatus includes: an input module for acquiring low-resolution Radon coefficients; an encoding / decoding module for obtaining first high-resolution Radon coefficients from the low-resolution Radon coefficients through a neural network with an encoding-decoding structure; and a sparsity module for increasing the sparsity of the first high-resolution Radon coefficients through an adaptive soft threshold function cascaded after the neural network to obtain second high-resolution Radon coefficients.

[0017] According to another aspect of this disclosure, an electronic device is provided, comprising: a processor; and a memory for storing executable instructions of the processor; wherein the processor is configured to perform the above-described data reconstruction method based on Ladon domain sparse representation by executing the executable instructions.

[0018] According to another aspect of this disclosure, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the above-described data reconstruction method based on sparse representation of Ladon domains.

[0019] In this disclosure, the encoding-decoding structure discards redundant data during the compression process before decompression, ensuring the spatiotemporal signal-to-noise ratio of the data, while simultaneously reducing the data size, improving the efficiency of reconstruction operations, and reducing computational costs.

[0020] Furthermore, by introducing sparsity constraints, the convergence of the inverted Radon coefficients is improved, and the coefficients have a stronger fitting ability. Therefore, when the Radon coefficients are forward modeled back to the spatiotemporal domain, there are fewer artifacts, a higher signal-to-noise ratio, and the reconstructed Radon coefficients have higher resolution.

[0021] Furthermore, a cascaded encoder-decoder structure and adaptive soft thresholding function are used to alter the distribution of the Radon coefficients, achieving sparse inversion. The adaptive soft thresholding function, based on the encoder-decoder structure, leverages the complex nonlinear representation capabilities of neural networks to accelerate the inversion process and improve the stability of the reconstructed data.

[0022] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and are not intended to limit this disclosure. Attached Figure Description

[0023] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this disclosure and, together with the description, serve to explain the principles of this disclosure. It is obvious that the drawings described below are merely some embodiments of this disclosure, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort.

[0024] Figure 1 The diagram illustrates a data reconstruction method based on sparse representation of a Ladon domain, according to an embodiment of this disclosure.

[0025] Figure 2 A simplified schematic diagram of a neural network with an encoder-decoder structure according to an embodiment of the present disclosure is shown.

[0026] Figure 3 This diagram illustrates a process for obtaining a first high-resolution Radon coefficient through an encoding-decoding structure in an embodiment of this disclosure.

[0027] Figure 4 The diagram shows a flowchart of an adaptive soft threshold function update method according to an embodiment of the present disclosure.

[0028] Figure 5 This diagram illustrates the training process of a neural network with an encoder-decoder structure and an adaptive soft threshold, according to an embodiment of this disclosure.

[0029] Figure 6 A schematic diagram of an adaptive soft threshold function is shown in an embodiment of this disclosure.

[0030] Figure 7 The diagram shows a structural schematic of a Fast Sparse Hyperbolic Radon Transform (FSHRT) model according to an embodiment of this disclosure.

[0031] Figure 8 This diagram illustrates the trend of the loss function value during the training process of the FSHRT model in this embodiment of the present disclosure.

[0032] Figure 9 The diagram illustrates a comparison of sparsity between the Radon coefficients (a) and (b) obtained by the Preconditioned conjugate gradient (PCG) algorithm and the Radon coefficients (c) and (d) obtained by the Fast Sparse Hyperbolic Radon Transform model in this embodiment.

[0033] Figure 10 This diagram illustrates a comparison of the fitting effects of the Radon coefficients obtained by the PCG algorithm and the FSHRT model in both the time intercept and velocity parameters.

[0034] Figure 11 This diagram illustrates the structure of a data reconstruction apparatus based on sparse representation of a Radon domain, according to an embodiment of the present disclosure.

[0035] Figure 12 A schematic block diagram of an electronic device is shown, illustrating a data reconstruction method based on sparse representation of a Radon domain according to an embodiment of this disclosure. Detailed Implementation

[0036] Exemplary embodiments will now be described more fully with reference to the accompanying drawings. However, these exemplary embodiments can be implemented in many forms and should not be construed as limited to the examples set forth herein; rather, they are provided so that this disclosure will be more comprehensive and complete, and will fully convey the concept of the exemplary embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0037] Furthermore, the accompanying drawings are merely illustrative of this disclosure and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and therefore repeated descriptions of them will be omitted. Some block diagrams shown in the drawings are functional entities and do not necessarily correspond to physically or logically independent entities. These functional entities may be implemented in software, in one or more hardware modules or integrated circuits, or in different network and / or processor devices and / or microcontroller devices.

[0038] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this disclosure, "multiple" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0039] In view of the technical problems existing in the above-mentioned related technologies, the present disclosure provides an encrypted traffic detection method to solve at least one or all of the above-mentioned technical problems.

[0040] It should be noted that the nouns or terms used in the embodiments of this application can be referenced from each other and will not be repeated here.

[0041] The following will describe in more detail each step of the data reconstruction method based on the sparse representation of the Ladon domain in this exemplary embodiment, with reference to the accompanying drawings and embodiments.

[0042] Figure 1 A flowchart illustrating a data reconstruction method based on sparse representation of a Ladon domain, as shown in an embodiment of this disclosure, is presented. Figure 1 As shown, method 100 may include the following steps:

[0043] In step S110, the low-resolution Radon coefficient is obtained.

[0044] Among them, the low-resolution Radon coefficient is the point generated by the convergence and focusing of the original data (represented as energy) on a specific path in the spatiotemporal domain through Radon transformation (data inversion) in the transform domain.

[0045] In step S120, the low-resolution Radon coefficients are input into the neural network of the encoder-decoder structure to obtain the first high-resolution Radon coefficients.

[0046] Among them, the encoder-decoder structure of the neural network can be, for example... Figure 2 The simplified diagram shown in the figure is as follows: Figure 2As shown, the low-resolution Radon coefficient m* is compressed after being fed into the neural network. In some embodiments, the compression process is achieved through max pooling. After compression and discarding most of the redundant data, a hidden layer Radon coefficient m is obtained. hidden Then m hidden Decompress to restore original size. By using an encoding-decoding structure, the data size is reduced, thereby shortening the computation time and reducing computational costs, while maintaining the spatiotemporal signal-to-noise ratio of the data.

[0047] In step S130, the sparsity of the first high-resolution Radon coefficient is increased by an adaptive soft thresholding function cascaded through a neural network to obtain a second high-resolution Radon coefficient.

[0048] The adaptive soft threshold (AdST) function has a non-fixed threshold and also has an activation function. Therefore, it can improve the expressive power and accuracy of the output of the aforementioned encoder-decoder neural network.

[0049] In this disclosure, the encoding-decoding structure discards redundant data during the compression process before decompression, ensuring the spatiotemporal signal-to-noise ratio of the data, while simultaneously reducing the data size, improving the efficiency of reconstruction operations, and reducing computational costs.

[0050] Furthermore, by introducing sparsity constraints, the convergence of the inverted Radon coefficients is improved, and the coefficients have a stronger fitting ability. Therefore, when the Radon coefficients are forward modeled back to the spatiotemporal domain, there are fewer artifacts, a higher signal-to-noise ratio, and the reconstructed Radon coefficients have higher resolution.

[0051] Furthermore, a cascaded encoder-decoder structure and adaptive soft thresholding function are used to alter the distribution of the Radon coefficients, achieving sparse inversion. The adaptive soft thresholding function, based on the encoder-decoder structure, leverages the complex nonlinear representation capabilities of neural networks to accelerate the inversion process and improve the stability of the reconstructed data.

[0052] In some embodiments of this disclosure, step S120 may further include, for example... Figure 3 The method flowchart is shown. Figure 3 As shown, the method 300 for obtaining the first high-resolution Radon coefficient through a neural network with an encoder-decoder structure may include the following steps:

[0053] In step S310, the low-resolution Radon coefficients are downsampled through the coding convolutional layer in the neural network to obtain coded data.

[0054] The encoder-decoder structure may include one or more encoder-decoder convolutional layers, which perform one or more rounds of downsampling accordingly.

[0055] In step S320, the encoded data is upsampled through the decoding convolutional layer in the neural network to obtain the decoded data, and then fused with the encoded data obtained during the downsampling process to obtain the first high-resolution Radon coefficient.

[0056] The decoding convolutional layer may include one or more layers, which perform one or more rounds of upsampling accordingly. In some embodiments of this disclosure, the number of encoding convolutional layers corresponds to the number of decoding convolutional layers. During the upsampling process, the upsampled object may include the decoded data output from the previous decoding convolutional layer and the encoded data output from the corresponding encoding convolutional layer.

[0057] Therefore, the method in this embodiment can effectively prevent data divergence and ensure stable convergence of function values ​​through the encoder-decoder structure. It can also remove most redundant information, ensuring the spatiotemporal signal-to-noise ratio of the data.

[0058] Furthermore, by concatenating shallow features with deep features, the receptive field of the features is increased, enhancing the adaptability of the neural network to the data.

[0059] In some embodiments of this disclosure, the threshold of the adaptive soft thresholding function is learnable during neural network training. For example... Figure 4 The flowchart illustrates the update method for the adaptive soft threshold function. Figure 4 As shown, method 400 may include the following steps:

[0060] In step S410, the training dataset is sequentially input into the neural network and the adaptive soft thresholding function to obtain the predicted transform domain coefficients.

[0061] In step S420, the loss value of the predicted transform domain coefficients is calculated.

[0062] In step S430, the adaptive soft thresholding function is updated according to the loss value.

[0063] The disclosed embodiments of the method effectively improve the sparsity of the transform domain coefficients by learning an adaptive soft threshold.

[0064] Specifically, for example Figure 5 The training process shown is 500, such as Figure 5 As shown, the training process 500 may include:

[0065] In step S502, a training dataset is constructed using a forward modeling method. First, the energy amplitude and position of the hyperbolic Radon transform domain are defined, resulting in several two-dimensional matrices. These matrices are then convolved with the eigenvectors of the data to obtain several ideal transform domain coefficient matrices m1, m2, ..., m... nPerforming a hyperbolic Radon inverse transform on the above coefficient matrix yields the corresponding data d1, d2, ..., d. n Then the conjugate solution is obtained. For synthetic data, For tags.

[0066] In some embodiments of this disclosure, conjugate solutions are used. and the corresponding least squares solution Construct a training dataset, using conjugate solutions as low-resolution input data for the model and least squares solutions as labels.

[0067] Using the least squares solution instead of some high-resolution solution as the label has the following advantages:

[0068] First, the least squares solution retains more original information. While less sparsity compared to other high-resolution solutions, the least squares solution boasts a higher signal-to-noise ratio. Choosing the least squares solution as the label helps control the spatiotemporal fitting error.

[0069] Second, least squares solutions are easier to obtain. Compared to other sparser inversion algorithms, least squares inversion is more efficient. It allows for the rapid creation of a dataset, reducing the overall time cost of the data reconstruction process.

[0070] Third, the least squares solution, as label data, cannot characterize the sparsity of the data reconstruction, thus improving the accuracy of neural network prediction.

[0071] In step S504, the conjugate solution is... As input, low-resolution data.

[0072] In steps S506-S508, the low-resolution Radon coefficients are sequentially input into the encoder-decoder neural network and the adaptive threshold function to obtain the predicted high-resolution Radon coefficients m. net .

[0073] Each encoding or decoding convolutional layer is followed by a hyperbolic tangent activation function (Tanh). The calculation method for each encoding or decoding convolutional layer and its activation function can be expressed as Equation (1) and Equation (2), respectively:

[0074]

[0075] map i+1 =f activation (map i (2)

[0076] Among them, map (c) It is the c-th feature map, k c and bias(c) These are the convolution kernel and bias corresponding to the c-th feature map, respectively.

[0077] In step S510, the loss value for predicting the high-resolution Radon coefficient is calculated based on the actual label value corresponding to the input conjugate solution.

[0078] In some embodiments of this disclosure, the loss function for calculating the loss value of the predicted transform domain coefficients is formula (3):

[0079]

[0080] Where L is the coefficient m of the target transform domain. n With predicted transform domain coefficients The mean square error (MSE) between the inputs. In some embodiments, L is the least squares solution corresponding to the conjugate solution of the input.

[0081] In step S512, the adaptive soft thresholding function is updated according to the loss value.

[0082] In the process of training the parameters of the encoder-decoder neural network, the adaptive soft thresholding function is also part of the network that needs to be trained, and the gradient is updated based on the loss value of each training round.

[0083] In some embodiments of this disclosure, the adaptive soft threshold (AdST) function can be expressed as formula (4):

[0084] AdST(m)=(|m|-σ) + sgn(m) (4)

[0085] Where σ≥0 is the threshold; m is the result after convolution.

[0086] Furthermore, the threshold σ in the gradient update AdST function can be calculated according to the Adam optimization algorithm, as shown in equations (5) and (6):

[0087] g t =▽ σ AdST t (σ t-1 (5)

[0088]

[0089] Here, m and v are initialized to 0, and these two variables store information about the σ gradient and the squared gradient; α, β1, β2, and ε are typically taken as 0.001, 0.9, 0.999, and 10, respectively. -8 .like Figure 6As shown, the AdST function performs a filtering process on the data at each position, setting data smaller than the threshold σ to 0, which effectively improves the sparsity of the Radon coefficient, thus contributing to high-resolution data reconstruction.

[0090] Repeat steps S502 to S512 until the loss function converges, then end the training process.

[0091] In some embodiments of this disclosure, there is also a Fast Sparse Hyperbolic Radon Transform (FSHRT) model that performs a data reconstruction method based on the sparse representation of Radon domains. For example... Figure 7 As shown, model 700 may include: a neural network 710 with an encoder-decoder structure and an adaptive soft thresholding function 720.

[0092] The neural network 710 with an encoder-decoder structure includes multiple encoded convolutional layers 712 connected in series. These encoded convolutional layers 712 are used to encode low-resolution Radon coefficients, and the number of channels in the resulting encoded data doubles each time.

[0093] In this process, multiple decoding convolutional layers 714 are connected in series after the encoding convolutional layer 712. The decoding convolutional layer 714 is used to decode the encoded data. The number of channels of the decoded data is reduced by half each time to obtain the first high-resolution Radon coefficient.

[0094] The encoding convolutional layer 712 and the decoding convolutional layer 714, which output the same number of channels, are skipped to reconstruct the data by combining the decoded data with the downsampled encoded data.

[0095] In this process, an adaptive soft thresholding function 720 is connected in series after the neural network 710 of the encoder-decoder structure to increase the sparsity of the first high-resolution Radon coefficient and obtain the second high-resolution Radon coefficient.

[0096] Specifically, model 700 first compresses low-resolution Radon coefficients with a size of 4M*4N and 32 channels using the encoding convolutional layer 712 in the encoding-decoding convolutional structure 710. With each compression, the data size is halved in both directions, and the number of channels is doubled. Figure 7The compression process includes three levels: from 4M*4N with 32 channels, to 2M*2N with 64 channels, and then to M*N with 128 channels. This compression process encodes the data, reducing its complexity and redundancy while preserving its useful features. The encoded data is then expanded by using skip connections between compression levels, directly concatenating shallow feature maps to deeper feature maps. These shallow features serve as additional information to aid in the generation of high-resolution results during upsampling, adding high-frequency information to the final output.

[0097] The FHSRT model uses an encoder-decoder structure to discard redundant data during the compression process before decompression, ensuring the spatiotemporal signal-to-noise ratio of the data while simultaneously reducing data size, improving computational efficiency, and reducing computational costs.

[0098] Furthermore, the FHSRT model introduces sparsity constraints to improve the convergence of the inverted Radon coefficients and enhance their fitting ability. Therefore, when the Radon coefficients are forward modeled back to the spatiotemporal domain, there are fewer artifacts, a higher signal-to-noise ratio, and the reconstructed Radon coefficients have higher resolution.

[0099] Furthermore, the FHSRT model employs a cascaded encoder-decoder structure and an adaptive soft thresholding function to alter the distribution of the Radon coefficients, achieving sparse inversion. The adaptive soft thresholding function, building upon the encoder-decoder structure, leverages the complex nonlinear representation capabilities of neural networks to accelerate the inversion process and improve the stability of the reconstructed data.

[0100] In some embodiments of this disclosure, a synthetic dataset was designed to verify the effectiveness of the data reconstruction method based on Radon domain sparse representation. Specific experimental background: The synthetic dataset was divided into a training set and a validation set, with the training set containing 180 data sets and the validation set containing 20 data sets. Sparse Radon coefficients were obtained by executing the FSHRT model based on the Radon domain sparse representation data reconstruction method. The Adam algorithm was used to optimize gradient updates. The initial learning rate was 0.0001, and the learning rate decayed to 70% of its original value every 100 epochs. The loss function was the MSE between the model input and output. Figure 8 It represents the change in the loss function value during the training of the FSHRT model, with the loss value in a logarithmic coordinate direction.

[0101] Figure 8(a) and (b) show the MSE of the training and validation sets, respectively. There are certain differences between different data points in the training set. These differences cause the direction of gradient updates to change continuously, resulting in significant fluctuations in the loss curve of the training set. However, overall, superimposing the directions of gradient updates points in the direction of decreasing loss function, so the loss value of the training set consistently shows a decreasing trend. Increasing the batch size during training can smooth the loss curve, but it will reduce the convergence speed. The change in the loss value of the validation set is a better indicator of the training effectiveness. As training progresses, the loss curve of the validation set decreases smoothly and tends to converge at the 200th epoch, demonstrating strong generalization performance.

[0102] Furthermore, the test data were inverted using the FSHRT model of this invention (trained for 500 epochs) and the Preconditioned conjugate gradient (PCG) algorithm to obtain sparse Radon coefficients. Figure 9 (a) and Figure 9 (b) is the inversion result of the PCG algorithm. Figure 9 (c) and 9(d) are the results of FSHRT inversion. In slightly more complex synthetic record inversion tasks, FSHRT performs significantly better than the PCG algorithm. Figure 9 In (a) and (b), the black arrows clearly show that energy diffusion still exists in the PCG algorithm inversion results. Although there is a significant improvement in resolution compared to the general conjugate solution, the residual artifacts indicate that its sparsity is not high enough. These artifacts will transfer to the spatiotemporal domain along with the effective signal during the forward modeling process, reducing the data SNR and affecting high-resolution data reconstruction. Figure 9 In (c) and 9(d), no energy diffusion was observed at the locations corresponding to the black arrows. This indicates that FSHRT has a strong sparsity characterization capability, greatly eliminating diffused energy while preserving the effective signal location and amplitude, and exhibiting high sparsity of the Radon coefficient.

[0103] Figure 10 To more intuitively illustrate the effect of the FSHRT model on the sparsity of the Radon coefficients, we can use the time intercept τ and velocity parameter v as two axes. A constant velocity v is selected to slice the τ-v plane. For example... Figure 10 (a) shows a schematic diagram of the Ladon slice direction. Figure 10 As shown in (b), the high-resolution coefficients obtained by the FSHRT based on a neural network in this invention can fit the ideal transform domain coefficients well. Similarly, Figure 10 (d) shows the results of slicing the τ-v plane at a constant time τ, and the FSHRT inversion results are equally accurate. Figure 10(c) and (e) represent the residuals in two directions of the inversion results obtained by the FSHRT and PCG algorithms, respectively. The FSHRT inversion results are more accurate and have smaller residuals than those obtained by the PCG algorithm. It is foreseeable that, since FSHRT has smaller errors in the Radon domain, the SNR of the Radon coefficients when modeled forward to the spatiotemporal domain will be higher than that of the PCG algorithm.

[0104] Figure 11 This diagram illustrates a data reconstruction apparatus based on a sparse representation of a Ladon domain, according to an embodiment of this disclosure. Figure 11 As shown, the device 1100 includes:

[0105] Input module 1110 is used to obtain low-resolution Radon coefficients; encoding / decoding module 1120 is used to obtain first high-resolution Radon coefficients by first passing the low-resolution Radon coefficients through a neural network with an encoding-decoding structure; sparse module 1130 is used to increase the sparsity of the first high-resolution Radon coefficients through an adaptive soft threshold function cascaded after the neural network to obtain second high-resolution Radon coefficients.

[0106] In some embodiments of this disclosure, the encoding / decoding module 1120 is further configured to downsample the low-resolution Radon coefficients through the encoding convolutional layer in the neural network to obtain encoded data; and to fuse the encoded data obtained during the downsampling process with the decoded data obtained by upsampling the encoded data through the decoding convolutional layer in the neural network to obtain the first high-resolution Radon coefficients.

[0107] In some embodiments of this disclosure, the device 1100 further includes a training module for sequentially inputting a training dataset into the neural network and the adaptive soft thresholding function to obtain predicted transform domain coefficients; calculating a loss value for the predicted transform domain coefficients; and updating the adaptive soft thresholding function according to the loss value.

[0108] In some embodiments of this disclosure, a training dataset is constructed using conjugate solutions and corresponding least squares solutions, wherein the conjugate solutions serve as model inputs and the least squares solutions serve as labels.

[0109] In some embodiments of this disclosure, the loss function for calculating the loss value of the predicted transform domain coefficients is expressed as formula (3).

[0110] In some embodiments of this disclosure, the adaptive soft threshold function AdST is expressed as Equation (4).

[0111] In some embodiments of this disclosure, the gradient update of the adaptive soft threshold function based on the loss value is calculated using formulas (5) and (6).

[0112] Regarding the data reconstruction device 1100 based on the sparse representation of the Ladon domain in the above embodiments, the specific manner in which each module performs its operation has been described in detail in the embodiments related to the method, and will not be elaborated here.

[0113] Those skilled in the art will understand that various aspects of this disclosure can be implemented as a system, method, or program product. Therefore, various aspects of this disclosure can be specifically implemented in the following forms: a completely hardware implementation, a completely software implementation (including firmware, microcode, etc.), or a combination of hardware and software aspects, collectively referred to herein as a "circuit," "module," or "system."

[0114] The following reference Figure 12 To describe an electronic device 1200 according to such an embodiment of the present disclosure. Figure 12 The electronic device 1200 shown is merely an example and should not impose any limitation on the functionality and scope of use of the embodiments disclosed herein.

[0115] like Figure 12 As shown, the electronic device 1200 is manifested in the form of a general-purpose computing device. The components of the electronic device 1200 may include, but are not limited to: at least one processing unit 1210, at least one storage unit 1220, and a bus 1230 connecting different system components (including storage unit 1220 and processing unit 1210).

[0116] The storage unit stores program code that can be executed by the processing unit 1210, causing the processing unit 1210 to perform the steps described in the "Exemplary Methods" section of this specification according to various exemplary embodiments of this disclosure. For example, the processing unit 1210 can perform actions such as... Figure 1 In step S120, a low-resolution Ladon coefficient is obtained; in step S120, an initial generator network and an initial discriminator network are generated for each edge node based on the first generator drop rate, the first discriminator drop rate, and the first generator network split point; in step S130, the sparsity of the first high-resolution Ladon coefficient is increased by the adaptive soft threshold function cascaded after the neural network to obtain a second high-resolution Ladon coefficient.

[0117] Storage unit 1220 may include a readable medium in the form of a volatile storage unit, such as random access memory (RAM) 1221 and / or cache memory 1222, and may further include a read-only memory (ROM) 1223.

[0118] Storage unit 1220 may also include a program / utility 1224 having a set (at least one) of program modules 1225, such program modules 1225 including but not limited to: operating system, one or more application programs, other program modules and program data, each or some combination of these examples may include an implementation of a network environment.

[0119] Bus 1230 can represent one or more of several types of bus structures, including a memory cell bus or memory cell controller, a peripheral bus, a graphics acceleration port, a processing unit, or a local bus using any of the various bus structures.

[0120] Electronic device 1200 can also communicate with one or more external devices (e.g., keyboard, pointing device, Bluetooth device, etc.), one or more devices that enable a user to interact with electronic device 1200, and / or any device that enables electronic device 1200 to communicate with one or more other computing devices (e.g., router, modem, etc.). This communication can be performed via input / output (I / O) interface 1250. Furthermore, electronic device 1200 can also communicate with one or more networks (e.g., local area network (LAN), wide area network (WAN), and / or public networks, such as the Internet) via network adapter 1260. As shown, network adapter 1260 communicates with other modules of electronic device 1200 via bus 1230. It should be understood that, although not shown in the figures, other hardware and / or software modules can be used in conjunction with electronic device 1200, including but not limited to: microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, tape drives, and data backup storage systems.

[0121] In exemplary embodiments of this disclosure, a computer-readable storage medium is also provided, on which a program product capable of implementing the methods described above is stored. In some possible implementations, various aspects of this disclosure may also be implemented as a program product including program code that, when the program product is run on a terminal device, causes the terminal device to perform the steps of the various exemplary embodiments of this disclosure described in the "Exemplary Methods" section above.

[0122] The program product for implementing the above-described method according to embodiments of the present disclosure may employ a portable compact disc read-only memory (CD-ROM) and include program code, and may run on a terminal device, such as a personal computer. However, the program product of the present disclosure is not limited thereto. In this document, the readable storage medium may be any tangible medium containing or storing a program that may be used or used in conjunction with an instruction execution system, server, terminal, or device.

[0123] The program product may employ any combination of one or more readable media. A readable medium may be a readable signal medium or a readable storage medium. A readable storage medium may be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, server, terminal, or device, or any combination thereof. More specific examples of readable storage media (a non-exhaustive list) include: an electrical connection having one or more wires, a portable disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof.

[0124] Computer-readable signal media may include data signals propagated in baseband or as part of a carrier wave, carrying readable program code. Such propagated data signals may take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. A readable signal medium may also be any readable medium other than a readable storage medium, capable of sending, propagating, or transmitting programs for use by or in conjunction with an instruction execution system, server, terminal, or device.

[0125] The program code contained on the readable medium may be transmitted using any suitable medium, including but not limited to wireless, wired, optical fiber, RF, etc., or any suitable combination thereof.

[0126] Program code for performing the operations of this disclosure can be written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Java and C++, and conventional procedural programming languages ​​such as C or similar languages. The program code can execute entirely on the user's computing device, partially on the user's computing device, as a standalone software package, partially on the user's computing device and partially on a remote computing device, or entirely on a remote computing device or server. In cases involving remote computing devices, the remote computing device can be connected to the user's computing device via any type of network, including a local area network (LAN) or a wide area network (WAN), or it can be connected to an external computing device (e.g., via the Internet using an Internet service provider).

[0127] According to one aspect of this disclosure, a computer program product or computer program is provided, comprising 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 methods provided in various optional implementations of the above embodiments.

[0128] It should be noted that although several modules or units for the device used to perform actions have been mentioned in the detailed description above, this division is not mandatory. In fact, according to embodiments of this disclosure, the features and functions of two or more modules or units described above can be embodied in one module or unit. Conversely, the features and functions of one module or unit described above can be further divided and embodied by multiple modules or units.

[0129] Furthermore, although the steps of the method in this disclosure are described in a specific order in the accompanying drawings, this does not require or imply that the steps must be performed in that specific order, or that all the steps shown must be performed to achieve the desired result. Additional or alternative steps may be omitted, multiple steps may be combined into one step, and / or a step may be broken down into multiple steps.

[0130] From the above description of the embodiments, those skilled in the art will readily understand that the exemplary embodiments described herein can be implemented by software or by combining software with necessary hardware. Therefore, the technical solutions according to the embodiments of this disclosure can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (such as a CD-ROM, USB flash drive, external hard drive, etc.) or on a network, including several instructions to cause a computing device (such as a personal computer, server, mobile terminal, or network device, etc.) to execute the methods according to the embodiments of this disclosure.

[0131] Other embodiments of this disclosure will readily occur to those skilled in the art upon consideration of the specification and practice of the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of this disclosure that follow the general principles of this disclosure and include common knowledge or customary techniques in the art not disclosed herein. The specification and examples are to be considered exemplary only, and the true scope and spirit of this disclosure are indicated by the appended claims.

Claims

1. A data reconstruction method based on sparse representation of the Ladon domain, characterized in that, The method includes: Obtain the low-resolution Radon coefficient of the image; The low-resolution Radon coefficients are input into a neural network with an encoder-decoder structure to obtain the first high-resolution Radon coefficients. The second high-resolution Radon coefficient is obtained by increasing the sparsity of the first high-resolution Radon coefficient through an adaptive soft thresholding function cascaded after the neural network. The step of obtaining the low-resolution Radon coefficients includes, prior to: sequentially inputting the training dataset into the neural network and the adaptive soft thresholding function to obtain the predicted transform domain coefficients; calculating the loss value of the predicted transform domain coefficients; and updating the adaptive soft thresholding function according to the loss value.

2. The data reconstruction method based on sparse representation of the Ladon domain according to claim 1, characterized in that, The steps of inputting the low-resolution Radon coefficients into a encoder-decoder neural network to obtain the first high-resolution Radon coefficients include: The low-resolution Radon coefficients are downsampled through the coding convolutional layer in the neural network to obtain coded data; The first high-resolution Radon coefficient is obtained by fusing the decoded data obtained during the downsampling process with the decoded data obtained during the upsampling process of the encoded data through the decoding convolutional layer in the neural network.

3. The data reconstruction method based on sparse representation of the Ladon domain according to claim 1, characterized in that, A training dataset is constructed using conjugate solutions and their corresponding least squares solutions, with the conjugate solutions serving as model inputs and the least squares solutions serving as labels.

4. The data reconstruction method based on sparse representation of the Ladon domain according to claim 3, characterized in that, The loss function for calculating the loss value of the predicted transform domain coefficients is: To measure the target transform domain coefficients With predicted transform domain coefficients The mean square error (MSE) between them.

5. The data reconstruction method based on sparse representation of the Ladon domain according to claim 4, characterized in that, The adaptive soft thresholding function AdST is expressed as: in, is the threshold; m is the result after convolution.

6. The data reconstruction method based on sparse representation of the Ladon domain according to claim 5, characterized in that, Based on the loss value, the gradient update of the adaptive soft threshold function is calculated as follows: ； in, and Initialized to 0, these two variables store information about the σ gradient and the squared gradient. α、β 1 、β 2 and ε Take 0.001, 0.9, 0.999 and 10 -8 .

7. A data reconstruction device based on sparse representation of a Ladon domain, characterized in that, The device includes: The input module is used to obtain the low-resolution Radon coefficients of the image; The encoding / decoding module is used to first obtain the first high-resolution Radon coefficients by passing the low-resolution Radon coefficients through a neural network with an encoding-decoding structure. A sparse module is used to increase the sparsity of the first high-resolution Radon coefficient through an adaptive soft thresholding function cascaded after the neural network to obtain a second high-resolution Radon coefficient. The input module is further configured to sequentially input the training dataset into the neural network and the adaptive soft thresholding function to obtain the predicted transform domain coefficients; calculate the loss value of the predicted transform domain coefficients; and update the adaptive soft thresholding function according to the loss value.

8. An electronic device, characterized in that, include: processor; as well as Memory for storing the executable instructions of the processor; The processor is configured to execute the data reconstruction method based on the sparse representation of the Ladon domain as described in any one of claims 1 to 6 by executing the executable instructions.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the data reconstruction method based on the sparse representation of the Ladon domain as described in any one of claims 1 to 6.

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