An air transient electromagnetic profile data noise suppression method

Abstract

The application is a kind of aviation transient electromagnetic profile data noise suppression method. It includes reading aviation transient electromagnetic profile data, estimating profile block size; using block matching algorithm to block profile data and construct similar block matrix; based on noise whitening weighted kernel norm minimization method to solve the low rank structure of similar block matrix, reduce the influence of noise on kernel norm solution, realize local noise reduction by noise optimization of similar block matrix; traverse all similar blocks matched in profile, integrate the results to the estimated profile data; multiple iterations of the above processing to realize the noise suppression of aviation transient electromagnetic profile data. The application uses noise whitening to improve the anti-interference ability of weighted kernel norm minimization to noise, and avoids the false anomaly caused by the decomposition algorithm based on inter-channel correlation by iterative solution of low rank matrix approximation, ensuring the reliability of the denoising result of aviation transient electromagnetic profile data.

Description

Technical Field

[0001] This invention belongs to the field of noise suppression in airborne transient electromagnetic profile data, specifically a method for suppressing noise in airborne transient electromagnetic profile data. Background Technology

[0002] Airborne Transient Electromagnetic (ATEM) detection is widely used in mineral and groundwater exploration. Its electromagnetic instruments are mounted on aircraft, enabling flexible large-area geophysical surveys. However, multi-source noise from human activities, the environment, aircraft motion, and the system itself limits the survey depth and identification of geophysical features in ATEM systems. ATEM noise suppression research generally falls into two categories: stepwise removal based on noise characteristics and unified suppression of multi-source noise. The former mainly focuses on power line noise, extremely low frequency noise, atmospheric noise, and motion noise. The most common denoising methods are superposition and channel decanting in synchronous detection (e.g., Macnae et al., Macnae, JC, Lamontagne, Y. & West, GF, 1984. Noise processing techniques for transient EM systems. Geophysics, 49, 934–948; Nyboe and...). Published in 2012 by Nyboe, NS& K., 2012. Noise reduction in TEM: Presenting a bandwidth - and sensitivity - optimized parallel recording setup and methods for adaptive synchronous detection. Geophysics, 77, E203–E212.; Peng, C., Zhu, K., Fan, T. & Yang, Y., 2022. Suppressing the very low - frequency noise by B - spline gating of transient electromagnetic data. Journal of Geophysics and Engineering, 19(4), 761 - 774.) and estimation and suppression based on noise characteristics (Munkholm, M.S., 1997. Motion - induced noise from vibration of a moving TEM detector coil: characterization and suppression. Journal of applied Geophysics, 37(1), 21 - 29.; Buselli, G., Hwang, H.S. & Pik, J.P., 1998. AEM noise reduction with remote referencing. Exploration Geophysics, 29(2), 71 - 76.; Bouchedda, A., Chouteau, M., Keating, P. & Smith, R., 2010. Sferics noise reduction in time - domain electromagnetic systems: application to MegaTEM II signal enhancement. Exploration Geophysics, 41(4), 225 - 239.; Wu, X., Xue, G., Xiao, P., Li, J., Liu, L. & Fang, G., 2019.The removal of high-frequency motion-induced noise in helicopter-borne transient electromagnetic data based on wavelet neural network. Geophysics, 84(1), K1-K9.). These processing methods implemented on attenuation curves evaluate denoising results by observing late channel noise levels, which typically require significant computational resources and parameter manipulation (Wu, X., Xue, G., He, Y. & Xue, J., 2020. Removal of multisource noise in airborne electromagnetic databased on deep learning. Geophysics, 85(6), B207-B222.), and computational errors introduced in certain steps of the processing flow may affect denoising accuracy. Unified suppression of multi-source noise is processed on attenuation curves or profiles, using algorithms such as filtering, noise estimation, and signal decomposition to enhance the signal-to-noise ratio of ATEM data. Low-pass filters are used in most commercial transient electromagnetic receivers to suppress transmitter noise. F.,Auken,E.& KI, 1999. Inversion of band-limited TEM responses. Geophysical Prospecting, 47, 551–564.; KI & Auken, E., 2004. SkyTEM - A new high-resolution helicopter transient electromagnetic system. Exploration Geophysics, 35(3), 194-202.). Trapezoidal filters were applied to the average SkyTEM data (Auken, E., Christiansen, AV, Westergaard, JH, Kirkegaard, C., Foged, N. & Viezzoli, A., 2009. An integrated processing scheme for high-resolution airborne electromagnetic surveys, the SkyTEM system. Exploration Geophysics, 40(2), 184-192.). Rasmussen, S., Nyboe, NS, Mai, S. & Larsen, JJ, 2018. Extraction and use of noise models from transient electromagnetic data. Geophysics, 83, E37–E46. Noise models were estimated from data obtained when the transmitter was turned on in the form of power spectral density. Since Green, A., 1998. The use of multivariate statistical techniques for the analysis and display of AEM data. Exploration Geophysics, 29(2), 77-82. introduced Principal Component Analysis (PCA) to compress the shape information of transient electromagnetic data, many PCA-based signal decomposition algorithms have emerged for noise suppression research. Reninger, PA, Martelet, G., Deparis, J., Perrin, J. & Chen, Y., 2011. Singular value decomposition as a denoising tool for airborne time domain electromagnetic data. Journal of Applied Geophysics, 75(2), 264-276. Singular value analysis was used to suppress spikes and oscillations on the attenuation curves in the original stacked TEM data.Chen, B., Lu, CD & Liu, GD, 2014. A Denising Method Based on Kernel Principal Component Analysis for Airborne Time-Domain Electromagnetic Data. Chinese Journal of Geophysics, 57(1), 103-111. A kernel PCA method for denoising transient electromagnetic data is proposed. Li, Y., Meng, Y., Lu, Y., Wang, L., Xie, B., Cheng, Y. & Zhu, K., 2018. Noise removal for airborne time domain electromagnetic data based on minimum noise fraction. Exploration Geophysics, 49(2), 127-133. The Minimum Noise Fraction (MNF) transform is introduced into the suppression of residual noise in ATEM.

[0003] Multi-source noise is complex and unpredictable; therefore, synchronous detection is inefficient, and threshold filtering cannot continuously and adequately remove noise (Reninger, PA, Martelet, G., Deparis, J., Perrin, J. & Chen, Y., 2011. Singular value decomposition as a denoising tool for airborne timedomain electromagnetic data. Journal of Applied Geophysics, 75(2), 264-276.). In particular, it is difficult to identify information about geological conduction structures in late-stage traces that are submerged below the noise level. PCA-based denoising methods typically combine attenuation curves or inter-trace correlations in profiles to extract features dominated by large-amplitude anomalies in early-stage traces, which are then used to mine similar conduction information submerged in late-stage traces. Such methods are effective and desirable because continuous geological conduction structures support “strong correlations” between traces. However, the extraction of “strongly correlated” features reduces the accuracy of late-stage traces with small-amplitude anomalies. When the correlation between early and late-stage traces weakens due to changes in geological structure, late-stage traces reconstructed using anomaly features from early-stage traces may exhibit “spurious” anomalies. Multi-source noise removal should utilize inter-channel correlation while avoiding the impact of significant anomalies in early channels on the extraction of information from later channels. Summary of the Invention

[0004] The technical problem this invention aims to solve is to provide a noise suppression method for airborne transient electromagnetic profile data, addressing the issue of low anomaly identification accuracy in late-stage trace data within the profile data. Based on the low-rank characteristics of signals and the non-local self-similarity of noise in the ATEM profile, a weighted nuclear norm minimization method is used to calculate the low-rank matrix of locally similar blocks in the profile, reconstructing these similar blocks to obtain the denoised profile data. This invention utilizes noise whitening to optimize the nuclear norm and solve for the operator's soft threshold function, enhancing the noise immunity of the weighted nuclear norm minimization method and improving the anomaly identification accuracy in late-stage trace data within the profile data.

[0005] A method for suppressing noise in airborne transient electromagnetic profile data, the method comprising:

[0006] a. Read the transient electromagnetic profile data of the aircraft and estimate the size of the profile block;

[0007] b. Use a block matching algorithm to divide the profile data into blocks and construct a similar block matrix;

[0008] c. Use principal component analysis algorithm to estimate the noise of similar block matrices;

[0009] d. Construct a noise whitening matrix and whiten the similar block matrix;

[0010] e. Perform singular value decomposition on the similar block matrices before and after whitening, and calculate the whitening factor;

[0011] f. Update the weighted soft threshold function using the whitening factor, and solve and reconstruct the low-rank approximation model of the similar block matrix;

[0012] g. Perform step cf processing on all similar block matrices and integrate the processing results into profile data;

[0013] h. Perform multiple iterations on step bg to obtain the noise suppression results of the profile data.

[0014] Further, the airborne transient electromagnetic profile data mentioned in step a is profile data with M measurement points and N channels that has been superimposed and preprocessed by channel extraction. The block size is selected according to the distribution of anomalies and noise blocks. After removing the DC of the profile data, the amplitude range of late channels without obvious anomalies is set as the noise level threshold range. When the amplitude of 50% or more of the sampling points in the profile block is not within the threshold range, the profile block is set as an anomaly block; otherwise, it is a noise block.

[0015] An adaptive estimation model for block size is designed, calculating the proportions of anomalous and noisy blocks in the profile under different block sizes, and using them as weights for the minimum and maximum block sizes, respectively; the estimated block size S is obtained after cumulative averaging.

[0016]

[0017] Where S max S represents the maximum block size. min Represents the minimum block size, r n This represents the proportion of anomalous blocks in a cross-section with a block size of n×n.

[0018] Further, the block matching algorithm described in step b includes: using a reference block as a sliding unit to calculate the Euclidean distance between adjacent blocks in the local search window; arranging all blocks in descending order of similarity, and stacking the first n blocks with higher similarity into a similar block matrix Y. j , represented as

[0019] Y j =X j +N j

[0020] Where X j and N j Let X represent the signal matrix and the corresponding noise matrix, respectively. j It is a low-rank matrix, and the low-rank matrix approximation method is used to obtain Y. j Estimation is performed in the process;

[0021] The similarity between the reference block and other blocks is represented as follows:

[0022]

[0023] Where y i For the i-th other block within the search window, y j Let j be the j-th reference block in the cross-section. This represents the Euclidean distance between two blocks.

[0024] Further, step c specifically includes: selecting the top k low-order components with a cumulative contribution rate of over 85% to reconstruct the matrix, and the difference between the reconstructed matrix and the original similar block matrix is ​​the estimated noise.

[0025] Furthermore, step d specifically includes:

[0026] The estimated noise matrix and the corresponding similar block matrix are processed to have zero mean;

[0027] Perform eigenvalue decomposition on the covariance matrix of the estimated noise:

[0028] C N =QΛQ T

[0029] Where C N Represents the estimated noise N jThe covariance of Λ is a matrix with eigenvalues ​​as diagonal elements, and Q is the eigenvector matrix;

[0030] The noise whitening matrix is ​​constructed as follows:

[0031] R = Λ -12 Q T

[0032] Using the above matrix, noise whitening of the similar block matrix is ​​as follows:

[0033]

[0034] Furthermore, the whitening factor mentioned in step e is the ratio of whitening singular values ​​to non-whitening singular values:

[0035]

[0036] Where, σ i (Y j )and They are Y j and The i-th singular value.

[0037] Furthermore, the low-rank approximation model of the similar block matrix described in step f is represented by the following energy equation:

[0038]

[0039] Where noise variance The term used for normalizing the F-norm data fidelity.

[0040] The optimal solution of the low-rank approximation model is obtained by using a weighted soft threshold function updated with the whitening factor:

[0041]

[0042] in yes Singular value decomposition, This represents the generalized soft thresholding operator with a noise whitening weight vector, i.e.

[0043]

[0044] weight w i The singular values ​​that are inversely assigned to the matrix are defined as follows:

[0045]

[0046] The constant c is set empirically as follows: n is the number of similar blocks, let ε = 10 -16To avoid division by zero, the initial value σ i (X j Approximately as follows:

[0047]

[0048] in It is a similar block matrix after noise whitening. The i-th singular value.

[0049] Furthermore, the iteration step size in step h is set to 0.1, and the number of iterations is set according to the noise level.

[0050] Compared with the prior art, the beneficial effects of this invention are as follows:

[0051] This invention minimizes the weighted nuclear norm of noise whitening. This method utilizes weighted nuclear norm minimization to find the optimal solution for the local low-rank matrix in anatomical profile data to suppress noise in the profile data. Simultaneously, it combines noise whitening to optimize the soft thresholding function, improving the noise immunity of the low-rank solution process.

[0052] This invention improves noise suppression of ATEM profile data by utilizing noise whitening to enhance weighted nuclear norm minimization. It leverages the advantages of PCA-based denoising algorithms, transforming inter-channel correlations in the ATEM profile into low-rank signal features, ensuring effective extraction of significant anomalies in early channels. Simultaneously, based on the non-local self-similarity of profile noise, a block matching algorithm is used to apply the low-rank solution process to the similarity block matrix of local profiles, weakening the PCA-based algorithm's dependence on inter-channel correlations and avoiding potential "spurious" anomalies in later channels, thus improving the accuracy of anomaly extraction. Furthermore, noise whitening optimizes the singular values ​​of the similarity block matrix, and the soft thresholding function is updated synchronously, enhancing the noise resistance of weighted nuclear norm minimization. This invention provides unified suppression of multivariate noise in profile data, achieving efficient and continuous denoising, and effectively identifying weak anomalies submerged in late channels below the noise level. Compared to traditional threshold filtering and PCA-based signal decomposition algorithms, it offers advantages in higher signal-to-noise ratio and more accurate anomaly extraction. Attached Figure Description

[0053] Figure 1 A flowchart of a method for suppressing noise in airborne transient electromagnetic profile data provided in an embodiment of the present invention;

[0054] Figure 2 A simulated profile of transient electromagnetic events in aerospace provided for embodiments of the present invention: Figure 2 (a) is the signal portion of the profile data; Figure 2 (b) is a noisy late-stage tunnel profile, in which anomalous information is covered by noise;

[0055] Figure 3Comparison chart of late-channel denoising results provided by four methods in embodiments of the present invention: Figure 3 (a) shows the late-channel denoising results of adaptive window width filtering; Figure 3 (b) shows the late-stage denoising results for minimum noise separation; Figure 3 (c) shows the denoising results of the late channel with weighted nuclear norm minimization; Figure 3 (d) is the late-channel denoising result with noise whitening weighted nuclear norm minimization provided by the present invention; Detailed Implementation

[0056] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0057] See Figure 1 As shown in the embodiment of the present invention, the noise suppression method for airborne transient electromagnetic profile data based on noise whitening weighted nuclear norm minimization involves: reading and dividing the airborne transient electromagnetic profile data into blocks; calculating the proportion of anomalous blocks and noise blocks in the profile; obtaining the estimated block size by weighted averaging; using a block matching algorithm to divide the profile data into blocks according to the estimated block size; searching for similar blocks within a certain window in the profile based on Euclidean distance; stacking the first n blocks with high similarity into a similar block matrix; performing principal component analysis on the similar block matrix and selecting low-order components to reconstruct the matrix; calculating the difference between the reconstructed matrix and the original similar block matrix to obtain the estimated noise of the similar block matrix; constructing a noise whitening matrix and whitening the similar block matrix; calculating the whitening factor using the singular values ​​of the similar block matrices before and after whitening, and updating the soft thresholding function using the whitening factor; solving and reconstructing the low-rank approximation of the similar block matrix using the updated soft thresholding function; integrating all similar block matrices into profile data after low-rank matrix approximation; and obtaining the final noise suppression result of the profile data through multiple iterations. Specifically:

[0058] a. Read the transient electromagnetic profile data of the aircraft and estimate the size of the profile block;

[0059] b. Use a block matching algorithm to divide the profile data into blocks and construct a similar block matrix;

[0060] c. Use principal component analysis algorithm to estimate the noise of similar block matrices;

[0061] d. Construct a noise whitening matrix and whiten the similar block matrix;

[0062] e. Perform singular value decomposition on the similar block matrices before and after whitening, and calculate the whitening factor;

[0063] f. Update the weighted soft threshold function using the whitening factor, and solve and reconstruct the low-rank approximation model of the similar block matrix;

[0064] g. Perform step cf processing on all similar block matrices and integrate the processing results into profile data;

[0065] h. Perform multiple iterations on step bg to obtain the noise suppression results of the profile data.

[0066] The airborne transient electromagnetic profile data mentioned in step a is profile data with M measurement points and N channels that has undergone preprocessing such as stacking and channel extraction. The profile block size is a key parameter directly affecting the quality of the low-rank approximation. If the block is too large, the estimation results are unstable and it is difficult to maintain the structure of local anomalies; if the block is too small, it is easily affected by noise, the data volume increases, and it is not conducive to effective estimation. Typically, the block size is manually set and adjusted by repeatedly testing the estimation effect, but this method lacks adaptability. For airborne transient electromagnetic profile data, the choice of block size mainly depends on the distribution of anomalies and noise blocks. After removing the direct current of the profile data, the amplitude range of late channels without obvious anomalies is set as the noise level threshold range. When the amplitude of 50% or more of the sampling points in a block is not within the threshold range, the block is set as an anomaly block; otherwise, it is a noise block.

[0067] Since noise whitening involves eigenvalue decomposition of noise blocks, when the block size is too large, the noise level decreases significantly with increasing iterations, leading to insufficient rank of the noise blocks and premature termination of the iteration. Therefore, the choice of block size is limited. To balance block size to improve the signal-to-noise ratio, an adaptive estimation model for block size is designed as follows. The proportions of anomalies and noise blocks in the profile under different block sizes are calculated and used as weights for the minimum and maximum block sizes, respectively; then, the estimated block size S is obtained after cumulative averaging.

[0068]

[0069] Where S max S represents the maximum block size. min Represents the minimum block size, r n This represents the proportion of anomalous blocks in a cross-section with a block size of n×n.

[0070] The block matching algorithm described in step b uses a reference block as a sliding unit to calculate the Euclidean distance between adjacent blocks in the local search window. All blocks are sorted in descending order of similarity, and the first n blocks with the highest similarity are stacked to form a similarity block matrix Y. j , represented as

[0071] Y j =X j +N j

[0072] Where X j and N j Let X represent the signal matrix and the corresponding noise matrix, respectively. j It is a low-rank matrix, and low-rank matrix approximation methods can be used to obtain Y. j The estimation is performed in the middle.

[0073] The similarity between the reference block and other blocks is represented as follows:

[0074]

[0075] Where y i For the i-th other block within the search window, y j Let j be the j-th reference block in the cross-section. This represents the Euclidean distance between two blocks.

[0076] Step c describes using principal component analysis to estimate the noise of the similar block matrix. The first k low-order components with a cumulative contribution rate of over 85% are selected to reconstruct the matrix. The difference between the reconstructed matrix and the original similar block matrix is ​​the estimated noise.

[0077] The steps described in step d for constructing the noise whitening matrix and whitening the similar block matrix are as follows:

[0078] The estimated noise matrix and the corresponding similar block matrix are subjected to zero-mean processing.

[0079] Perform eigenvalue decomposition on the covariance matrix of the estimated noise:

[0080] C N =QΛQ T

[0081] Where C N Represents the estimated noise N j The covariance of Λ is a matrix with eigenvalues ​​as diagonal elements, and Q is the eigenvector matrix.

[0082] The noise whitening matrix is ​​constructed as follows:

[0083] R = Λ -1 / 2 Q T

[0084] Noise whitening is performed on the similar block matrix using the above matrix:

[0085]

[0086] The whitening factor described in step e is used to adjust the magnitude of the noise variance in the initial singular value estimation so that the updated soft thresholding function can solve for the global solution of the noise whitening weighted nuclear norm minimization model. The whitening factor is defined as the ratio of whitened singular values ​​to non-whitened singular values:

[0087]

[0088] Where, σ i (Y j )and They are Y j and The i-th singular value.

[0089] The low-rank approximation model of the similar block matrix described in step f is represented by the following energy equation:

[0090]

[0091] Where noise variance The term used for normalizing the F-norm data fidelity.

[0092] The optimal solution for this model is obtained by using a weighted soft threshold function updated with the whitening factor:

[0093]

[0094] in yes Singular value decomposition, This represents the generalized soft thresholding operator with a noise whitening weight vector, i.e.

[0095]

[0096] weight w i The singular values ​​that are inversely assigned to the matrix are defined as follows:

[0097]

[0098] The constant c is set empirically as follows: n is the number of similar blocks, let ε = 10 -16 To avoid division by zero. Initial value σ i (X j It can be approximated as follows:

[0099]

[0100] in It is a similar block matrix after noise whitening. The i-th singular value.

[0101] The iteration step size mentioned in step h is generally set to 0.1, and the number of iterations is set according to the noise level. The higher the noise level, the more iterations are needed.

[0102] This invention uses a set of simulation profile data of an airborne transient electromagnetic system as an example to illustrate the method mentioned above.

[0103] a. Read the simulation profile data of the airborne transient electromagnetic system. The simulation parameters are as follows: The simulation model uses the measured data collected by the CHTEM system in Qiqihar City, China in 2017, after strong denoising, as the signal, and adds white noise to form the simulation profile. In order to eliminate the interference of large amplitude anomalies in the early traces on similar small anomalies in the later traces, strong denoising processing is used to obtain profile signals with different anomaly information between traces. Because the airborne transient electromagnetic signal has a large dynamic range with approximately exponential decay, such as... Figure 2 As shown in (a), the early channels in the simulation model are almost unaffected by noise, while the later channels are covered by noise. Figure 2 As shown in (b), its local SNR is -4.3151dB.

[0104] After removing the direct current from the profile data, the amplitude range of late-stage traces without obvious anomalies was observed and set as the noise level threshold range, i.e., [-5×10]. -8 5×10 -8 When the amplitude of 50% or more of the sampling points in a block is outside the threshold range, the block is designated as an anomalous block; otherwise, it is considered a noise block. Since noise whitening involves eigenvalue decomposition of the noise block, when the block size is too large, the noise level decreases significantly with increasing iterations, leading to insufficient rank in the noise block and premature termination of the iteration. Therefore, the choice of block size is limited, and the maximum block size S of this model... max The minimum block size is 8. min The value is 4. The proportions of anomalous blocks in the cross-section under different block sizes are calculated, yielding r4 = 0.3523, r5 = 0.3376, r6 = 0.3523, r7 = 0.3358, and r8 = 0.3358, which are used as weights for the minimum block size. These are then substituted into the adaptive estimation model for block size.

[0105]

[0106] We get S = 6.6238, which means the estimated block size is 6×6.

[0107] b. The block matching algorithm uses reference blocks as sliding units to calculate the Euclidean distance between adjacent blocks in the local search window. All blocks are sorted in descending order of similarity, and the top 50 most similar blocks are stacked into a similarity block matrix Y. j , represented as

[0108] Y j =X j +N j

[0109] Where X j and N j Let X represent the signal matrix and the corresponding noise matrix, respectively. jIt is a low-rank matrix, and low-rank matrix approximation methods can be used to obtain Y. j The estimation is performed in the middle.

[0110] The similarity between the reference block and other blocks is represented as follows:

[0111]

[0112] Where y i For the i-th other block within the search window, y j Let j be the j-th reference block in the cross-section. This represents the Euclidean distance between two blocks.

[0113] c. Use principal component analysis (PCA) to estimate the noise of the similar block matrix. Taking the first similar block matrix as an example, the cumulative contribution rate of the first principal component is 97%. Select the first low-order component to reconstruct the matrix. The difference between this reconstructed matrix and the original similar block matrix is ​​the estimated noise.

[0114] d. The steps for constructing the noise whitening matrix and whitening the similar block matrix are as follows:

[0115] The estimated noise matrix and the corresponding similar block matrix have been zero-mean processed.

[0116] Perform eigenvalue decomposition on the covariance matrix of the estimated noise:

[0117] C N =QΛQ T

[0118] Where C N Represents the estimated noise N j The covariance of Λ is a matrix with eigenvalues ​​as diagonal elements, and Q is the eigenvector matrix.

[0119] The noise whitening matrix is ​​constructed as follows:

[0120] R = Λ -12 Q T

[0121] Noise whitening is performed on the similar block matrix using the above matrix:

[0122]

[0123] e. Calculate the whitening factor by the ratio of the singular values ​​of the similar block matrix before and after whitening.

[0124]

[0125] Where, σ i (Y j )and They are Y j and The i-th singular value.

[0126] f. Constructing the energy equation for a low-rank approximation model of similar block matrices:

[0127]

[0128] Where noise variance The term used for normalizing the F-norm data fidelity.

[0129] The optimal solution for this model is obtained by using a weighted soft threshold function updated with the whitening factor:

[0130]

[0131] in yes Singular value decomposition, This represents the generalized soft thresholding operator with a noise whitening weight vector, i.e.

[0132]

[0133] weight w i The singular values ​​that are inversely assigned to the matrix are defined as follows:

[0134]

[0135] The constant c is set empirically as follows: The number of similar blocks is n = 50, and let ε = 10. -16 To avoid division by zero. Initial value σ i (X j It can be approximated as follows:

[0136]

[0137] in It is a similar block matrix after noise whitening. The i-th singular value.

[0138] g. Perform step cf processing on a total of 10746 similar block matrices, and integrate the processing results into profile data.

[0139] h. Iterate through step bg to obtain the noise suppression results of the profile data, as shown below. Figure 3 As shown in (d), the iteration step size is set to 0.1 and the number of iterations is set to 8.

[0140] To observe the beneficial effects of this invention, the simulated profile was denoised using Adaptive Width Smoothing (AWS), Minimum Noise Fraction (MNF), and Weighted Nuclear Norm Minimization (WNNM). Compared with the Noise-whitening-based Weighted Nuclear Norm Minimization (NW-WNNM) provided in this invention, the denoised late-stage trace profile is as follows: Figure 3 As shown.

[0141] AWS uses the second-order difference of local values ​​of the data to optimize the filter window width for adaptive noise suppression. The maximum window width selected for AWS in the simulation profile is 91, and the late-channel denoising results are as follows: Figure 3 As shown in (a), the abnormal information is too smooth, causing severe distortion, and the flat areas fluctuate greatly.

[0142] MNF arranges feature components according to SNR through orthogonal transformation. MNF can remove noise by reconstructing components with high SNR and significant signal characteristics. However, this information extraction is highly dependent on inter-channel correlation, especially for ATEM profiles with large amplitude variations. Large-amplitude anomalies in early channels will provide the main signal characteristics of MNF components, which may distort small-amplitude late-stage anomalies in the reconstruction results that are not entirely consistent with the characteristics of early anomalies. Figure 3 As shown in (b), in the MNF denoising results, a false anomaly similar to the early anomaly structure appeared near measurement point 1520, and a reverse anomaly also appeared at measurement point 1850, which is inconsistent with the real signal.

[0143] WNNM uses the LRMA strategy to remove noise, eliminating the dependence of PCA-based signal decomposition methods on inter-channel correlations and avoiding spurious anomalies. However, WNNM is sensitive to noise, therefore... Figure 3 The abnormal curves around measurement points 1960 and 2290 shown in (c) are similar to the real data, but the amplitude is too high and contradicts the real signal.

[0144] NW-WNNM incorporates noise whitening to reduce noise interference with LRMA in WNNM. For example... Figure 3 As shown in (d), NW-WNNM can not only extract effective late-stage anomaly information, but is also not constrained by inter-channel correlation, and can also reduce the influence of noise on the amplitude of sharp anomalies.

[0145] Table 1 shows the late-channel SNR and correlation coefficient (CC) results for denoising using the four methods described above under three noise intensities.

[0146] Table 1

[0147]

[0148] SNR assesses the energy change of the denoising result, while CC measures the curve detail of the denoising result. AWS and MNF achieve significant improvements in SNR and can extract partial signals from data completely covered by noise, but they are insufficient in extracting local anomalies when CC is low. WNNM can recover anomalous features better, but its SNR results are worse than the previous two methods. NW-WNNM outperforms the above three methods in both signal energy recovery and local anomaly information extraction. In the example with full-coverage noise (late channel SNR of -4.3151dB), the SNR of the NW-WNNM denoising result increased by more than 15%, and the CC increased by about 0.08%. In the example with low noise (late channel SNR of 7.6849dB), the SNR of the NW-WNNM denoising result increased by more than 7%, and the CC increased by about 0.33%.

[0149] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. An airborne transient electromagnetic profile data noise suppression method, characterized in that, The method comprises: a. reading the airborne transient electromagnetic profile data, and estimating the profile block size; b. using a block matching algorithm to block the profile data and construct a similar block matrix; c. using a principal component analysis algorithm to estimate the noise of the similar block matrix; d. constructing a noise whitening matrix to whiten the similar block matrix; e. singular value decomposition is performed on the similar block matrix before and after whitening respectively, and a whitening factor is calculated; the whitening factor in step e is the ratio of the whitened singular value to the non-whitened singular value: ， wherein, and are the i-th singular values of and respectively. f. using the whitening factor to update the weighted soft threshold function, solving and reconstructing the low-rank approximation model of the similar block matrix; the low-rank approximation model of the similar block matrix in step f is represented by the following energy equation: ， where the noise variance for normalizing the F-norm data fidelity term ; The weighted soft threshold function updated by the whitening factor is used to obtain the optimal solution of the low-rank approximation model: ， wherein is the singular value decomposition of denotes a generalized soft threshold operator with noise whitening weight vector, i.e. ， Weights The singular values assigned to the matrix in reverse, are defined as follows: ， where the constant is set empirically to , is the number of similar blocks, set to avoid division by zero, the initial value is approximated as follows: ， wherein is the ith singular value of the noise whitened similar block matrix is the ith singular value of the noise whitened similar block matrix g. processing all similar block matrices according to steps c-f, and integrating the processing results into profile data; h. multiple iterations are performed on steps b-g to obtain the noise suppression result of the profile data.

2. The method of claim 1, wherein, The airborne transient electromagnetic profile data in step a is profile data after superposition and channel preprocessing to form M measuring points and N channels; the block size is selected according to the distribution of abnormal and noise blocks; after removing the direct current of the profile data, the amplitude range of the late channel without obvious abnormality is set as the noise level threshold range; when the amplitude of 50% or more sampling points in the profile block is not within the threshold range, the profile block is set as an abnormal block; otherwise, it is a noise block; An adaptive estimation model of block size is designed, the proportion of abnormal and noise blocks in the profile under different block sizes is calculated, and is used as the weight of the minimum and maximum block size respectively; Obtaining an estimated block size after cumulating averages : ， wherein represents the maximum block size, represents the minimum block size, represents the proportion of abnormal blocks in a profile of a block size of n x n.

3. The method of claim 1, wherein, The block matching algorithm of step b comprises: using the reference block as a sliding unit to calculate the Euclidean distance of adjacent blocks in a local search window; all blocks are arranged in descending order of similarity, and the first several blocks with large similarity are stacked into a similar block matrix ​​ ， wherein and denote the signal matrix and the corresponding noise matrix, respectively, is a low-rank matrix estimated from using a low-rank matrix approximation method; The similarity between the reference block and other blocks is represented as follows: ， wherein is the Euclidean distance between the two blocks. is the Euclidean distance between the two blocks. is the Euclidean distance between the two blocks. is the Euclidean distance between the two blocks. is the Euclidean distance between the two blocks.

4. The method of claim 1, wherein, Step c specifically comprises: selecting the first k low-order components whose cumulative contribution rate of principal components reaches 85% or more to reconstruct the matrix, and the difference between the reconstructed matrix and the original similar block matrix is the estimated noise.

5. The method of claim 1, wherein, Step d specifically comprises: The estimated noise matrix and the corresponding similar block matrix are subjected to zero mean processing; The eigenvalue decomposition is performed on the covariance matrix of the estimated noise: ， wherein represents an estimate of the noise covariance, is a matrix with eigenvalues as diagonal elements, is a matrix of eigenvectors; The noise whitening matrix is constructed as follows: ， The similar block matrix is whitened using the above matrix as: 。 6. The method of claim 1, wherein, The iteration step in step h is set to 0.1, and the iteration number is set according to the noise level.

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