A Controllable Source Electromagnetic Data Denoising Method Based on Residual Denoising Convolutional Network and Time-Invariant Sparse Coding

Abstract

This invention discloses a method for denoising controllable source electromagnetic data based on a residual denoising convolutional network and time-invariant sparse coding. The method includes the following steps: Step 1: Separating signal and noise from typical measured controllable source electromagnetic data using time-invariant sparse coding to obtain high-quality data and measured noise; Step 2: Constructing a residual denoising convolutional network and training it with the obtained sample library to obtain a network model for denoising controllable source electromagnetic data; Step 3: Inputting the noisy controllable source electromagnetic data to be processed into the trained denoising model for noise reduction to obtain preliminary denoising results; Step 4: Performing signal and noise separation again on the denoising results obtained in Step 3 using time-invariant sparse coding to obtain the final denoised signal. This invention is used for denoising controllable source electromagnetic data, achieving automated and rapid removal of various types and intensities of noise; further enhanced by a dictionary learning method, it maximizes the data denoising effect.

Description

Technical Field

[0001] This invention belongs to the field of geophysical signal processing technology, specifically relating to a controllable source electromagnetic data denoising method based on residual denoising convolutional networks and shift-invariant sparse coding. Background Technology

[0002] Controlled-source electromagnetic methods (CMEs) primarily use controlled artificial field sources to replace natural field sources, thus exhibiting higher anti-interference capabilities. They are currently finding wider application in shale gas exploration, metal ore exploration, and engineering geophysical exploration. However, during actual exploration, the collected signals are inevitably contaminated by noise, mainly from geological noise and human-caused noise. While geological noise poses a far less significant threat to CMEs than human-caused noise, the negative impact of human-caused noise is expanding and its signal contamination is becoming increasingly severe with the increasing prevalence of urban industrialization. Therefore, removing human-caused noise from signals remains an important task.

[0003] Faced with severe human noise pollution, the most common approach is to manually filter the data and set a relevance threshold. However, this method is inefficient and easily affected by the subjective factors of the selectors, and the final selection results may not be satisfactory. Therefore, traditional methods are not effective in denoising when human noise pollution is severe.

[0004] With the rise of deep learning technology in recent years, its application in the field of geophysics has become increasingly widespread. Deep learning is highly adaptable, capable of building different networks to meet diverse needs. For the requirement of denoising controlled-source data, residual and convolutional methods are better suited. Therefore, how to utilize these technologies to build deep learning networks for denoising controlled-source data warrants further exploration and research. Summary of the Invention

[0005] The purpose of this invention is to address the shortcomings of existing technologies and provide a controllable source electromagnetic data denoising method based on residual denoising convolution-shift invariant sparse coding.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] A method for denoising controllable source electromagnetic data based on residual denoising convolutional networks and time-invariant sparse coding includes the following steps:

[0008] Step 1: Separate the signal-to-noise ratio (SNR) of the measured controllable source electromagnetic data using time-invariant sparse coding (SISC) to obtain high-quality data and measured noise. Multiply the measured noise by different factors to obtain a series of noises with different amplitudes, and add them to the high-quality data to obtain a series of noisy signals with measured noise of different intensities. To improve the diversity of the samples, generate some simulated noises of different types and SNRs through numerical simulation, and add them to the high-quality data extracted by time-invariant sparse coding to obtain a series of noisy signals with simulated noise of different intensities. Segment and pair the above noisy signals with the high-quality signals to construct a controllable source electromagnetic data sample library.

[0009] Step 2: Build a residual denoising convolutional network, input the obtained sample library into the residual denoising convolutional network for training, and obtain a network model for denoising controllable source electromagnetic data.

[0010] Step 3: Input the electromagnetic noise data of the controllable source to be processed into the trained denoising model to obtain preliminary denoising results.

[0011] Step 4: Use shift-invariant sparse coding to perform signal-to-noise separation again on the denoising result obtained in step 3 to obtain the final denoised signal.

[0012] Furthermore, the controllable source electromagnetic data is a one-dimensional periodic signal with a sampling rate of 1200Hz. Based on the data characteristics, this invention sets the length of each data period to 1200 sampling points, resulting in a data size of 1×1200 for each period.

[0013] Furthermore, the sample library creation process for the residual denoising convolutional network is as follows: The high-quality data separated by SISC is copied 120 times and numbered 1-120. 1-30 dB Gaussian white noise is added to data points 1-30; after adding 1-30 dB Gaussian white noise to data points 31-60, impulse noise of different amplitudes is randomly added to each; after adding 1-30 dB Gaussian white noise to data points 61-90, square wave noise of different amplitudes is randomly added to each; and 1-30 times the actual noise separated by SISC is added to data points 91-120. This results in 120 pairs of samples containing different types and amplitudes of noise. By selecting different typical noisy data and creating a training set according to the above process, the sample size is expanded to over 20,000.

[0014] Furthermore, the residual denoising convolutional network contains two types of residual modules. The first type, the identity residual module, is represented as follows:

[0015] x l+1 =x l +F(x l W l (1)

[0016] In the formula, x l It is a residual block input, x l+1 It is the residual block output, F(x) l W l ) is the residual part;

[0017] The identity residual block is responsible for ensuring that the input data and output data have the same dimensions before and after;

[0018] The second type of convolutional residual module is represented as follows:

[0019] x l+1 =h(x l )+F(x l W l (2)

[0020] In the formula, h(x) l )=W′ l x. W′ l It is a 1×1 convolution operation, x l It is a residual block input, x l+1 It is the residual block output, F(x) l W l ) is the residual part;

[0021] The convolutional residual module is responsible for upsampling or downsampling through a convolutional layer to ensure that the shape and size of the input and output data are consistent.

[0022] Furthermore, the residual denoising convolutional network consists of an input layer, a hidden layer, and an output layer. Its hidden layer includes several convolutional layers, batch normalization, corrected linear units, and residual modules.

[0023] The shape of the input layer is: sample length multiplied by the number of channels, i.e., n×1.

[0024] The hidden layer consists of twenty-eight parts arranged in sequence: convolutional layer 1, convolutional layers 2-17, convolutional layer 18, convolutional layer 19, identity residual block 20, identity residual block 21, convolutional residual block 22, identity residual block 23, convolutional residual block 24, identity residual block 25, convolutional residual block 26, identity residual block 27, and average pooling layer 28. The hidden layer is:

[0025] Convolutional layer 1 consists of a 3×1 convolutional kernel and a ReLU activation function.

[0026] Convolutional layers 2-17 consist of 64 3×1 convolutional kernels, batch normalization (BN) layers, and a ReLU activation function, repeated 16 times.

[0027] Convolutional layer 18 consists of 64 convolutional kernels with a size of 3×1.

[0028] Convolutional layer 19 consists of two 3×1 convolutional kernels, a batch normalization (BN) layer, and a ReLU activation function.

[0029] The identity residual block 20 consists of 64 convolutional kernels of size 3×1, a batch normalization layer (BN), a ReLU activation function, and a summation function.

[0030] The identity residual block 21 consists of 64 convolutional kernels of size 3×1, a batch normalization layer (BN), a ReLU activation function, and a summation function.

[0031] The convolutional residual block 22 consists of: 128 one-dimensional convolutions with a size of 3×1 and a stride of 2, 128 one-dimensional pointwise convolutions with a size of 1×1 and a stride of 2, a batch normalization layer (BN), a ReLU activation function, and a summation function.

[0032] The identity residual block 23 consists of 128 convolutional kernels of size 3×1, a batch normalization layer (BN), a ReLU activation function, and a summation function.

[0033] The convolutional residual block 24 consists of: 256 one-dimensional convolutions with a size of 3×1 and a stride of 2, 256 one-dimensional pointwise convolutions with a size of 1×1 and a stride of 2, a batch normalization layer (BN), a ReLU activation function, and a summation function.

[0034] The identity residual block 25 consists of 256 convolutional kernels of size 3×1, batch normalization (BN) layers, a ReLU activation function, and a summation function.

[0035] The convolutional residual block 26 consists of: 512 one-dimensional convolutions with a size of 3×1 and a stride of 2, 512 one-dimensional pointwise convolutions with a size of 1×1 and a stride of 2, a batch normalization layer (BN), a ReLU activation function, and a summation function.

[0036] The identity residual block 27 consists of 512 convolutional kernels of size 3×1, batch normalization (BN) layers, a ReLU activation function, and a summation function.

[0037] The average pooling layer 28 is: a convolutional layer with a kernel size of 3 and a stride of 1, using the average value as the filter.

[0038] It should be noted that the number of residual blocks, the number of convolutional kernels, and their sizes are set based on the model training effect. Therefore, the above examples are only illustrative, and the number of residual blocks, the size of convolutional kernels, and their sizes can be adjusted without departing from the concept of this invention.

[0039] The output layer consists of a Dropout layer, a fully connected layer, and a summation function.

[0040] During training, the number of input data channels increases regularly, but after training, the number of channels is changed through a fully connected layer to make the output data size the same as the input data.

[0041] Furthermore, before using time-invariant sparse coding, the pre-processed signal X is divided into K segments. With a sampling rate of 1200Hz and a segment duration of 1 minute, each segment occupies 72000 sampling points, i.e., X = [x1, x2, ..., x...]. k ] T x k = [x1, x2, ..., x N ] T N = 72000, SISC uses an overcomplete dictionary D = [d1, d2, ..., d...] containing M bases (or atoms). M ]∈R Q×M , will x k Represented as the sum of the convolutions of the basis and coefficients:

[0042]

[0043] In the formula, "*" represents convolution, and the encoding coefficient vector s m,k ∈R p It is sparse, meaning it has only a small number of non-zero coefficients; ε is Gaussian white noise; Q < N, P < N, and Q + P - 1 = N; dictionary atom d m and coding coefficients s m,k Since both are unknown, simultaneously solving them results in a non-convex optimization problem, making it difficult to obtain a stable solution. Therefore, by alternating updates, the problem is transformed into a convex optimization problem, which is iteratively solved repeatedly. When d is fixed... m When the sparse representation coefficients s are constant, the convex optimization method is used to solve for them. m,k When s is fixed m,k When the dictionary atom d remains unchanged, solve for the dictionary atom d using a convex optimization method. m Sparsity is a common objective of the two optimization problems mentioned above, and the evaluation of y k The cost function for sparsity is:

[0044]

[0045] In the formula ||·|| F Indicate l F Norm, β is a constraint used to balance reconstruction error and sparsity, d m Normalization is usually required, i.e. The basic process of shift-invariant sparse coding is as follows:

[0046] Input: Preliminary processing signal X, type of feature atom α, width of feature atom W = [W1, W2, ... W2] α The total number of characteristic atoms (i.e., sparsity) L, the maximum number of iterations z (15 in this invention), and the convergence target e < 10 -6 ;

[0047] Initialization: Randomly assign initial values ​​to D and s;

[0048] Execute the following content z times in a loop:

[0049] {

[0050] Solving for coefficients

[0051] Dictionary update

[0052] }

[0053] The loop stops when the maximum number of iterations is reached or the convergence target is achieved.

[0054] Output: Complete dictionary D and reconstructed signal This refers to the extracted valid signal.

[0055] Furthermore, let g i，u Characteristic atom d i The length of the atom after shifting point u and filling in zeros is the same as that of x. k Same, and ||g i，u || = 1, maximum number of loops L max The residual after the Lth iteration is r L The set of atoms ψ selected after the Lth iteration L The steps for solving the coefficients are as follows:

[0056] 1) Parameter initialization, r 0 =x k , L = 1;

[0057] 2) Select the atom g that best matches the current residual. i，u It satisfies:

[0058]

[0059] 3) Update the set of selected atoms.

[0060] 4) Calculate the projection coefficients using the least squares method. residual r L =x k -s L ψ L Reconstructed signal

[0061] 5) Determine if L has reached its maximum value. max If not, L = L + 1, and proceed to step 2) to execute the loop; otherwise, output the reconstruction signal.

[0062] Furthermore, the shift-invariant sparse coding dictionary update is achieved through the following steps: keeping the coefficients unchanged and updating only the base. This optimization function can be simplified to:

[0063]

[0064]

[0065] In the formula, matrix E i，k This represents all errors of the k-th signal excluding the i-th basis; updating the i-th basis is transformed into solving for d. i The system of equations, due to d i *s i，k =s i，k *d i First, we analyze the optimization problem when there is only the k-th signal, which is equivalent to solving the following equation:

[0066]

[0067] The matrix on the left side of the above formula is considered as coefficients s. i，k A special type of Toeplitz matrix, the above equation can be written as Toep(s i，k )·d i =E i，k Due to the coefficient s i，k It is sparse, the matrix Toep(s) i，k Many rows in Toep(s) are O vectors, which have no effect on the result. These rows are removed from the matrix Toep(s). i，k Remove from ) and simultaneously remove vector E i The corresponding row is removed, represented as When considering K signals simultaneously, the optimization function ψ(θ) can be expressed as:

[0068]

[0069] The above formula can be simplified to S·d i =E, and according to the least squares method, d can be obtained. i =(S T S) -1 (S T E), matrix (S) T S)∈R Q×QIn general, Q << N, so the solution ultimately becomes finding the solution to a small-scale system of linear equations. This solution process directly obtains the optimal value through Cholesky decomposition, updating each basis in a random order to find the optimal solution for the basis in the current cycle. Then, the basis d is updated sequentially. i Standardized processing This will give you the complete dictionary D.

[0070] The beneficial effects of this invention are as follows: 1. Addressing the problems of traditional controllable source electromagnetic data denoising methods requiring manual threshold setting and insufficient adaptability to different types of noise, this invention proposes a highly efficient, automated, and adaptable denoising method based on deep learning. By introducing the concept of residual modules and convolutional denoising from deep learning, complementary advantages are achieved, improving the accuracy of controllable source electromagnetic data denoising while reducing the loss of high-quality data during the denoising process, effectively avoiding the subjective bias caused by traditional manually set threshold denoising.

[0071] 2. To address the pseudo-random square wave characteristics of controllable source electromagnetic data, a novel deep learning network is constructed. The residual denoising convolutional network built in this invention has undergone the following optimizations: The network employs skip connections, ensuring that even if the data in the residual layer changes, the input data is preserved and transmitted intact to the output, guaranteeing that the chained multiplication in the residual layer becomes a chained addition, thus preventing gradient vanishing or gradient explosion during node parameter updates. Secondly, the network in this invention uses an identity mapping to the input of the redundant layer above, ensuring that the network performance remains unchanged even with redundant layers, largely solving the network degradation problem. Through these optimizations, the denoising effect of this invention for controllable source electromagnetic data is significantly improved.

[0072] 3. The residual denoising convolutional network constructed in this invention uses a sample library created from data obtained through SISC signal-to-noise separation of actual measured data during training. SISC can autonomously learn the characteristic structure of noise in noisy signals, thereby constructing a learning-based redundant dictionary. This dictionary can be flexibly modified for different measured data, achieving good denoising results without manual intervention. Compared with other time series editing methods, Li Guanget. (2021) has proven that SISC performs best and is most reliable among traditional methods in controlled-source denoising, but this is limited to cases where the noise intensity is not too high. Using data obtained through SISC signal-to-noise separation to create a sample library is beneficial to improving the realism of the network training results. Moreover, some noise in the sample library comes from real data, which matches the real situation and is beneficial for deep networks to learn the features of actual noise. By using time-invariant sparse coding to create a training set for training deep learning networks, a denoising effect far exceeding that of time-invariant sparse coding is finally obtained.

[0073] 4. The effectiveness of deep learning denoising mainly depends on the training set and is not significantly related to the noise intensity. This invention uses deep learning to suppress strong noise, but the data processed by deep learning still retains a large amount of weak noise. Shift-invariant sparse coding has an excellent denoising effect on weak noise. After deep learning denoising, shift-invariant sparse coding is used again for denoising to remove the weak noise remaining in the unsmooth signal and maximize the improvement of signal quality.

[0074] This invention can intelligently and efficiently denoise multiple types of controllable source electromagnetic data, significantly improve the signal-to-noise ratio of controllable source electromagnetic data, and enhance the detection effect of controllable source electromagnetic methods. Attached Figure Description

[0075] Figure 1 This is a flowchart illustrating the structure of the present invention;

[0076] Figure 2 This is a sample library data diagram provided by the present invention;

[0077] Figure 3 This is a schematic diagram of the residual denoising convolutional network structure;

[0078] Figure 4 This is a schematic diagram of the residual block structure provided by the present invention;

[0079] Figure 5 This is a training result diagram of the network model loss;

[0080] Figure 6 This is a diagram showing the effect of using the model to denoise the simulation data;

[0081] Figure 7 It represents the time series effect before and after synthetic data processing;

[0082] Figure 8 It is a comparison chart of apparent resistivity-phase curves before and after synthetic data processing;

[0083] Figure 9 It is a comparison chart of apparent resistivity-phase curves before and after actual data processing. Detailed Implementation

[0084] A method for denoising controllable source electromagnetic data based on residual denoising convolutional networks and time-invariant sparse coding includes the following steps:

[0085] Step 1: Separate the signal-to-noise ratio (SNR) of the measured controllable source electromagnetic data using time-invariant sparse coding (SISC) to obtain high-quality data and measured noise. Multiply the measured noise by different factors to obtain a series of noises with different amplitudes, and add them to the high-quality data to obtain a series of noisy signals with measured noise of different intensities. To improve the diversity of the samples, generate some simulated noises of different types and SNRs through numerical simulation, and add them to the high-quality data extracted by time-invariant sparse coding to obtain a series of noisy signals with simulated noise of different intensities. Segment and pair the above noisy signals with the high-quality signals to construct a controllable source electromagnetic data sample library.

[0086] Step 2: Construct a residual denoising convolutional network, and train it with the obtained sample database to obtain a network model for denoising controllable source electromagnetic data.

[0087] Step 3: Input the noisy electromagnetic data A from the controllable source to be processed into the trained denoising model to obtain the preliminary denoising result B;

[0088] Step 4: Use shift-invariant sparse coding to perform signal-to-noise separation again on the denoised result B obtained in step 3 to obtain the final denoised signal C.

[0089] Furthermore, the controllable source electromagnetic data is a one-dimensional periodic signal with a sampling rate of 1200Hz. Based on the data characteristics, this invention sets the length of each data period to 1200 sampling points, resulting in a data size of 1×1200 for each period.

[0090] Furthermore, the sample library creation process for the residual denoising convolutional network is as follows: The high-quality data separated by SISC is copied 120 times and numbered 1-120. 1-30 dB Gaussian white noise is added to data points 1-30; after adding 1-30 dB Gaussian white noise to data points 31-60, impulse noise of different amplitudes is randomly added to each; after adding 1-30 dB Gaussian white noise to data points 61-90, square wave noise of different amplitudes is randomly added to each; and 1-30 times the actual noise separated by SISC is added to data points 91-120. This results in 120 pairs of samples containing different types and amplitudes of noise. By selecting different typical noisy data and creating a training set according to the above process, the sample size is expanded to over 20,000.

[0091] Furthermore, the residual denoising convolutional network contains two types of residual modules. The first type, the identity residual module, is represented as follows:

[0092] x l+1 =x l +F(x l W l (1)

[0093] In the formula, x l It is a residual block input, x l+1 It is the residual block output, F(x) l W l ) is the residual part;

[0094] The identity residual block is responsible for ensuring that the input data and output data have the same dimensions before and after;

[0095] The second type of convolutional residual module is represented as follows:

[0096] x l+1 =h(x l )+F(x l W l (2)

[0097] In the formula, h(x) l )=W′ l x. W′ l It is a 1×1 convolution operation, x l It is a residual block input, x l+1 It is the residual block output, F(x) l W l ) is the residual part;

[0098] The convolutional residual module is responsible for upsampling or downsampling through a convolutional layer to ensure that the shape and size of the input and output data are consistent.

[0099] Furthermore, the residual denoising convolutional network consists of an input layer, a hidden layer, and an output layer. Its hidden layer includes several convolutional layers, batch normalization, corrected linear units, and residual modules.

[0100] The shape of the input layer is: sample length multiplied by the number of channels, i.e., n×1.

[0101] The hidden layer consists of twenty-eight parts arranged in sequence: convolutional layer 1, convolutional layers 2-17, convolutional layer 18, convolutional layer 19, identity residual block 20, identity residual block 21, convolutional residual block 22, identity residual block 23, convolutional residual block 24, identity residual block 25, convolutional residual block 26, identity residual block 27, and average pooling layer 28. The hidden layer is:

[0102] Convolutional layer 1 consists of a 3×1 convolutional kernel and a ReLU activation function.

[0103] Convolutional layers 2-17 consist of 64 3×1 convolutional kernels, batch normalization (BN) layers, and a ReLU activation function, repeated 16 times.

[0104] Convolutional layer 18 consists of 64 convolutional kernels with a size of 3×1.

[0105] Convolutional layer 19 consists of two 3×1 convolutional kernels, a batch normalization (BN) layer, and a ReLU activation function.

[0106] The identity residual block 20 consists of 64 convolutional kernels of size 3×1, a batch normalization layer (BN), a ReLU activation function, and a summation function.

[0107] The identity residual block 21 consists of 64 convolutional kernels of size 3×1, a batch normalization layer (BN), a ReLU activation function, and a summation function.

[0108] The convolutional residual block 22 consists of: 128 one-dimensional convolutions with a size of 3×1 and a stride of 2, 128 one-dimensional pointwise convolutions with a size of 1×1 and a stride of 2, a batch normalization layer (BN), a ReLU activation function, and a summation function.

[0109] The identity residual block 23 consists of 128 convolutional kernels of size 3×1, a batch normalization layer (BN), a ReLU activation function, and a summation function.

[0110] The convolutional residual block 24 consists of: 256 one-dimensional convolutions with a size of 3×1 and a stride of 2, 256 one-dimensional pointwise convolutions with a size of 1×1 and a stride of 2, a batch normalization layer (BN), a ReLU activation function, and a summation function.

[0111] The identity residual block 25 consists of 256 convolutional kernels of size 3×1, batch normalization (BN) layers, a ReLU activation function, and a summation function.

[0112] The convolutional residual block 26 consists of: 512 one-dimensional convolutions with a size of 3×1 and a stride of 2, 512 one-dimensional pointwise convolutions with a size of 1×1 and a stride of 2, a batch normalization layer (BN), a ReLU activation function, and a summation function.

[0113] The identity residual block 27 consists of 512 convolutional kernels of size 3×1, batch normalization (BN) layers, a ReLU activation function, and a summation function.

[0114] The average pooling layer 28 is: a convolutional layer with a kernel size of 3 and a stride of 1, using the average value as the filter.

[0115] It should be noted that the number of residual blocks, the number of convolutional kernels, and their sizes are set based on the model training effect. Therefore, the above examples are only illustrative, and the number of residual blocks, the size of convolutional kernels, and their sizes can be adjusted without departing from the concept of this invention.

[0116] The output layer consists of a Dropout layer, a fully connected layer, and a summation function.

[0117] During training, the number of input data channels increases regularly, but after training, the number of channels is changed through a fully connected layer to make the output data size the same as the input data.

[0118] Furthermore, before using time-invariant sparse coding, the pre-processed signal X is divided into K segments. With a sampling rate of 1200Hz and a segment duration of 1 minute, each segment occupies 72000 sampling points, i.e., X = [x1, x2, ..., x...]. k ] T x k = [x1, x2, ..., x N ] T N = 72000, SISC uses an overcomplete dictionary D = [d1, d2, ..., d...] containing M bases (or atoms). M ]∈R Q×M , will x k Represented as the sum of the convolutions of the basis and coefficients:

[0119]

[0120] In the formula, "*" represents convolution, and the encoding coefficient vector s m，k ∈R p It is sparse, meaning it has only a small number of non-zero coefficients; ε is Gaussian white noise; Q < N, P < N, and Q + P - 1 = N; dictionary atom d m and coding coefficients s m，k Since both are unknown, simultaneously solving them results in a non-convex optimization problem, making it difficult to obtain a stable solution. Therefore, by alternating updates, the problem is transformed into a convex optimization problem, which is iteratively solved repeatedly. When d is fixed... m When the sparse representation coefficients s are constant, the convex optimization method is used to solve for them. m，k When s is fixed m，k When the dictionary atom d remains unchanged, solve for the dictionary atom d using a convex optimization method. m Sparsity is a common objective of the two optimization problems mentioned above, and the evaluation of y k The cost function for sparsity is:

[0121]

[0122] In the formula ||·|| F Indicate l F Norm, β is a constraint used to balance reconstruction error and sparsity, d m Normalization is usually required, i.e. The basic process of shift-invariant sparse coding is as follows:

[0123] Input: Preliminary processing signal X, type of feature atom α, width of feature atom W = [W1, W2, ... W α The total number of feature atoms L represents the sparsity, the maximum number of iterations z (15 in this invention), and the convergence target e < 10. -6 ;

[0124] Initialization: Randomly assign initial values ​​to D and s;

[0125] Execute the following content z times in a loop:

[0126] {

[0127] Solving for coefficients

[0128] Dictionary update

[0129] }

[0130] The loop stops when the maximum number of iterations is reached or the convergence target is achieved.

[0131] Output: Complete dictionary D and reconstructed signal This refers to the extracted valid signal.

[0132] Furthermore, let g i，u Characteristic atom d i The length of the atom after shifting point u and filling in zeros is the same as that of x. k Same, and ||g i，u || = 1, maximum number of loops L max The residual after the Lth iteration is r L The set of atoms ψ selected after the Lth iteration L The steps for solving the coefficients are as follows:

[0133] 1) Parameter initialization, r 0 =x k , L = 1;

[0134] 2) Select the atom g that best matches the current residual. i，u It satisfies:

[0135]

[0136] 3) Update the set of selected atoms.

[0137] 4) Calculate the projection coefficients using the least squares method. residual r L =x k -s L ψ L Reconstructed signal

[0138] 5) Determine if L has reached its maximum value. max If not, L = L + 1, and proceed to step 2) to execute the loop; otherwise, output the reconstruction signal.

[0139] Furthermore, the shift-invariant sparse coding dictionary update is achieved through the following steps: keeping the coefficients unchanged and updating only the base. This optimization function can be simplified to:

[0140]

[0141] In the formula, matrix E i，k This represents all errors of the k-th signal excluding the i-th basis; updating the i-th basis is transformed into solving for d. i The system of equations, due to d i *s i，k =s i，k *d i First, we analyze the optimization problem when there is only the k-th signal, which is equivalent to solving the following equation:

[0142]

[0143] The matrix on the left side of the above formula is considered as coefficients s. i，k A special type of Toeplitz matrix, the above equation can be written as Toep(s i，k )·d i =E i，k Due to the coefficient s i，k It is sparse, the matrix Toep(s) i，k Many rows in Toep(s) are zero vectors, which have no effect on the result. These rows are removed from the matrix Toep(s). i，k Remove from ) and simultaneously remove vector E i The corresponding row is removed, represented as When considering K signals simultaneously, the optimization function ψ(θ) can be expressed as:

[0144]

[0145] The above formula can be simplified to Sd i =E, and according to the least squares method, d can be obtained. i =(S T S) -1 (S T E), matrix (S) T S)∈R Q×QIn general, Q << N, so the solution ultimately becomes finding the solution to a small-scale system of linear equations. This solution process directly obtains the optimal value through Cholesky decomposition, updating each basis in a random order to find the optimal solution for the basis in the current cycle. Then, the basis d is updated sequentially. i Standardized processing This will give you the complete dictionary D.

[0146] The present invention will now be further described in conjunction with the accompanying drawings and embodiments.

[0147] like Figure 1 As shown in the figure, this embodiment provides a controllable source electromagnetic data denoising method based on residual denoising convolutional networks and time-invariant sparse coding, which includes the following steps:

[0148] Step 1: Separate the signal-to-noise ratio (SNR) of the measured controllable source electromagnetic data using time-invariant sparse coding (SISC) to obtain high-quality data and measured noise. Multiply the measured noise by different factors to obtain a series of noises with different amplitudes, and add them to the high-quality data to obtain a series of noisy signals with measured noise of different intensities. To improve the diversity of the samples, generate some simulated noises of different types and SNRs through numerical simulation, and add them to the high-quality data extracted by time-invariant sparse coding to obtain a series of noisy signals with simulated noise of different intensities. Segment and pair the above noisy signals with the high-quality signals to construct a controllable source electromagnetic data sample library.

[0149] In this embodiment, a sample library is created using measured controllable source electromagnetic data as units, with each sample consisting of 1200 data segments. Let the data used to create the samples be X = {x1, x2, ..., x...}. m}, where m is the data length. Then the time series corresponding to the i-th sample is S. i ={x (i-1)*n+1 x (i-1)*n+2 , ..., x (i-1)*n+n}, Where n is the number of sampling points occupied by a sample, that is, the length of each sample.

[0150] In this example, it is preferable to add different types of simulated noise and noise contained in actual data to the data. The sample library creation process of the residual denoising convolutional network is as follows: high-quality data separated by SISC is copied 120 times and numbered 1-120. 1-30dB Gaussian white noise is added to data 1-30 respectively; after adding 1-30dB Gaussian white noise to data 31-60, impulse noise of different amplitudes is randomly added to each; after adding 1-30dB Gaussian white noise to data 61-90, square wave noise of different amplitudes is randomly added to each; 1-30 times the actual noise separated by SISC is added to data 91-120. Finally, 120 pairs of samples containing different types and amplitudes of noise are obtained. By selecting different typical noisy data and creating training sets according to the above process, the number of samples is expanded to more than 20,000.

[0151] like Figure 2 The diagram shows some of the noise addition types in the sample library. (a), (b), and (c) are high-quality sample signals containing different sizes of Gaussian white noise; (d), (e), and (f) are high-quality sample signals containing different Gaussian white noise and different impulse noise; and (g), (h), and (i) are high-quality sample signals containing different Gaussian white noise and different square wave noise.

[0152] Step 2: Build a residual denoising convolutional network, input the obtained sample library into the residual denoising convolutional network for training, and obtain a network model for denoising controllable source electromagnetic data.

[0153] Residual denoising convolutional networks are constructed using the concept of residual modules and the idea of ​​convolutional denoising. They are a variant of convolutional neural networks used for sequence modeling tasks.

[0154] like Figure 3 As shown, the residual denoising convolutional network model consists of three parts: an input layer, a hidden layer, and an output layer. The shape of the input layer is: the sample length multiplied by the number of channels, i.e., n×1.

[0155] In this embodiment, the hidden layer consists of twenty-eight parts arranged sequentially: convolutional layer 1, convolutional layers 2-17, convolutional layer 18, convolutional layer 19, identity residual block 20, identity residual block 21, convolutional residual block 22, identity residual block 23, convolutional residual block 24, identity residual block 25, convolutional residual block 26, identity residual block 27, and average pooling layer 28. The identity residual block contains two 3×1 convolutional kernels in one-dimensional convolution and one identity connection. The convolutional residual block contains two one-dimensional convolutions and one one-dimensional pointwise convolution. (See...) Figure 4 .

[0156] In this embodiment, the calculation process for the 19 convolutional layers, 5 identity residual blocks, 3 convolutional residual blocks, and max pooling layer 1 is as follows:

[0157] The steps for convolutional layer 1 are as follows: convolve the sample database data using a 3×1 convolutional kernel and activate it with "ReLU", then output the result of convolutional layer 1.

[0158] The steps of convolutional layers 2-17 are as follows: each layer convolves the input data of the previous layer with 64 convolutional kernels of size 3×1, then uses batch normalization (BN) layer to normalize the output data to stabilize the output distribution, and uses "ReLU" activation. This process is repeated for 16 layers, and finally outputs the result of convolutional layer 17.

[0159] The steps of convolutional layer 18 are as follows: convolve the result of convolutional layer 17 using 64 convolutional kernels of size 3×1, and output the result of convolutional layer 18.

[0160] The steps of convolutional layer 19 are as follows: the result of convolutional layer 18 and the initial input data are concatenated vertically, then two 3×1 convolutional kernels are used to perform one-dimensional convolution, followed by batch normalization layer processing, and "ReLU" activation is used to output the result of convolutional layer 19.

[0161] The steps for the identity residual block 20 are as follows: First, perform a one-dimensional convolution on the result of convolutional layer 19 using 64 convolutional kernels of size 3×1, then process it using a batch normalization layer, and activate it using "ReLU"; Second, perform a one-dimensional convolution on the activation value of the first convolution of identity residual block 20 again using 64 convolutional kernels of size 3×1, and then process it using a batch normalization layer; Third, sum the result of convolutional layer 19 and the second unactivated one-dimensional convolution of identity residual block 20, activate it using "ReLU", and output the result of identity residual block 20.

[0162] The steps for identity residual block 21 are as follows: First, perform one-dimensional convolution on the result of identity residual block 20 using 64 convolution kernels of size 3×1, then process it using a batch normalization layer and activate it with "ReLU"; Second, perform one-dimensional convolution on the activation value of the first convolution of identity residual block 21 again using 64 convolution kernels of size 3×1, then process it using a batch normalization layer; Third, sum the result of identity residual block 20 and the second unactivated one-dimensional convolution of identity residual block 21, activate it with "ReLU", and output the result of identity residual block 21.

[0163] The steps of convolutional residual block 22 are as follows: First, perform 128 one-dimensional convolutions with a kernel size of 3×1 and a stride of 2, and 128 one-dimensional pointwise convolutions with a kernel size of 1×1 and a stride of 2 on the result of residual block 21 respectively. Then, use a batch normalization layer to normalize the two output data. After that, the one-dimensional convolution is activated with "ReLU", and the pointwise convolution is not activated. Second, use 128 kernels with a size of 3×1 to perform one-dimensional convolution on the activation value of the first convolution of convolutional residual block 22 again, and then use a batch normalization layer for processing. Third, sum the result of the pointwise convolution of convolutional residual block 22 and the second one-dimensional convolution of convolutional residual block 22 that is not activated, and activate it with "ReLU" to output the result of convolutional residual block 22.

[0164] The steps for identity residual block 23 are as follows: First, perform one-dimensional convolution on the result of residual block 22 using 128 convolution kernels of size 3×1, then process it using a batch normalization layer and activate it with "ReLU"; Second, perform one-dimensional convolution on the activation value of the first convolution of identity residual block 23 again using 128 convolution kernels of size 3×1, then process it using a batch normalization layer; Third, sum the result of convolution residual block 22 and the second unactivated one-dimensional convolution of identity residual block 23, activate it with "ReLU", and output the result of identity residual block 23.

[0165] The steps of convolutional residual block 24 are as follows: First, perform 256 one-dimensional convolutions with a kernel size of 3×1 and a stride of 2 and 256 one-dimensional pointwise convolutions with a kernel size of 1×1 and a stride of 2 on the result of residual block 23 respectively. Then, use a batch normalization layer to normalize the two output data. After that, the one-dimensional convolution is activated with "ReLU", and the pointwise convolution is not activated. Second, use 256 kernels with a size of 3×1 to perform one-dimensional convolution on the activation value of the first convolution of convolutional residual block 24 again, and then use a batch normalization layer for processing. Third, sum the result of the pointwise convolution of convolutional residual block 24 and the second one-dimensional convolution of convolutional residual block 24 that is not activated, and activate it with "ReLU" to output the result of convolutional residual block 24.

[0166] The steps for identity residual block 25 are as follows: First, perform one-dimensional convolution on the result of residual block 24 using 256 convolution kernels of size 3×1, then process it using a batch normalization layer and activate it with "ReLU"; Second, perform one-dimensional convolution on the activation value of the first convolution of identity residual block 25 again using 256 convolution kernels of size 3×1, then process it using a batch normalization layer; Third, sum the result of convolution residual block 24 and the second unactivated one-dimensional convolution of identity residual block 25, activate it with "ReLU", and output the result of identity residual block 25.

[0167] The steps of convolutional residual block 26 are as follows: First, perform 512 one-dimensional convolutions with a kernel size of 3×1 and a stride of 2, and 512 one-dimensional pointwise convolutions with a kernel size of 1×1 and a stride of 2 on the result of residual block 25 respectively. Then, use a batch normalization layer to normalize the two output data. After that, the one-dimensional convolution is activated with "ReLU", and the pointwise convolution is not activated. Second, use 512 kernels of 3×1 to perform one-dimensional convolution on the activation value of the first convolution of convolutional residual block 26 again, and then use a batch normalization layer for processing. Third, sum the result of the pointwise convolution of convolutional residual block 26 and the second unactivated one-dimensional convolution of convolutional residual block 26, and activate it with "ReLU" to output the result of convolutional residual block 26.

[0168] The steps for identity residual block 27 are as follows: First, perform one-dimensional convolution on the result of convolutional layer 1 using 512 convolutional kernels of size 3×1, then process it using a batch normalization layer, and activate it using "ReLU"; Second, perform one-dimensional convolution on the activation value of the first convolution of identity residual block 27 again using 512 convolutional kernels of size 3×1, and then process it using a batch normalization layer; Third, sum the result of convolutional residual block 26 and the second unactivated one-dimensional convolution of identity residual block 27, activate it using "ReLU", and output the result of identity residual block 27.

[0169] The steps of the average pooling layer 28 are as follows: the results of the identity residual block 27 are filtered using the average value of the convolution kernel with a kernel size of 3 and a stride of 1, and the results of the average pooling layer 28 are output.

[0170] It should be noted that the number of residual blocks, the number of convolutional kernels, and their sizes are set based on the model training effect. Therefore, the above examples are only illustrative, and the number of residual blocks, the size of convolutional kernels, and their sizes can be adjusted without departing from the concept of this invention.

[0171] Finally, the output layer of the residual denoising convolutional network consists of a Dropout layer, a fully connected layer, and a summation function. The Dropout layer zeroes the result of the average pooling layer 28 with a specific probability to prevent overfitting during network training. The fully connected layer flattens the result of the Dropout layer into a 1200×1 one-dimensional sequence. Finally, the result of the fully connected layer is summed with the initial input data to compensate for features lost during training. After training, the trained residual denoising convolutional network model is obtained. The output layer outputs the denoised result of the input data.

[0172] like Figure 5The graph shows the training loss process of the network model. The blue curve represents the change in loss on the training set during model training, and the orange curve represents the change in loss on the validation set after training on the training set. (a) is the training loss curve of our proposed method; (b) and (c) are the loss curves of the comparison methods, where (b) is the training loss curve of the DnCNN network, and (c) is the training loss curve of the ResNet network. From the perspective of the number of training iterations, as the number of training iterations increases, the loss value of our proposed method gradually decreases and eventually stabilizes. This indicates that the model's adaptability to the data is increasing, and the model error is decreasing. The graph shows that the DnCNN network loss is higher than our proposed method. Although the ResNet network loss is lower than our proposed method, the training set loss curve and the validation set loss curve of our proposed method are closer, and the loss curve of our proposed method is smoother. This means that the model has better stability and reliability. The ResNet network's training set loss curve and validation set loss curve differ significantly, and the loss fluctuates greatly, indicating that the ResNet network is unstable and prone to unpredictable results.

[0173] like Figure 6 The figures show the simulation results of the model training. (a), (b), and (c) represent the denoising results of a high-quality sample signal containing different amounts of Gaussian white noise; (d), (e), and (f) represent the denoising results of a high-quality sample signal containing different amounts of Gaussian white noise and different impulse noise; and (g), (h), and (i) represent the denoising results of a high-quality sample signal containing different amounts of Gaussian white noise and different square wave noise. The blue line represents the high-quality signal, and the black line represents the model's denoising results. The good fit between these two lines indicates that the model's simulation denoising effect is very good.

[0174] In this embodiment, the Adam optimizer is selected for model training, with an initial learning rate of 1×10⁻⁶. -5 The learning rate decays by 0.9 every 10 training iterations, the batch size is 130, and the training lasts for 300 epochs. Other feasible implementations are not specifically limited to this, and other optimizers can be selected.

[0175] Step 3: Input the electromagnetic noise-containing data A from the controllable source to be processed into the trained denoising model to obtain the preliminary denoising result B.

[0176] Step 4: Use shift-invariant sparse coding to perform signal-to-noise separation again on the denoised result B obtained in step 3 to obtain the final denoised signal C.

[0177] Figure 7 To compare the denoising performance of this invention with that of denoising convolutional neural networks and deep residual networks, the signal in the figure is contaminated with simulated Gaussian white noise, impulse noise, and square wave noise, which we call synthetic data. Figure 7 It can be seen that the method of the present invention has a better denoising effect than the other two methods. The present invention can reduce the reconstruction error of the signal to 0.1298, while the signal processed by the denoising convolutional neural network and the deep residual network can only reduce the reconstruction error to 0.2239 and 0.3875 respectively. Moreover, the present invention can effectively suppress noise and restore the high-quality curve of the signal when the signal contains impulse noise and square wave noise.

[0178] Figure 8 This is a comparison of the apparent resistivity-phase curves of multiple synthesized data before and after processing by the present invention and denoising convolutional neural networks and deep residual network methods. For example... Figure 8 Before processing, there were frequency jumps in the range of 100Hz to 1Hz, and some data points at 1Hz showed severe frequency distortion. These issues were improved after processing with three different methods. However, the curve obtained by this invention is smoother and more continuous in the range of 100Hz to 1Hz, showing a significant improvement. The error bars are significantly reduced, and the distortion at the 1Hz frequency point is also improved. Overall, the quality of the apparent resistivity-phase curve obtained by this invention is significantly improved.

[0179] Figure 9 This is a comparison of the apparent resistivity-phase curves of multiple measured data before and after processing by the present invention and denoising convolutional neural network and deep residual network methods. From Figure 9 As can be seen, the noise in the measured data is weaker than that in the synthesized noise, so the distortion of the original apparent resistivity curve is smaller. However, the present invention is still able to reduce frequency jumps in the apparent resistivity curve and improve the quality of the apparent resistivity-phase curve to a certain extent compared with the other two networks.

[0180] In summary, this invention can significantly improve data quality while effectively removing strong human noise in controllable source electromagnetic data, achieving results that are significantly better than existing methods.

[0181] To address the shortcomings of traditional controlled-source electromagnetic data denoising methods, which require manual threshold setting and lack adaptability to different noise types, this invention proposes a highly efficient, automated, and adaptable denoising method based on deep learning. By introducing the residual module concept and convolutional denoising approach from deep learning, the method achieves complementary advantages, improving the accuracy of controlled-source electromagnetic data denoising while reducing the loss of high-quality data during the denoising process, effectively avoiding the subjective bias caused by traditional manually set threshold denoising.

[0182] To address the pseudo-random square wave characteristics of controllable source electromagnetic data, a novel deep learning network is constructed. The residual denoising convolutional network built in this invention features the following optimizations: First, the network employs skip connections, ensuring that even if the data in the residual layer changes, the input data is preserved and transmitted intact to the output, guaranteeing that the chained multiplication in the residual layer becomes a chained addition, preventing gradient vanishing or exploding during node parameter updates. Second, the network uses an identity mapping to the input of the redundant layer above, maintaining network performance even with redundant layers and significantly mitigating network degradation. These optimizations result in a significant improvement in the denoising performance of controllable source electromagnetic data.

[0183] The residual denoising convolutional network constructed in this invention uses a sample library created from data obtained through SISC signal-to-noise separation of real-world data during training. SISC can autonomously learn the characteristic structure of noise in noisy signals, thereby constructing a learned redundant dictionary. This dictionary can be flexibly modified for different real-world data, achieving good denoising results without manual intervention. Compared to other time series editing methods, Li Guanget. (2021) has demonstrated that SISC performs best and is most reliable among traditional methods in controlled-source denoising, but this is limited to cases where the noise intensity is not too high. Using data obtained through SISC signal-to-noise separation to create a sample library is beneficial to improving the realism of the network training results. Furthermore, some noise in the sample library comes from real data, which matches the actual situation and is beneficial for deep networks to learn the characteristics of real noise. By using time-invariant sparse coding to create a training set for training the deep learning network, a denoising effect far exceeding that of time-invariant sparse coding is finally obtained.

[0184] The effectiveness of deep learning denoising depends mainly on the training set and is not significantly related to the noise intensity. This invention utilizes deep learning to suppress strong noise, but the data processed by deep learning still retains a large amount of weak noise. Shift-invariant sparse coding has an excellent denoising effect on weak noise. After deep learning denoising, shift-invariant sparse coding is used again for denoising to remove the weak noise remaining in the unsmooth signal and maximize the improvement of signal quality.

[0185] This invention can intelligently and efficiently denoise multiple types of controllable source electromagnetic data, significantly improve the signal-to-noise ratio of controllable source electromagnetic data, and enhance the detection effect of controllable source electromagnetic methods.

[0186] The examples described in this invention are illustrative and not limiting. Therefore, this invention is not limited to the examples described in the specific embodiments. Any other embodiments derived by those skilled in the art based on the technical solutions of this invention, without departing from the spirit and scope of this invention, whether modifications or substitutions, are also within the protection scope of this invention.

Claims

1. A method for controlled source electromagnetic data denoising based on residual denoising convolutional network and shift-invariant sparse coding, characterized in that, The method comprises the following steps: Step 1: signal-to-noise separation of the measured controllable source electromagnetic data is performed by shift-invariant sparse coding (SISC) to obtain high-quality data and measured noise; the measured noise is multiplied by different multiples to obtain a series of noise with different amplitudes, which are added to the high-quality data to obtain a series of noisy signals with different intensities of measured noise; in order to improve the diversity of samples, a part of simulated noise of different types and different signal-to-noise ratios is generated by numerical simulation and added to the high-quality data extracted by the shift-invariant sparse coding to obtain a series of noisy signals with different intensities of simulated noise; the above noisy signals and high-quality signals are paired and segmented to construct a controllable source electromagnetic data sample library; Step 2: a residual denoising convolutional network is built, and the obtained sample library is input into the residual denoising convolutional network for training to obtain a network model for denoising of controllable source electromagnetic data; Step 3: the controllable source electromagnetic noisy data to be processed is input into the trained denoising model for noise reduction to obtain a preliminary denoising result; Step 4: the shift-invariant sparse coding is used to perform signal-to-noise separation on the denoising result obtained in step 3 to obtain a final denoised signal; There are two kinds of residual modules in the residual denoising convolutional network; The first kind of identity residual module is represented as: x l+1 = x l + F(x l , W l ), (1) In the formula, x l is a residual block input, x l+1 is a residual block output, F(x l ,W l ) is a residual part; The identity residual block is responsible for ensuring that the size of the input data and the output data is the same before and after; The second kind of convolution residual module is represented as: x l+1 = h(x l ) + F(x l , W l ), (2) where h(x l ) = W′ l x,W′ l is a 1 x 1 convolution operation, x l is the residual block input, x l+1 is the residual block output, and F(x l ,W l ) is the residual part. The convolution residual module is responsible for upgrading or down-sampling through a convolution layer to ensure that the shape and size of the input data and the output data are consistent; The residual denoising convolutional network is composed of an input layer, a hidden layer and an output layer, and the hidden layer comprises a plurality of convolution layers, batch normalization, a rectified linear unit and residual modules; The shape of the input layer is: sample length multiplied by the number of channels, that is, n x 1; The hidden layer is composed of convolution layer 1, convolution layers 2-17, convolution layer 18, convolution layer 19, identity residual block 20, identity residual block 21, convolution residual block 22, identity residual block 23, convolution residual block 24, identity residual block 25, convolution residual block 26, identity residual block 27, average pooling layer 28, a total of twenty-eight parts in order; the hidden layer: Convolution layer 1: 1 convolution kernel with a size of 3 x 1 and a "Relu" activation function; Convolution layers 2-17: each layer is composed of 64 convolution kernels with a size of 3 x 1, a batch normalization layer and a "Relu" activation function, and the process is repeated for 16 layers; Convolution layer 18: 64 convolution kernels with a size of 3 x 1; Convolution layer 19: 2 convolution kernels with a size of 3 x 1, a batch normalization layer and a "Relu" activation function; Identity residual block 20: 64 convolution kernels with a size of 3 x 1, a batch normalization layer, a "Relu" activation function and a summation function; Identity residual block 21: 64 convolution kernels with a size of 3 x 1, a batch normalization layer, a "Relu" activation function and a summation function; Convolution residual block 22: 128 convolution kernels with a size of 3 x 1, one-dimensional convolution with a step of 2, 128 one-dimensional point-by-point convolution kernels with a size of 1 x 1, a batch normalization layer, a "Relu" activation function and a summation function; The identity residual block 23 is: 128 convolution kernels with a size of 3×1, a batch normalization layer, a "Relu" activation function and a summation function; The convolution residual block 24 is: 256 one-dimensional convolutions with a size of 3×1 and a step of 2, 256 one-dimensional pointwise convolutions with a size of 1×1 and a step of 2, a batch normalization layer, a "Relu" activation function and a summation function; The identity residual block 25 is: 256 convolution kernels with a size of 3×1, a batch normalization layer, a "Relu" activation function and a summation function; The convolution residual block 26 is: 512 one-dimensional convolutions with a size of 3×1 and a step of 2, 512 one-dimensional pointwise convolutions with a size of 1×1 and a step of 2, a batch normalization layer, a "Relu" activation function and a summation function; The identity residual block 27 is: 512 convolution kernels with a size of 3×1, a batch normalization layer, a "Relu" activation function and a summation function; The average pooling layer 28 is: an average filter with a size of 3 and a step of 1; The output layer: a Dropout layer, a fully connected layer and a summation function; During the training process, the number of channels of the input data is regularly increased, but after the training is completed, the number of channels is changed through the fully connected layer, so that the size of the output data is unified with the input data.

2. The method of claim 1, wherein, The controllable source electromagnetic data is a one-dimensional periodic signal, and the sampling rate is 1200 Hz; According to the data characteristics, the length of each data cycle is set to 1200 sampling points, so that the size of each cycle data is 1×1200.

3. The method of claim 1, wherein, The sample library of the residual denoising convolution network is prepared as follows: the high-quality data separated by SISC is copied 120 times, numbered 1-120, and 1-30 dB Gaussian white noise is added to the data numbered 1-30; after 1-30 dB Gaussian white noise is added to the data numbered 31-60, different amplitude pulse noise is randomly added; after 1-30 dB Gaussian white noise is added to the data numbered 61-90, different amplitude square wave noise is randomly added; 1-30 times of the actual noise separated by SISC is added to the data numbered 91-120; finally, 120 pairs of samples containing different types and amplitudes of noise are obtained.

4. The method of claim 1, wherein, Before using shift-invariant sparse coding, the signal X which has been processed preliminarily is divided into K segments. In the case that the sampling rate is 1200 Hz and the time length of each segment is 1 minute, the sampling points of each segment are 72000, i.e. X = [x1, x2, …, xK]. k ] T , x k = [x1, x2, …, xK] N T N = 72000, SISC represents x k as the sum of the convolution of bases and coefficients:​ where "*" denotes convolution, the coding coefficient vector s m,k ∈R p is sparse, i.e., only a small number of non-zero coefficients, ε is Gaussian white noise, Q < N, P < N and Q + P - 1 = N; the dictionary atom d m and the coding coefficient s m,k are both unknown, which are converted into convex optimization problems by alternately updating and iteratively solving; when fixing d m unchanged, the sparse representation coefficient s m,k is solved based on the convex optimization method; when fixing s m,k unchanged, the dictionary atom d m is solved based on the convex optimization method; the sparsity is the common goal of the above two optimization problems, and the cost function for evaluating the sparsity of x k is where ||·|| denotes the l F represents l F norm, and β is a constraint that balances the reconstruction error with sparsity, d m Normalization is usually needed, i.e. The basic procedure of shift-invariant sparse coding is as follows: Input: preliminary processed signal X, the type of characteristic atom a, the width of characteristic atom W = [W1, W2,... W α ], the total number of characteristic atoms L, i.e. sparsity, the maximum number of iterations z, the convergence target e < 10 -6 ; Initialization: randomly assign initial values to D and s; The following contents are executed in a loop for z times: Stop the loop when the maximum number of iterations is reached or the convergence target is reached; Output: overcomplete dictionary D and the reconstructed signal i.e. the extracted valid signal.

5. The method of claim 4, wherein, Let g i,u Characteristic atom d i The length of the atom after shifting point u and filling in zeros is the same as that of x. k Same, and ||g i,u || = 1, maximum number of loops L max The residual after the Lth iteration is r L The set of atoms ψ selected after the Lth iteration L The steps for solving the coefficients are as follows: 1) Parameter initialization, r 0 = x k ; 2) Select the atom g that best matches the current residual i,u which satisfies: 3) update the set of selected atoms, 4) Calculate projection coefficients according to least squares method Residual r L = x k - s L ψ L , reconstructed signal 5) Determine if L has reached a maximum value L max , if not, L = L + 1, and go to step 2) and loop; otherwise, output the reconstructed signal.

6. The method of claim 4, wherein, The shift-invariant sparse coding is realized by the following steps: keeping the coefficients unchanged and updating only the atoms, and the cost function can be simplified as: where E i,k represents the reconstruction error of the kth signal excluding all bases of the ith basis; the update of the ith basis is converted into solving the equation group about d i , since d i * S i,k = s i,k * d i , first only analyze the optimization problem when there is only the kth signal, which is equivalent to solving the solution of the following formula: The left matrix of equation (7) can be considered as a special Toeplitz matrix with coefficients s i,k , so the above equation can be written as Toep(s i,k ) · d i = E i,k ; since the coefficients s i,k are sparse, many of the rows in the matrix Toep(s i,k ) are zero vectors, which have no effect on the result, these rows are removed from the matrix Toep(s i,k ) while the corresponding rows in the vector E i are removed, denoted as When considering K signals simultaneously, the cost function ψ(θ) can be represented as: Sd i = E, d can be obtained according to the least square method i = (S T S)Ed -1 = (S T S)Ed T S) ∈ R Q×Q When Q « N, it is transformed into solving a small scale linear equation group solution; This solution process directly obtains the optimal value by Cholesky decomposition, sequentially updates each basis in random order, can obtain the optimal solution of the basis in this round of loop, and then sequentially updates the basis d i Normalization processing That is, the complete dictionary D is obtained.

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