Magnetic Anomaly Detection Method and System Based on Structured Hankel Total Variation Regularization

Abstract

The present invention relates to the field of magnetic anomaly detection, and provides a magnetic anomaly detection method and system based on structured Hankel total variation regularization, including: S1: Collect magnetic anomaly signals through a magnetic gradient sensor array, construct an original matrix from the magnetic anomaly signals, and alternately perform row scanning and column scanning on the original matrix to obtain a covering matrix; S2: Transform the covering matrix into a block Hankel matrix through a structured Hankel transform operator, and perform singular value decomposition on the block Hankel matrix to obtain a target matrix; S3: Construct an ST-TVR model through the target matrix and introducing a total variation regularization term; S4: Optimize the parameters of the ST-TVR model through a particle swarm algorithm to obtain an optimized ST-TVR model, and solve the optimized ST-TVR model through an ADMM algorithm to obtain the denoised magnetic anomaly signals. The present invention uses a particle swarm optimization algorithm and an ADMM algorithm to optimize the parameters and solve the model of the ST-TVR model respectively, improving the algorithm convergence, effectiveness, and robustness.

Description

Technical Field

[0001] The present invention relates to the field of magnetic anomaly detection, and in particular, to a magnetic anomaly detection method and system based on structured Hankel total variation regularization. Background Art

[0002] Magnetic anomaly detection is a method of detecting magnetic field information of a target measurement area by using a magnetic measurement instrument, so as to detect a visually blurred magnetic target, and is often applied to fields such as resource exploration and target recognition. As the exploration depth increases, the magnetic anomaly signal becomes weaker and weaker. When the volume of the measured magnetic target is small and the environment is complex, the original signal collected by the magnetic measurement instrument often contains a large amount of noise, such as current noise, electromagnetic interference, harmonic interference, etc. Therefore, the effect of noise suppression is a key factor in the effectiveness of magnetic anomaly signal detection. In addition, in magnetic exploration, in order to achieve accurate inversion of magnetic anomaly targets, it is also particularly important to extract the boundary features of anomalies.

[0003] At present, magnetic anomaly signal detection methods mainly include two types: target-based and noise-based. Target-based detection methods mainly include detection methods based on orthogonal basis function decomposition and their improved algorithms, principal component analysis method, and robust principal component analysis method RPCA, etc.; noise signal feature-based detection methods mainly include minimum entropy detection method, wavelet transform method WT, singular value decomposition method SVD, etc. However, the above methods all have certain problems: 1) When improving the signal-to-noise ratio, it is easy to ignore the boundary features of the magnetic anomaly original signal, reduce the authenticity of anomaly signal extraction, and there is a problem of noise overfitting; 2) It is difficult to determine the optimal threshold, and it is often used to process one-dimensional signals.

[0004] In summary, the existing algorithms are difficult to simultaneously take into account magnetic anomaly signal noise suppression and boundary feature extraction.

[0005] The above content is only used to assist in understanding the technical solution of the present invention, and does not represent an admission that the above content is prior art. Summary of the Invention

[0006] To solve the above technical problems, the present invention provides a magnetic anomaly detection method based on structured Hankel total variation regularization, including:

[0007] S1: Collect magnetic anomaly signals through a magnetic gradient sensor array, construct an original matrix through the magnetic anomaly signals, and alternately perform row scanning and column scanning on the original matrix to obtain a coverage matrix;

[0008] S2: Transform the coverage matrix into a block Hankel matrix through a structured Hankel transform operator, and perform singular value decomposition on the block Hankel matrix to obtain a target matrix;

[0009] S3: Construct the ST-TVR model by means of the target matrix and introducing the total variation regularization term;

[0010] S4: Optimize the parameters of the ST-TVR model through the particle swarm optimization algorithm to obtain the optimized ST-TVR model, and solve the optimized ST-TVR model through the ADMM algorithm to obtain the denoised magnetic anomaly signal.

[0011] Preferably, step S1 is specifically as follows:

[0012] S11: Construct an original matrix of size a×b through multiple groups of magnetic anomaly signals;

[0013] S12: Set a sliding window of size m×n, and alternately perform column scanning and row scanning on the original matrix through the sliding window to obtain a covering matrix S. The expression of the elements in the covering matrix S is:

[0014]

[0015] where i is the row number of the covering matrix, j is the column number of the covering matrix, x i,j is an element in the original matrix, i = 1, 2, …, a - m + 1; j = 1, 2, …, b - n + 1; a, b, m, and n are all positive integers greater than 0, and m is less than a, and n is less than b.

[0016] Preferably, step S2 is specifically as follows:

[0017] S21: Transform the covering matrix into a block Hankel matrix through the structured Hankel transform operator H. The expression of the structured Hankel transform is:

[0018] H(S) = [H(S i,j )]

[0019] = [H(S 1,1 ) H(S 1,2 ) … H(S 1,b-n+1 ) H(S 2,1 ) H(S 2,2 ) … H(S 2,b-n+1 ) … H(S a-m+1,b-n+1 )] T

[0020] where i is the row number of the covering matrix, j is the column number of the covering matrix, i = 1, 2, …, a - m + 1; j = 1, 2, …, b - n + 1; a, b, m, and n are all positive integers greater than 0, and m is less than a, and n is less than b;

[0021] S22: Perform singular value decomposition on the block Hankel matrix to obtain the original reconstruction signal The calculation formula is as follows:

[0022]

[0023] Among them, S * is the ideal magnetic signal that is clean and noise-free, and r is the rank of the known true noise-free magnetic signal;

[0024] Construct the target matrix through the original reconstructed signal Build the target matrix

[0025] Preferably, the expression of the ST-TVR model described in step S3 is:

[0026]

[0027] Among them, is the target matrix, is the data fidelity term, is the nuclear norm regularization term, is the total variation regularization term, is the variational symbol, λ1 is the first parameter, and λ2 is the second parameter.

[0028] Preferably, step S4 is specifically as follows:

[0029] S41: Optimize the parameters of the ST-TVR model through the particle swarm optimization algorithm, using SNR and SSIM as the fitness values to evaluate the ST-TVR model, so as to obtain the first parameter λ1 and the second parameter λ2 in the optimized ST-TVR model;

[0030] S42: Solve the optimized ST-TVR model through the ADMM algorithm;

[0031] Introduce the auxiliary variable P and make Construct the augmented Lagrangian function of the optimized ST-TVR model, and the expression is:

[0032]

[0033] Among them, is the target matrix, Y is the Lagrange multiplier matrix, μ is the penalty factor, H is the structured Hankel transform operator, S * is the ideal magnetic signal that is clean and noise-free, is the data fidelity term, λ1||H(P)|| * is the nuclear norm regularization term, is the total variation regularization term, is the variational symbol;

[0034] S43: Obtain the optimal target matrix by solving the augmented Lagrangian function in a loop and the optimal auxiliary variable P k+1 , and the calculation formula is:

[0035]

[0036]

[0037] where k is the number of loops to reach the optimum;

[0038] S44: Calculate and obtain the optimal Lagrange multiplier matrix Y k+1 and the optimal penalty factor μ k+1 , and the calculation formula is:

[0039]

[0040] μ k+1 = ρυ k

[0041] where ρ is the third parameter;

[0042] S45: Substitute P k+1 , Y k+1 and μ k+1 into the optimized ST-TVR model, and calculate and obtain the denoised magnetic anomaly signal.

[0043] A magnetic anomaly detection system based on structured Hankel total variation regularization, comprising:

[0044] A matrix construction module, configured to collect a magnetic anomaly signal through a magnetic gradient sensor array, construct an original matrix through the magnetic anomaly signal, and alternately perform row scanning and column scanning on the original matrix to obtain a coverage matrix;

[0045] A matrix conversion module, configured to transform the coverage matrix into a block Hankel matrix through a structured Hankel transform operator, and perform singular value decomposition on the block Hankel matrix to obtain a target matrix;

[0046] An ST-TVR model construction module, configured to construct an ST-TVR model through the target matrix and introduce a total variation regularization term;

[0047] An ST-TVR model solving module, configured to perform parameter optimization on the ST-TVR model through a particle swarm algorithm to obtain an optimized ST-TVR model, and solve the optimized ST-TVR model through an ADMM algorithm to obtain a denoised magnetic anomaly signal.

[0048] The present invention has the following beneficial effects:

[0049] 1. A ST-TVR model based on structured Hankel transform is proposed, which maximally preserves the abnormal boundary features while improving the signal-to-noise ratio;

[0050] 2. A total variation regularization term is introduced to achieve the preservation of boundary signal features and weaken the noise overfitting problem caused by excessive improvement of the signal-to-noise ratio;

[0051] 3. The particle swarm optimization algorithm and the ADMM algorithm are used to optimize the parameters and solve the ST-TVR model respectively, improving the algorithm convergence, effectiveness, and robustness. Brief Description of the Drawings

[0052] Figure 1 It is a flowchart of the method in the embodiment of the present invention;

[0053] Figure 2 It is a result diagram of magnetic anomaly signals after noise suppression by different methods;

[0054] The realization, functional characteristics, and advantages of the object of the present invention will be further described in conjunction with the embodiments with reference to the drawings. Detailed Embodiment

[0055] It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0056] Referring to Figure 1 , the present invention provides a magnetic anomaly detection method based on structured Hankel total variation regularization, which effectively overcomes the problem of fuzzy edge feature extraction of existing algorithms, improves the signal-to-noise ratio of the signal at the same time, and the signal-to-noise ratio is more significantly improved in a strong noise environment, and can be applied to military detection, medical diagnosis, industrial non-destructive testing and other fields;

[0057] Including:

[0058] S1: Collect magnetic anomaly signals through a magnetic gradient sensor array, construct an original matrix from the magnetic anomaly signals, and alternately perform row scanning and column scanning on the original matrix to obtain a coverage matrix;

[0059] S2: Transform the coverage matrix into a block Hankel matrix through a structured Hankel transform operator, and perform singular value decomposition on the block Hankel matrix to obtain a target matrix;

[0060] S3: Construct a ST-TVR model through the target matrix and introduce a total variation regularization term;

[0061] S4: Optimize the parameters of the ST-TVR model through the particle swarm algorithm to obtain an optimized ST-TVR model, and solve the optimized ST-TVR model through the ADMM algorithm to obtain the denoised magnetic anomaly signal.

[0062] In this embodiment, step S1 is specifically as follows:

[0063] S11: Construct an original matrix of size a×b through multiple groups of magnetic anomaly signals;

[0064] S12: Set a sliding window of size m×n, and alternately perform column scanning and row scanning on the original matrix through the sliding window to obtain a covering matrix S. The expression of the elements in the covering matrix S is:

[0065]

[0066] where i is the row number of the covering matrix, j is the column number of the covering matrix, x i,j is an element in the original matrix, i = 1, 2, …, a - m + 1; j = 1, 2, …, b - n + 1; a, b, m, and n are all positive integers greater than 0, and m is less than a, and n is less than b.

[0067] In this embodiment, step S2 is specifically as follows:

[0068] S21: Transform the covering matrix into a block Hankel matrix through the structured Hankel transform operator H. The expression of the structured Hankel transform is:

[0069] H(S) = [H(S i,j )]

[0070] = [H(S 1,1 ) H(S 1,2 ) … H(S1, b-n+1 ) H(S 2,1 ) H(S 2,2 ) … H(S 2,b-n+1 ) … H(S a-m+1,b-n+1 )] T

[0071] where i is the row number of the covering matrix, j is the column number of the covering matrix, i = 1, 2, …, a - m + 1; j = 1, 2, …, b - n + 1; a, b, m, and n are all positive integers greater than 0, and m is less than a, and n is less than b;

[0072] S22: Perform singular value decomposition on the block Hankel matrix to obtain the original reconstructed signal The calculation formula is:

[0073]

[0074] where S * is the ideal magnetic signal that is clean and noise-free, and r is the rank of the known true noise-free magnetic signal;

[0075] Through the original reconstructed signal Construct the target matrix

[0076] In this embodiment, the rank r of the known true noise-free magnetic signal is transformed into a nuclear norm constraint related to the matrix rank, and added as a regularization constraint to the ST-TVR model. Then, a total variation regularization term is added to obtain the function expression of the ST-TVR model;

[0077] The expression of the ST-TVR model described in step S3 is:

[0078]

[0079] Wherein, is the target matrix, is the data fidelity term, is the nuclear norm regularization term, is the total variation regularization term, is the variational symbol, λ1 is the first parameter, and λ2 is the second parameter; specifically, the nuclear norm regularization term mainly performs noise suppression, and the total variation regularization term mainly performs signal smoothing.

[0080] In this embodiment, step S4 is specifically as follows:

[0081] S41: Optimize the parameters of the ST-TVR model through the particle swarm optimization algorithm, and use SNR and SSIM as the fitness values to evaluate the ST-TVR model, so as to obtain the first parameter λ1 and the second parameter λ2 in the optimized ST-TVR model;

[0082] Specifically, SNR is the signal-to-noise ratio, and SSIM is the structural similarity;

[0083] S42: Solve the optimized ST-TVR model through the ADMM algorithm;

[0084] Introduce an auxiliary variable P and make Construct the augmented Lagrangian function of the optimized ST-TVR model, and the expression is:

[0085]

[0086] Wherein, is the target matrix, Y is the Lagrange multiplier matrix, μ is the penalty factor, H is the structured Hankel transform operator, S * is the clean noise-free ideal magnetic signal, is the data fidelity term, λ1||H(P)|| * is the nuclear norm regularization term, is the total variation regularization term, is the variational symbol;

[0087] S43: Obtain the optimal target matrix and the optimal auxiliary variable P by solving the augmented Lagrangian function through iteration and the optimal auxiliary variable P k+1 , and the calculation formula is as follows:

[0088]

[0089]

[0090] where k is the number of iterations to reach the optimum;

[0091] S44: Calculate the optimal Lagrange multiplier matrix Y and the optimal penalty factor μ through the optimal target matrix and the optimal auxiliary variable k+1 and the optimal penalty factor μ k+1 , and the calculation formula is as follows:

[0092]

[0093] μ k+1 = ρμ k

[0094] where ρ is the third parameter;

[0095] S45: Substitute P k+1 , Y k+1 and μ k+1 into the optimized ST-TVR model, and calculate the denoised magnetic anomaly signal

[0096] Implementation effect of a magnetic anomaly detection method based on structured Hankel total variation regularization:

[0097] Figure 2 is the result diagram of the magnetic anomaly signal after adding five groups of Gaussian noises with different intensities to the magnetic anomaly signal measured in the actual environment and then suppressing the noise through different methods, as well as the structural similarity diagram SSIM reflecting the relationship between the denoised magnetic anomaly signal and the magnetic anomaly signal without added noise Figure 2 In, the 1st, 2nd, 4th, 6th, and 8th columns are the results of the denoised magnetic anomaly signal obtained by the present invention, and the signal-to-noise ratio SNR can be calculated according to this diagram; the gray image is the SSIM image, and the structural similarity SSIM can be calculated according to this diagram. The specific SNR index for measuring the noise suppression effect and the SSIM index for measuring the boundary feature extraction effect are given in Table 1

[0098] Analysis Figure 2As can be seen from Table 1, the SVD method will cause serious signal distortion to the signal, that is, the abnormal morphology after processing shows a mosaic shape and displacement; as the signal-to-noise ratio decreases, the boundary features of the signals processed by the RPCA and WT methods gradually disappear, and the structural similarity graph intuitively reflects this phenomenon. Under the 5 groups of signal-to-noise ratios tested, the SNR index of the signal processed by the ST-TVR method is increased by 14.68% on average compared with other methods, and the SSIM index is increased by 87.23% on average. In particular, when the signal-to-noise ratio ≤ -20 dB, the SNR index of the signal processed by the ST-TVR method is increased by 55.13% on average compared with other methods, and the SSIM average index is increased by 89.21%. It can be seen that the method proposed by the present invention can not only effectively improve the signal-to-noise ratio of the signal under different signal-to-noise ratios, but also extract the boundary features of the signal with high quality, indicating that the method has robustness.

[0099] Table 1: Evaluation index table of noise suppression comparison results of different methods

[0100]

[0101] The present invention provides a magnetic anomaly detection system based on structured Hankel total variation regularization, including:

[0102] A matrix construction module, configured to collect magnetic anomaly signals through a magnetic gradient sensor array, construct an original matrix through the magnetic anomaly signals, alternately perform row scanning and column scanning on the original matrix, and obtain a covering matrix;

[0103] A matrix transformation module, configured to transform the covering matrix into a block Hankel matrix through a structured Hankel transform operator, perform singular value decomposition on the block Hankel matrix, and obtain a target matrix;

[0104] An ST-TVR model construction module, configured to construct an ST-TVR model through the target matrix and introducing a total variation regularization term;

[0105] An ST-TVR model solving module, configured to perform parameter optimization on the ST-TVR model through a particle swarm algorithm to obtain an optimized ST-TVR model, and solve the optimized ST-TVR model through an ADMM algorithm to obtain a denoised magnetic anomaly signal.

[0106] It should be noted that in this article, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or system including a series of elements not only includes those elements, but also includes other elements not expressly listed, or further includes elements inherent in such a process, method, article or system. Without further limitation, an element defined by the statement "including one..." does not exclude the existence of another identical element in the process, method, article or system including the element.

[0107] The serial numbers of the embodiments of the present invention above are only for description and do not represent the advantages or disadvantages of the embodiments. In the several device unit claims listing several devices, several of these devices may be embodied by the same hardware item. The use of the words first, second, and third, etc. does not indicate any order and these words may be interpreted as identifiers.

[0108] The above are only the preferred embodiments of the present invention, and do not limit the patent scope of the present invention accordingly. Any equivalent structure or equivalent process transformation made by using the content of the specification and drawings of the present invention, or directly or indirectly applied in other related technical fields, shall be similarly included in the patent protection scope of the present invention.

Claims

1. A magnetic anomaly detection method based on structured Hankel total variation regularization, characterized in that, Including: S1: Collect magnetic anomaly signals through a magnetic gradient sensor array, construct an original matrix from the magnetic anomaly signals, and alternately perform row scanning and column scanning on the original matrix to obtain a covering matrix; S2: Transform the covering matrix into a block Hankel matrix through a structured Hankel transform operator, and perform singular value decomposition on the block Hankel matrix to obtain a target matrix; S3: Construct an ST-TVR model by using the target matrix and introducing a total variation regularization term; The expression of the ST-TVR model described in step S3 is: Among them, is the target matrix, is the data fidelity term, is the nuclear norm regularization term, is the total variation regularization term, is the variational symbol, λ1 is the first parameter, and λ2 is the second parameter; S4: Optimize the parameters of the ST-TVR model through a particle swarm algorithm to obtain an optimized ST-TVR model, and solve the optimized ST-TVR model through an ADMM algorithm to obtain the denoised magnetic anomaly signals.

2. The magnetic anomaly detection method based on structured Hankel total variation regularization according to claim 1, characterized in that, Step S1 is specifically as follows: S11: Construct an original matrix of size a×b from multiple groups of magnetic anomaly signals; S12: Set a sliding window of size m×n, and alternately perform column scanning and row scanning on the original matrix through the sliding window to obtain a covering matrix S. The expression of the elements in the covering matrix S is: where i is the row number of the coverage matrix, j is the column number of the coverage matrix, and x i,j is an element in the original matrix, i = 1, 2, …, a - m + 1; j = 1, 2, …, b - n + 1; a, b, m, and n are all positive integers greater than 0, and m is less than a, and n is less than b.

3. The magnetic anomaly detection method based on structured Hankel total variation regularization according to claim 1, characterized in that Step S2 is specifically as follows: S21: Transform the covering matrix into a block Hankel matrix through a structured Hankel transform operator H. The expression of the structured Hankel transform is: H(S) = [H(S i,j )] = [H(S 1,1 ) H(S 1,2 ) … H(S 1,b-n+1 ) H(S 2,1 ) H(S 2,2 ) … H(S 2,b-n+1 )… H(S a-m+1,b-n+1 )] T where i is the row number of the covering matrix, j is the column number of the covering matrix, i = 1, 2, …, a - m + 1; j = 1, 2, …, b - n + 1; a, b, m, and n are all positive integers greater than 0, and m is less than a, and n is less than b; S22: Perform singular value decomposition on the block Hankel matrix to obtain the original reconstructed signal The calculation formula is as follows: Among them, S * is an ideal magnetic signal that is clean and noise-free, and r is the rank of the known true noise-free magnetic signal; Through the original reconstructed signal Construct the target matrix 4. The magnetic anomaly detection method based on structured Hankel total variation regularization according to claim 1, characterized in that Step S4 is specifically as follows: S41: Optimize the parameters of the ST-TVR model through a particle swarm algorithm, use SNR and SSIM as the fitness values for evaluating the ST-TVR model, so as to obtain the first parameter λ1 and the second parameter λ2 in the optimized ST-TVR model; S42: Solve the optimized ST-TVR model through an ADMM algorithm; Introduce an auxiliary variable P and make Construct the augmented Lagrangian function of the optimized ST-TVR model, and the expression is as follows: Among them, is the target matrix, Y is the Lagrange multiplier matrix, μ is the penalty factor, H is the structured Hankel transform operator, and S * is the clean and noise-free ideal magnetic signal, is the data fidelity term, λ1‖H(P)‖ * is the nuclear norm regularization term, is the total variation regularization term, is the variational symbol; S43: Obtain the optimal objective matrix and the optimal auxiliary variable P by solving the augmented Lagrangian function iteratively. The calculation formula is as follows: and the optimal auxiliary variable P k+1 , the calculation formula is: where k is the number of cycles to reach the optimum; S44: Calculate and obtain the optimal Lagrange multiplier matrix Y through the optimal objective matrix and the optimal auxiliary variables k+1 and the optimal penalty factor μ k+1 , and the calculation formula is as follows: μ k+1 = ρμ k where ρ is the third parameter; S45: Bring P k+1 , Y k+1 and μ k+1 into the optimized ST-TVR model to calculate the denoised magnetic anomaly signal.

5. A magnetic anomaly detection system based on structured Hankel total variation regularization, which is used to implement a magnetic anomaly detection method based on structured Hankel total variation regularization as described in any one of claims 1-4, characterized in that, Including: A matrix construction module, which is used to collect magnetic anomaly signals through a magnetic gradient sensor array, construct an original matrix from the magnetic anomaly signals, and alternately perform row scanning and column scanning on the original matrix to obtain a covering matrix; A matrix conversion module, which is used to transform the covering matrix into a block Hankel matrix through a structured Hankel transform operator, and perform singular value decomposition on the block Hankel matrix to obtain a target matrix; An ST-TVR model construction module, which is used to construct an ST-TVR model by using the target matrix and introducing a total variation regularization term; The expression of the ST-TVR model is: Among them, is the target matrix, is the data fidelity term, is the nuclear norm regularization term, is the total variation regularization term, is the variational symbol, λ1 is the first parameter, and λ2 is the second parameter; An ST-TVR model solving module, which is used to optimize the parameters of the ST-TVR model through a particle swarm algorithm to obtain an optimized ST-TVR model, and solve the optimized ST-TVR model through an ADMM algorithm to obtain the denoised magnetic anomaly signals.

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