A method and system for magnetotelluric data compressed sensing reconstruction

Abstract

The present application is suitable for the field of geophysical exploration technology, and provides a magnetotelluric data compression sensing reconstruction method and system, which comprises the following steps: obtaining original magnetotelluric time series data, segmenting and standardizing preprocessing to obtain a plurality of standardized signal segments; transforming each standardized signal segment to obtain a transform domain sparse representation, compressively sampling the transform domain sparse representation to obtain a compressed measurement vector; extracting a multi-dimensional feature vector of each signal segment, predicting a corresponding regularization parameter scaling factor according to the multi-dimensional feature vector based on a neural network model, and calculating an adaptive regularization parameter; taking the adaptive regularization parameter as the regularization strength, constructing a convex optimization model containing an L2 data fidelity term and an L1 sparse regularization term, and reconstructing the magnetotelluric time series data based on a greedy acceleration iterative shrinkage threshold algorithm. The present application can reduce the bandwidth and facilitate real-time monitoring in field environments and other occasions with high transmission requirements.

Description

Technical Field

[0001] This invention belongs to the field of geophysical exploration technology, and in particular relates to a method and system for compressed sensing and reconstruction of magnetotelluric data. Background Technology

[0002] Magnetotelluric sounding (MT) is an important method in geophysical exploration, offering advantages such as large exploration depth and low cost. Currently, MT is widely used in mineral resource exploration, energy detection, and deep Earth structure analysis.

[0003] Compressed sensing technology is widely used in the field of earthquakes. Its introduction has greatly improved the efficiency of data acquisition and reduced storage requirements. Real-time acquisition of magnetotelluric signals in the field often requires high-quality communication networks. However, magnetotelluric experiments are often conducted in remote areas with little electromagnetic interference, making the transmission of high-frequency, large amounts of data challenging. Furthermore, magnetotelluric signals have a natural sparsity, allowing for sparse representation under certain conditions. Summary of the Invention

[0004] The purpose of this invention is to provide a method and system for compressive sensing and reconstruction of magnetotelluric data, in order to solve the above-mentioned technical problems.

[0005] This invention is implemented as follows: a magnetotelluric data compression sensing reconstruction method, comprising the following steps:

[0006] The raw magnetotelluric time series data were acquired and segmented and standardized preprocessed to obtain multiple standardized signal segments;

[0007] Each standardized signal segment is transformed to obtain a sparse representation in the transform domain, and the sparse representation in the transform domain is compressed and sampled to obtain a compressed measurement vector;

[0008] Based on the compressed measurement vector, a multidimensional feature vector is extracted for each signal segment;

[0009] Based on the preset neural network model, the corresponding regularization parameter scaling factor is predicted according to the multi-dimensional feature vector, and the adaptive regularization parameter for the L1 sparse regularization term is calculated.

[0010] Using adaptive regularization parameters as the regularization strength, a convex optimization model containing L2 data fidelity terms and L1 sparse regularization terms is constructed, and magnetotelluric time series data are reconstructed based on a greedy accelerated iterative shrinkage threshold algorithm.

[0011] Furthermore, the segments are divided into non-overlapping or partially overlapping segments using a preset fixed length.

[0012] Furthermore, the transformation can be any one of wavelet transform, Fourier transform, and DCT transform.

[0013] Furthermore, the compressed sampling method includes:

[0014] For each signal segment Using a random Gaussian matrix Perform linear compressed sampling:

[0015] ;

[0016] in, For compressing the measurement vector; measurement number Compression ratio Random Gaussian matrix The elements satisfy:

[0017] .

[0018] Furthermore, the transformation is a Discrete Cosine Transform (DCT); the convex optimization model containing L2 data fidelity terms and L1 sparse regularization terms is as follows:

[0019] ;

[0020] Let be the sparse coefficient vector of the DCT domain to be reconstructed, and ;remember For L2 data fidelity items; This is an L1 sparse regularization term; For adaptive regularization parameters;

[0021] Then the objective function for:

[0022] ;

[0023] Define linear operators Then the gradient of the L2 data fidelity term f(z) for:

[0024]

[0025] in, Represents the inverse discrete cosine transform matrix; Represents the discrete cosine transform matrix of the DCT;

[0026] For L1 sparse regularization terms, the proximal operator is: :

[0027] ;

[0028] In the formula, The input vector is the result of subtracting the gradient from the current iteration point; Step size; This is a sign function that operates on each element of the vector. If the element is greater than 0, it outputs 1; if it is less than 0, it outputs -1; and if it is equal to 0, it outputs 0. It represents the Hadamardi (or Hadama) stack.

[0029] Furthermore, a greedy, accelerated iterative threshold shrinkage algorithm is employed to solve the convex optimization model containing L2 data fidelity terms and L1 sparse regularization terms; the greedy, accelerated iterative threshold shrinkage algorithm performs the following operations in each iteration:

[0030] First, set the initial values ​​for optimization. And set the initial value of the acceleration iteration point. Set the maximum number of iterations (maxits) and tolerance. and initial step size ;

[0031] In the In the next iteration, based on the current accelerated iteration point Calculate the gradient of the current solution And use near-end operations to update the current solution. The proximal operation is performed through: Completed; among them, For the proximal operator of L1 sparse regularization terms, in the proximal operator For the adaptive regularization parameters of the current signal segment, during the online prediction stage: Predicted by a neural network model; Offline training phase: , which are candidate regularization parameters; For the first The step size of the next iteration; The gradient function for the L2 data fidelity term;

[0032] Introducing a momentum mechanism, in each iteration, the current solution is calculated... Compared with the last solution The difference, combined with the momentum parameter For the next iteration point Update;

[0033] After each iteration, compute the current solution. And the last solution The difference; when the difference exceeds a preset threshold, a greedy restart is performed, and the iteration point is accelerated. Reset to the current solution Simultaneously, the current solution is calculated after each iteration. Compared with the last solution The residuals between them are used to determine whether convergence has occurred; when the residuals are less than a preset tolerance... When the iteration ends, proceed.

[0034] In each iteration, record the current value of the objective function. The step size is dynamically adjusted through a step size control strategy; if the current residual increases beyond the set safety factor, the step size will be reduced; when the residual is less than the preset tolerance... When the residual exceeds the preset divergence threshold, the algorithm stops early and outputs the final result.

[0035] Furthermore, the adaptive regularization parameter The calculation method is as follows:

[0036] Extract each standardized signal segment Multidimensional feature vectors ;

[0037] Will Input a pre-trained neural network model to obtain the predicted value of the regularization parameter scaling factor. ;

[0038] Calculate the signal segment and take its maximum absolute value. The online adaptive regularization parameters are obtained. :

[0039] .

[0040] Furthermore, the neural network model constructs a "pseudo-optimal" Learning multidimensional feature vectors and adaptive regularization parameters on datasets labeled "scale factor" The mapping relationship between them; wherein, the pseudo-optimal The scaling factor is generated as follows:

[0041] Define a set of candidate regularization parameter scaling factors :

[0042] ;

[0043] For each signal segment First, calculate its DCT coefficients. Based on this, the maximum absolute value of the DCT coefficients of the signal is selected as the key feature value of the signal. :

[0044] ;

[0045] For each candidate regularization parameter scaling factor Define the corresponding regularization parameters. :

[0046] ;

[0047] For the same signal segment , in turn Substituting into the convex optimization model, we obtain the corresponding reconstructed signal. And calculate its mean square error. and signal-to-noise ratio :

[0048] ;

[0049] ;

[0050] Among all candidate regularization parameter scaling factors, the one that maximizes the signal-to-noise ratio is selected as the pseudo-optimal for that signal segment. Scale factor :

[0051] ;

[0052] in, The length of the signal. The original signal, For the corresponding adaptive regularization parameters Reconstructed signal.

[0053] Furthermore, the method for extracting the multidimensional feature vector includes:

[0054] Extract the time-domain features of the signal segment;

[0055] Extract the frequency domain features of the signal segment;

[0056] By fusing time-domain features and frequency-domain features, a multi-dimensional feature vector is obtained.

[0057] Another object of the present invention is to provide a magnetotelluric data compressed sensing reconstruction system for implementing the above-mentioned magnetotelluric data compressed sensing reconstruction method, comprising:

[0058] The data preprocessing module is used to acquire raw magnetotelluric time series data and perform segmentation and standardization preprocessing to obtain multiple standardized signal segments;

[0059] The compression modeling module is used to transform each standardized signal segment to obtain a sparse representation in the transform domain, and to compress and sample the sparse representation in the transform domain to obtain a compressed measurement vector.

[0060] The feature extraction module is used to extract multi-dimensional feature vectors for each signal segment based on the compressed measurement vector;

[0061] The regularization parameter prediction module is used to predict the corresponding regularization parameter scaling factor based on the multidimensional feature vector of the preset neural network model, and to calculate the adaptive regularization parameter for the L1 sparse regularization term.

[0062] The data reconstruction module is used to construct a convex optimization model containing L2 data fidelity terms and L1 sparse regularization terms with adaptive regularization parameters as the regularization strength, and to reconstruct magnetotelluric time series data based on a greedy acceleration iterative shrinkage threshold algorithm.

[0063] The magnetotelluric data compressed sensing reconstruction method provided by this invention introduces compressed sensing technology into the processing of magnetotelluric signals. Specifically, it extracts the sparse features of the signal by performing appropriate transformations on the electromagnetic signal (such as Fourier transform, wavelet transform, etc.) and uses a non-uniform random sampling method to significantly reduce the number of sampling points, thereby reducing the number of sensors and data storage capacity required. This method can reduce the storage and transmission burden while ensuring signal quality. In field environments and other situations with high transmission requirements, it can reduce bandwidth, facilitating real-time monitoring. Attached Figure Description

[0064] Figure 1 This is a flowchart illustrating the magnetotelluric data compression sensing reconstruction method provided in an embodiment of the present invention.

[0065] Figure 2 This is a schematic diagram of the structure of a neural network model provided in an embodiment of the present invention. Detailed Implementation

[0066] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0067] like Figure 1 As shown, in one embodiment of the present invention, a magnetotelluric data compressed sensing reconstruction method is provided, comprising the following steps:

[0068] S100: Acquire raw magnetotelluric time series data (such as electric or magnetic field components), and perform preprocessing such as segmentation and standardization to obtain multiple standardized signal segments;

[0069] S200. Transform each standardized signal segment to obtain a sparse representation in the transform domain, and compress and sample the sparse representation in the transform domain to obtain a compressed measurement vector.

[0070] S300: Based on compressed measurement vectors, extract multi-dimensional feature vectors for each signal segment;

[0071] S400: Based on the preset neural network model, predict the corresponding regularization parameter scaling factor according to the multi-dimensional feature vector, and calculate the adaptive regularization parameter for the L1 sparse regularization term.

[0072] S500 uses adaptive regularization parameters as the regularization strength to construct a convex optimization model containing L2 data fidelity terms and L1 sparse regularization terms, and reconstructs magnetotelluric time series data based on the Greedy FISTA algorithm.

[0073] The magnetotelluric data compressed sensing reconstruction method provided in this invention can directly perform linear measurements on the signal during sampling using a redundant (rows fewer than columns) measurement matrix. This results in sampled data that is much smaller than the original signal data. The original signal can be accurately reconstructed from a small number of observations while satisfying sparsity, thereby reducing storage and transmission burdens. In field environments and other situations with high transmission requirements, bandwidth can be reduced, facilitating real-time monitoring.

[0074] In a preferred embodiment of the present invention, the segments are divided into non-overlapping or partially overlapping segments using a preset fixed length. Step S1 specifically includes: reading the electric / magnetic field time-domain data of a single or multiple magnetotelluric sounding point as the original magnetotelluric time-series data; dividing the long-time series into segments according to a preset length; performing preprocessing such as standardization and masking on each segment to obtain a standardized one-dimensional time-series signal segment, making each segment of data comparable in amplitude scale, thereby improving the numerical stability and generalization ability of subsequent compressed sensing modeling and neural network model prediction.

[0075] In practical applications, raw time-series data files are exported from magnetotelluric acquisition systems, preferably in CSV or binary format. The data in each column is then read into a one-dimensional array according to the acquisition sequence. According to the preset segment length (For example The data is divided into several non-overlapping or partially overlapping time periods. For each original data segment, a standardization operation is performed, and the sample mean and standard deviation are calculated to obtain the standardized signal segment. This serves as a reference truth value for subsequent sparse modeling and reconstruction.

[0076] In a preferred embodiment of the present invention, the above transformation is any one of wavelet transform, Fourier transform, and discrete cosine transform (DCT transform); preferably, it is DCT transform; specifically, DCT transform is performed on each segment of the standardized signal to obtain a sparse representation in the DCT domain; a random measurement matrix is ​​constructed, and the signal is linearly compressed and sampled using the matrix to obtain a compressed measurement vector with a dimension lower than the original length, which is used to simulate or realize the compressed acquisition process of magnetotelluric signals.

[0077] In a preferred embodiment of the present invention, for each standardized signal segment... A DCT transform is performed to obtain its coefficient vector in the DCT domain. Both theoretical and experimental experience show that magnetotelluric energy in the DCT domain exhibits a significant concentration characteristic; that is, most coefficients are close to zero or small, with only a few low-frequency coefficients being large, demonstrating sparsity or compressibility. The aforementioned compressed sampling method specifically includes:

[0078] For each signal segment The embodiments of the present invention employ a random Gaussian matrix. Linear compressed sampling is performed as a random measurement matrix:

[0079] ;

[0080] in, For compressing the measurement vector; measurement number Compression ratio It can be set to etc.; random Gaussian matrix The elements satisfy:

[0081] ;

[0082] It can also perform appropriate normalization on rows to enhance the stability of condition numbers.

[0083] In a preferred embodiment of the present invention, the above transformation employs a DCT transformation; given a measurement matrix Compression measurement and adaptive regularization parameters Under the premise of L2 data fidelity terms and L1 sparse regularization terms, the convex optimization model is as follows:

[0084] ;

[0085] in, Let be the sparse coefficient vector of the DCT domain to be reconstructed, and ;remember For L2 data fidelity items; This is an L1 sparse regularization term; For adaptive regularization parameters;

[0086] Then the objective function for:

[0087] ;

[0088] The above model belongs to the standard "smooth + non-smooth" convex optimization model, which can be solved using the forward-backward splitting idea;

[0089] The gradient of the smoothing term is calculated as follows:

[0090] Define linear operators Then the gradient of the L2 data fidelity term f(z) for:

[0091]

[0092] in, The inverse discrete cosine transform matrix is ​​represented by DCT; the discrete cosine transform matrix is ​​represented by DCT. In implementation, the above equation is achieved through combination... Efficient implementation of IDCT and DCT operations;

[0093] For L1 sparse regularization terms, the proximal operator is: :

[0094] ;

[0095] That is, amplitude contraction with sign preservation is applied to each component; where, The input vector is the result of subtracting the gradient from the current iteration point; Step size; This is a sign function that operates on each element of the vector. If the element is greater than 0, it outputs 1; if it is less than 0, it outputs -1; and if it is equal to 0, it outputs 0. It represents the Hadamardi (or Hadama) stack;

[0096] In a preferred embodiment of the present invention, an improved GreedyFISTA algorithm is used to perform forward-backward iterative solutions on a convex optimization model containing L2 data fidelity terms and L1 sparse regularization terms. The DCT coefficients are updated alternately using gradient descent and proximal operators, and fast convergence is achieved by combining momentum acceleration and step size control. Finally, an inverse DCT transform is performed on the reconstructed DCT coefficients to obtain the time-domain reconstructed magnetotelluric signal. Specifically, the GreedyFISTA algorithm performs the following operations in each iteration:

[0097] First, set the initial values ​​for optimization. And set the initial value of the acceleration iteration point. Set the maximum number of iterations (maxits) and tolerance. and initial step size ;

[0098] In the In the next iteration, based on the current accelerated iteration point Calculate the gradient of the current solution And use near-end operations to update the current solution. The proximal operation is performed through: Completed; among them, For the proximal operator of L1 sparse regularization terms, in the proximal operator For the adaptive regularization parameters of the current signal segment, during the online prediction stage: Predicted by a neural network model; Offline training phase: , which are candidate regularization parameters; For the first The step size of the next iteration; The gradient function for the L2 data fidelity term;

[0099] Introducing a momentum mechanism, in each iteration, the current solution is calculated... Compared with the last solution The difference, combined with the momentum parameter For the next iteration point Update;

[0100] After each iteration, compute the current solution. And the last solution The difference; when the difference exceeds a preset threshold, a greedy restart is performed, and the iteration point is accelerated. Reset to the current solution Simultaneously, the current solution is calculated after each iteration. Compared with the last solution The residuals between them are used to determine whether convergence has occurred; when the residuals are less than a preset tolerance... When the iteration ends, proceed.

[0101] In each iteration, record the current value of the objective function. The step size is dynamically adjusted through a step size control strategy; if the current residual increases beyond the set safety factor, the step size will be reduced; when the residual is less than the preset tolerance... When the residual exceeds the preset divergence threshold, the algorithm stops early and outputs the final result.

[0102] Regarding adaptive regularization parameters Traditionally, the selection of parameters is determined using fixed empirical rules or manual parameter tuning. Therefore, how to select appropriate parameters for different signal segments remains a challenge. This is the key to further improvements in the embodiments of the present invention.

[0103] Specifically, in a preferred embodiment of the present invention, a multi-dimensional feature vector, including time-domain features (such as statistical features) and frequency-domain features (such as DCT low-frequency coefficients), is constructed for each magnetotelluric signal segment. A multilayer sensing deep regression network is then established to map the features to... The scaling factor, and with "pseudo-optimal" The scaling factor is used as a supervisory signal for offline training to obtain adaptive prediction capabilities. The neural network model was used; during the offline training phase, a grid search was performed on a set of candidate regularization coefficient scaling factors for multiple magnetotelluric signal segments; Greedy FISTA reconstruction was run for each candidate value and reconstruction quality indicators (such as SNR) were calculated; the scaling factor that optimizes the method performance was selected as the "pseudo-optimal" for that signal segment. The "Scale Factor" label; in practical applications, new magnetotelluric time series data segments are first preprocessed and feature extracted. Then, a trained neural network model is used to predict the corresponding regularization parameter, the scale factor, and calculate the specific... and the By substituting the above convex optimization model and Greedy FISTA algorithm, the magnetotelluric signal of the compressed data can be reconstructed.

[0104] In practical applications, such as Figure 2 As shown, the neural network model internally employs a multilayer perceptron structure, including an input layer, several fully connected hidden layers, and an output layer. The hidden layers use non-linear activation functions to characterize the non-linear relationship between features and adaptive regularization parameters. The output layer uses activation functions that guarantee positive values ​​to output positive values. Scale factor prediction. During training, a multi-dimensional feature vector is used as input, and the corresponding regularization parameter, the scale factor prediction, is output. It is used to control the training process of the neural network model and update the network parameters.

[0105] Specifically, neural network models construct "pseudo-optimal" Learning multidimensional feature vectors and adaptive regularization parameters on datasets labeled "scale factor" The mapping relationship between them is determined by calculating the loss function (e.g., mean squared error) and using the Adam optimization algorithm to backpropagate and iteratively update the network parameters. Through multiple rounds of iterative training, the network gradually learns the mapping relationship between "magnetic signal features and adaptive regularization parameters" until the loss converges or the preset number of training rounds is reached, ultimately obtaining a regularized parameter prediction model that can be used for online prediction. Furthermore, this embodiment of the invention employs [a specific method / mechanism] in the offline stage. The grid search method generates supervision labels for each segment of the magnetotelluric signal; among them, pseudo-optimal... The scaling factor is generated as follows:

[0106] Define a set of candidate regularization parameter scaling factors :

[0107] ;

[0108] For each signal segment First, calculate its DCT coefficients. Based on this, the maximum absolute value of the DCT coefficients of the signal is selected as the key feature value of the signal. :

[0109] ;

[0110] For each candidate regularization parameter scaling factor Define the corresponding regularization parameters. :

[0111] ;

[0112] For the same signal segment , in turn Substituting into the convex optimization model, we obtain the corresponding reconstructed signal. And calculate its mean square error. and signal-to-noise ratio :

[0113] ;

[0114] ;

[0115] Among all candidate regularization parameter scaling factors, the one that maximizes the signal-to-noise ratio is selected as the pseudo-optimal for that signal segment. Scale factor :

[0116] ;

[0117] in, The length of the signal. The original signal, For the corresponding adaptive regularization parameters Reconstructed signal.

[0118] Through the above steps, each signal segment can be... We obtain a scalar label pseudo-optimal Scale factor This is used for supervised learning of subsequent neural network models. To enable the neural network model to predict appropriate signals based on the characteristics of the signal itself... This invention proposes a multi-domain feature extraction method that combines time-domain and frequency-domain information. This method comprehensively extracts key information from a signal from multiple dimensions by simultaneously utilizing both time-domain and frequency-domain features.

[0119] Specifically, in a preferred embodiment of the present invention, the method for extracting multidimensional feature vectors includes:

[0120] Extracting the temporal features of a signal segment: Temporal features reflect the temporal structure and dynamic changes of a signal, and are usually extracted by calculating statistical measures such as the signal's mean, variance, kurtosis, and skewness. In addition, signal features such as autocorrelation function and short-time energy can be used to help neural network models better understand the temporal characteristics of a signal.

[0121] Extracting frequency domain features of a signal segment: In the frequency domain, the main frequency components of a signal are often closely related to the signal's properties. By performing Fourier transform or Discrete Cosine Transform (DCT) on the signal, the signal's spectral features, such as peak values, bandwidth, and energy distribution, can be extracted. Frequency domain features help capture the signal's frequency characteristics and provide... This provides an important basis for the selection;

[0122] By fusing time-domain and frequency-domain features, a multi-dimensional feature vector is obtained: After extraction, the time-domain and frequency-domain features are further fused to produce a multi-dimensional feature vector containing rich information. This multi-dimensional feature vector can not only effectively describe the time-frequency characteristics of a signal, but also enhance the neural network model's ability to understand the signal structure.

[0123] During the online application phase, adaptive regularization parameters are applied to newly acquired magnetotelluric time-series data segments. The calculation method is as follows:

[0124] Extract each standardized signal segment Multidimensional feature vectors ;

[0125] Will Input a pre-trained neural network model to obtain the predicted value of the regularization parameter scaling factor. ;

[0126] Calculate this signal segment DCT coefficients Take its largest absolute value The online adaptive regularization parameters are obtained. :

[0127] .

[0128] The above online adaptive regularization parameters Substituting the above convex optimization model and Greedy FISTA algorithm, the compressed measurement vector of this signal segment can be reconstructed to obtain the reconstructed time-domain signal. .

[0129] Through the above steps, this embodiment of the invention achieves adaptive regularization parameters using a neural network model. The adaptive selection allows for the selection of a more suitable sparse canonical intensity for magnetotelluric signal segments with different time-domain and frequency-domain characteristics, thereby achieving a more stable and slightly better reconstruction effect.

[0130] In this embodiment of the invention, considering the concentrated and approximately sparse energy characteristics of magnetotelluric data in the DCT transform domain, DCT is used as a sparse representation basis. At the measurement end, compressed sampling of the original signal is achieved through random linear observations, and at the reconstruction end, signal recovery is achieved through Greedy FISTA. Compared with traditional processing methods, this embodiment explicitly introduces the concept of "sparse prior + compressed sensing" into the mathematical model, achieving higher fidelity magnetotelluric signal reconstruction results while ensuring the compression ratio, thus balancing data compression efficiency and reconstruction quality.

[0131] Furthermore, in the core reconstruction stage, this embodiment of the invention employs DCT and Greedy FISTA for solving. Compared to methods that directly generate reconstructed signals end-to-end using large neural networks, the backbone algorithm of this embodiment maintains a clear objective function form, standardized iterative update steps, and analyzable convergence characteristics, exhibiting good physical meaning and mathematical interpretability. In magnetotelluric exploration, where data reliability and interpretability are crucial, the solution provided by this embodiment is easier for engineers to understand, debug, and verify, improving the stability and controllability of engineering applications.

[0132] In another embodiment of the present invention, a magnetotelluric data compressed sensing reconstruction system is also provided for implementing the above-described magnetotelluric data compressed sensing reconstruction method, specifically including:

[0133] The data preprocessing module 10 is used to acquire raw magnetotelluric time series data and perform segmentation and standardization preprocessing to obtain multiple standardized signal segments;

[0134] The compression modeling module 20 is used to transform each standardized signal segment to obtain a sparse representation in the transform domain, and to compress and sample the sparse representation in the transform domain to obtain a compressed measurement vector.

[0135] Feature extraction module 30 is used to extract multi-dimensional feature vectors for each signal segment based on compressed measurement vectors;

[0136] The regularization parameter prediction module 40 is used to predict the corresponding regularization parameter scaling factor based on the multidimensional feature vector according to the preset neural network model, and to calculate the adaptive regularization parameter for the L1 sparse regularization term.

[0137] The data reconstruction module 50 is used to construct a convex optimization model containing L2 data fidelity terms and L1 sparse regularization terms with adaptive regularization parameters as the regularization intensity, and to reconstruct magnetotelluric time series data based on a greedy acceleration iterative shrinkage threshold algorithm.

[0138] It should be noted that each of the above modules can be implemented as a computer program, which can run on a computer device. The computer device's memory can store the computer program comprising each module, enabling the processor to execute the various steps of the above method. The modules of this system can be integrated into the same computing platform via software, or they can be deployed in a distributed manner, running on different processing nodes, and achieving data interaction and task coordination through network communication.

[0139] It should be understood that although the steps in the flowcharts of the embodiments of the present invention are shown sequentially according to the arrows, these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least some steps in each embodiment may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be performed alternately or in turn with other steps or at least a portion of the sub-steps or stages of other steps.

[0140] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods.

[0141] The above embodiments merely illustrate several implementation methods of the present invention, and their descriptions are relatively specific and detailed, but they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this patent should be determined by the appended claims.

Claims

1. A method for compressed sensing and reconstruction of magnetotelluric data, characterized in that, Includes the following steps: The raw magnetotelluric time series data were acquired and segmented and standardized preprocessed to obtain multiple standardized signal segments; Each standardized signal segment is transformed to obtain a sparse representation in the transform domain, and the sparse representation in the transform domain is compressed and sampled to obtain a compressed measurement vector; Based on the compressed measurement vector, a multidimensional feature vector is extracted for each signal segment; Based on the preset neural network model, the corresponding regularization parameter scaling factor is predicted according to the multi-dimensional feature vector, and the adaptive regularization parameter for the L1 sparse regularization term is calculated. Using adaptive regularization parameters as the regularization strength, a convex optimization model containing L2 data fidelity terms and L1 sparse regularization terms is constructed, and magnetotelluric time series data are reconstructed based on a greedy accelerated iterative shrinkage threshold algorithm. The compressed sampling method includes: For each signal segment Using a random Gaussian matrix Perform linear compressed sampling: ； in, For compressing the measurement vector; measurement number Compression ratio Random Gaussian matrix The elements satisfy: ； The transformation is a DCT transformation; the convex optimization model containing L2 data fidelity terms and L1 sparse regularization terms is as follows: ； in, Let be the sparse coefficient vector of the DCT domain to be reconstructed, and ;remember For L2 data fidelity items; This is an L1 sparse regularization term; For adaptive regularization parameters; Then the objective function for: ； Define linear operators Then the gradient of the L2 data fidelity term f(z) for: in, Represents the inverse discrete cosine transform matrix; Represents the discrete cosine transform matrix; For L1 sparse regularization terms, the proximal operator is: : ； In the formula, The input vector is the result of subtracting the gradient from the current iteration point; Step size; This is a sign function that operates on each element of the vector. If the element is greater than 0, it outputs 1; if it is less than 0, it outputs -1; and if it is equal to 0, it outputs 0. It represents the Hadamardi (or Hadama) stack; A greedy, accelerated iterative threshold shrinkage algorithm is used to solve a convex optimization model containing L2 data fidelity terms and L1 sparse regularization terms. The greedy, accelerated iterative threshold shrinkage algorithm performs the following operations in each iteration: First, set the initial values ​​for optimization. And set the initial value of the acceleration iteration point. Set the maximum number of iterations (maxits) and tolerance. and initial step size ; In the In the next iteration, based on the current accelerated iteration point Calculate the gradient of the current solution And use near-end operations to update the current solution. The proximal operation is performed through: Completed; among them, For the proximal operator of L1 sparse regularization terms, in the proximal operator For the adaptive regularization parameters of the current signal segment, during the online prediction stage: Predicted by a neural network model; Offline training phase: , which are candidate regularization parameters; For the first The step size of the next iteration; The gradient function for the L2 data fidelity term; Introducing a momentum mechanism, in each iteration, the current solution is calculated... Compared with the last solution The difference, combined with the momentum parameter For the next iteration point Update; After each iteration, compute the current solution. And the last solution The difference; when the difference exceeds a preset threshold, a greedy restart is performed, and the iteration point is accelerated. Reset to the current solution Simultaneously, the current solution is calculated after each iteration. Compared with the last solution The residuals between them are used to determine whether convergence has occurred; when the residuals are less than a preset tolerance... When the iteration ends, proceed. In each iteration, record the current value of the objective function. The step size is dynamically adjusted through a step size control strategy; if the current residual increases beyond the set safety factor, the step size will be reduced; when the residual is less than the preset tolerance... When the residual exceeds the preset divergence threshold, the algorithm stops early and outputs the final result.

2. The magnetotelluric data compressed sensing reconstruction method according to claim 1, characterized in that, The segments are divided using a preset fixed length, with either no overlap or partial overlap.

3. The magnetotelluric data compressed sensing reconstruction method according to claim 1, characterized in that, The transformation can be any one of wavelet transform, Fourier transform, and DCT transform.

4. The magnetotelluric data compressed sensing reconstruction method according to claim 1, characterized in that, The adaptive regularization parameter The calculation method is as follows: Extract each standardized signal segment Multidimensional feature vectors ; Will Input a pre-trained neural network model to obtain the predicted value of the regularization parameter scaling factor. ; Calculate this signal segment DCT coefficients Take its largest absolute value The online adaptive regularization parameters are obtained. : 。 5. The magnetotelluric data compressed sensing reconstruction method according to claim 4, characterized in that, The neural network model constructs a "pseudo-optimal" structure. Learning multidimensional feature vectors and adaptive regularization parameters on datasets labeled "scale factor" The mapping relationship between them; wherein, the pseudo-optimal The scaling factor is generated as follows: Define a set of candidate regularization parameter scaling factors : ； For each signal segment First, calculate its DCT coefficients. Based on this, the maximum absolute value of the DCT coefficients of the signal is selected as the key feature value of the signal. : ； For each candidate regularization parameter scaling factor Define the corresponding regularization parameters. : ； For the same signal segment , in turn Substituting into the convex optimization model, we obtain the corresponding reconstructed signal. And calculate its mean square error. and signal-to-noise ratio : ； ； Among all candidate regularization parameter scaling factors, the one that maximizes the signal-to-noise ratio is selected as the pseudo-optimal for that signal segment. Scale factor : ； in, The length of the signal. The original signal, For the corresponding adaptive regularization parameters Reconstructed signal.

6. The magnetotelluric data compressed sensing reconstruction method according to claim 1, 4, or 5, characterized in that, The method for extracting the multidimensional feature vector includes: Extract the time-domain features of the signal segment; Extract the frequency domain features of the signal segment; By fusing time-domain features and frequency-domain features, a multi-dimensional feature vector is obtained.

7. A magnetotelluric data compressed sensing reconstruction system, used to implement the magnetotelluric data compressed sensing reconstruction method according to any one of claims 1-6, characterized in that, include: The data preprocessing module is used to acquire raw magnetotelluric time series data and perform segmentation and standardization preprocessing to obtain multiple standardized signal segments; The compression modeling module is used to transform each standardized signal segment to obtain a sparse representation in the transform domain, and to compress and sample the sparse representation in the transform domain to obtain a compressed measurement vector. The feature extraction module is used to extract multi-dimensional feature vectors for each signal segment based on the compressed measurement vector; The regularization parameter prediction module is used to predict the corresponding regularization parameter scaling factor based on the multidimensional feature vector of the preset neural network model, and to calculate the adaptive regularization parameter for the L1 sparse regularization term. The data reconstruction module is used to construct a convex optimization model containing L2 data fidelity terms and L1 sparse regularization terms with adaptive regularization parameters as the regularization strength, and to reconstruct magnetotelluric time series data based on a greedy acceleration iterative shrinkage threshold algorithm.

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