Power grid disturbance signal denoising method based on improved BM3D

Abstract

The application discloses a power grid disturbance signal denoising method based on improved BM3D. The method comprises the following steps: firstly, collecting an original power grid disturbance signal to obtain a one-dimensional sampling signal sequence; then, performing a block matching operation on the sampling sequence in one-dimensional DCT, and extracting similar matching blocks according to the correlation between signal segments; then, in two-dimensional DCT, the sparsity of the matching blocks is utilized, and an OMP algorithm is used to select appropriate coefficients to filter the signal; finally, the denoised power grid disturbance signal is obtained by re-estimating and weightedly averaging and integrating the overlapping blocks. The application can significantly improve the signal-to-noise ratio of the power grid signal, effectively reduce the mean square error, retain more signal detail information, achieve good denoising effect, and provide reliable support for accurate detection and analysis of the power system signal.

Description

Technical Field

[0001] This application relates to the field of power system analysis, specifically to a method for denoising power grid disturbance signals based on an improved BM3D. Background Technology

[0002] With the rapid development of new power systems, a large number of nonlinear and impulsive loads have been connected to the power grid, leading to increasingly prominent power quality problems. These problems not only affect the stable operation of the power system but may also cause significant economic losses to industrial production and daily life. Therefore, improving the stability and reliability of power quality has become an important goal in the current development of power systems. In actual power grid operation, due to the influence of uncontrollable factors such as load changes, line switching, and equipment failures, grid disturbance signals are often accompanied by a large amount of noise. This noise not only interferes with the normal operation of sensitive power equipment but also greatly reduces the accuracy of identifying and analyzing grid disturbance signals. Therefore, effectively denoising noisy grid disturbance signals is the primary prerequisite for achieving accurate detection and analysis, and is of great significance for ensuring the safe and stable operation of the power system and improving power supply quality.

[0003] In recent years, with the rapid development of electronic technology and digital signal processing, many denoising algorithms for power grid disturbance signals have been proposed. These methods mainly include wavelet denoising algorithms, mathematical morphology-based denoising algorithms, and kernel regression denoising algorithms. However, these methods still have some limitations in practical applications, specifically as follows:

[0004] 1. Wavelet Denoising Algorithm: Due to its excellent time-frequency analysis capabilities, wavelet transform is widely used in signal denoising, leading to the development of many improved wavelet denoising algorithms. However, the performance of wavelet transform-based denoising algorithms largely depends on the choice of wavelet basis and the determination of the decomposition level. Different wavelet bases exhibit significant differences in denoising effects, and in the processing of power grid disturbance signals containing complex noise, the performance of traditional wavelet denoising algorithms is relatively low, making it difficult to meet high-precision requirements.

[0005] 2. Mathematical Morphology Denoising Algorithm: Mathematical morphology is a nonlinear time-domain signal processing method based on set theory, which has advantages such as low computational cost and strong real-time performance. However, its denoising effect is highly dependent on the selection of structuring elements in the morphological filter, including parameters such as shape and size. If the structuring elements are not selected properly, it will seriously affect the denoising effect of the signal, thereby weakening the ability to identify power grid disturbance signals.

[0006] 3. Kernel Regression Denoising Algorithm: Kernel regression is a non-parametric regression method that uses a kernel function (such as a Gaussian kernel function) to smooth the signal and achieve denoising. Its advantage lies in the fact that it does not require estimating the noise variance or setting a filtering threshold, and it has strong adaptability. However, when processing strong noise or complex perturbation signals, the denoising performance of this algorithm is limited, and the reconstructed signal is prone to distortion, making it difficult to meet the needs of practical applications. Summary of the Invention

[0007] The technical problem this application aims to solve is as follows: Addressing the limitations of existing denoising techniques, such as limited signal-to-noise ratio improvement, severe loss of signal details, and high mean square error, this application proposes a power grid disturbance signal denoising method based on an improved BM3D. This method combines the advantages of both BM3D and OMP, fully utilizing the block-level correlation and sparsity characteristics of the signal to achieve efficient denoising while significantly reducing mean square error and preserving more signal detail information.

[0008] To solve the above-mentioned technical problems, this application adopts the following technical solution:

[0009] A method for denoising power grid disturbance signals based on improved BM3D includes:

[0010] S101, collect the original power grid disturbance signal to obtain a one-dimensional sampling signal X of length N;

[0011] S102, for the sampled signal X, the signal is divided into equal-sized preparatory blocks using a segmentation method. These preparatory blocks are arranged sequentially to form an M×L noisy two-dimensional matrix.

[0012] S103, for each preparatory block of the segmented two-dimensional matrix P, perform a block matching operation within the specified search range. Select the current block p as the execution block, and select a region with diameter R centered on p as the search region. All blocks within the search region are considered as candidate matching blocks. Taking p1 as an example, for each candidate matching block p within the search region... m The condition is that m must be selected within the search range, and the distance d between them and the execution block p1 is calculated using the following formula:

[0013] d(p1,p m )=∑abs(γ(p1)-γ(p m ))

[0014] Where m∈(-R / 2,…,M)∪(1,…,R / 2); γ(p) is the one-dimensional DCT filtering operation performed on the preparatory block within the search range;

[0015] When performing one-dimensional DCT filtering on the execution block and the matching block, assume p m One-dimensional DCT coefficients using Zm It is indicated that the selection of the threshold can be defined by the following formula:

[0016] α = max{Z m (floor(L / 2)), …, Z m (L)}

[0017] After the above processing, all the preliminary blocks in P are filtered to achieve the initial denoising of the noisy two-dimensional matrix P and obtain the two-dimensional matrix P1 after preliminary denoising. By comparing the average amplitude difference between the matrices P and P1 before and after preliminary denoising, the noise intensity of the original noisy signal can be preliminarily estimated. Using the average amplitude difference, when selecting subsequent coefficients, the OMP algorithm can be used to select an appropriate residual threshold as the termination condition for iteration;

[0018] S104. Perform one-dimensional inverse DCT on the set A of similar matching blocks p to obtain the two-dimensional coefficient matrix S p , and then perform two-dimensional DCT on S p to obtain the sparse coefficient matrix in the two-dimensional DCT domain

[0019] S105. Use the OMP algorithm to retain the best coefficients, complete the filtering, and obtain the coefficient matrix T;

[0020] S106. Re-evaluate and perform weighted averaging by integrating overlapping blocks to obtain the finally denoised signal.

[0021] Optionally, the detailed steps of S102 include:

[0022] For the test signal X, the signal is segmented and combined using split blocks to obtain P: Using a sliding block Q with a length of L, which needs to satisfy L < N and a sliding step of ξ, the signal is segmented from left to right, and the signal is segmented into a total of preliminary blocks of equal size. These preliminary blocks are arranged in order to form a noisy two-dimensional matrix P of M × L. The specific expression of P is:

[0023]

[0024] Optionally, the detailed steps of S104 include:

[0025] After determining the similar matching blocks of the execution block, two-dimensional co-transformation and final filtering processing need to be performed on the similar matching blocks, which specifically include the following steps:

[0026] S201. Perform one-dimensional inverse DCT on the similar matching block A p to obtain the block matrix S p ;

[0027] S202, perform a two-dimensional DCT on it, that is, first perform a one-dimensional DCT on each row of the matrix, and then perform a one-dimensional DCT on each column to obtain a two-dimensional DCT sparse coefficient matrix.

[0028] S203, in the two-dimensional transform domain, the OMP algorithm can utilize the block matrix S p The sparsity in the two-dimensional transform domain enables the sparse representation of signals and the selection of appropriate coefficients.

[0029] Optionally, the detailed steps of S105 include:

[0030] The specific process of the OMP algorithm is as follows:

[0031] S301, Initialization: Let the sensing matrix be A, the number of iterations be t1, r0 = y, and the number of iterations t1 = 1. The threshold for terminating the iteration is ε;

[0032] S302, calculate the inner product and find the corresponding number of atoms to form the support set and calculate θ. i :S i =max(<A,y> ,K),C i =F i-1 ∪S i ,

[0033] S303, backtrack to select the best atoms, form a new support set and recalculate θ. i F = max(abs(θ) i ),K),

[0034] S304, Calculate the residual: r new =yA F θ i ;

[0035] S305, if ||r new If -r||≤ε, then let t1=t1+1 and repeat step S302; otherwise, let r=r t Stop the iteration and use the obtained atoms to get the reconstruction coefficients T;

[0036] In the above process, y is the measurement vector with size M×1; Λ0 is the index set for the 0th iteration; r0, r is the current residual, initialized to r0 = y, and updated in each round; θ i S is the estimate of the sparse coefficients calculated by the least squares method in the i-th iteration; i Let K be the set of candidate atom indices selected from the inner product in step i; K is the sparsity; C i As an intermediate variable, representing a portion of the least squares coefficients; Fi-1 The support set from the previous iteration; A is a submatrix on the current support set, i.e., the corresponding column is selected from A; A F The submatrix corresponding to the currently updated support set; F is the index of the most relevant atom selected from the projection of the current atom and the residual; r new The residual after the current iteration is the difference between the measurement vector y and the current reconstructed signal.

[0037] Optionally, the detailed steps of S106 include:

[0038] After two-dimensional transform domain filtering, due to overlap between blocks, different similar groups may contain the same matching blocks. Therefore, it is necessary to perform a weighted average of these filtering results from different combinations to obtain the estimated value of the block. The weighted estimation process includes the following steps:

[0039] S301, Define the base weight W of the current block. P for:

[0040]

[0041] Where, N P This represents the number of non-zero elements in the matrix coefficients of the current block after two-dimensional transform domain filtering.

[0042] S302, Since the two-dimensional DCT process may cause boundary effects, in order to reduce their impact, this application introduces the Kaiser window function W for weighting, and performs inverse two-dimensional DCT on the filtered coefficient matrix T to obtain the reconstruction estimate.

[0043] S303, the final denoising result of the noisy signal is integrated as follows:

[0044]

[0045] in, This is an estimate of the denoised disturbance signal; To reconstruct the estimation matrix; M is the total number of matching blocks; S is the number of similar matching blocks; L is the length of similar matching blocks; is the feature function of similar matching blocks.

[0046] Compared with traditional denoising methods, this application significantly improves the denoising effect of power grid disturbance signals by combining the advantages of BM3D and OMP, and has the following main advantages:

[0047] 1. The improved BM3D algorithm uses only 5 parameters, which simplifies the complexity of parameter setting, reduces computational overhead, and reduces the difficulty of parameter tuning, making the algorithm more convenient and efficient in practical use.

[0048] 2. The improved BM3D algorithm introduces the OMP algorithm to replace the traditional hard threshold filtering in controlling the optimization process of sparse coefficients. This allows for more effective selection of appropriate coefficients and reduces the loss of signal details during filtering. The use of similar matching block-based grouping technology and sparse optimization methods effectively enhances the correlation and sparsity of the signal, improving signal reconstruction accuracy.

[0049] 3. The improved BM3D algorithm utilizes block matching and weighted estimation techniques to efficiently eliminate the influence of noise on the signal, thereby significantly reducing the mean square error. Attached Figure Description

[0050] Figure 1 This is a schematic diagram of the basic process of the method in the embodiments of this application.

[0051] Figure 2 This is a diagram showing the selection of parameters R and S in the embodiments of this application.

[0052] Figure 3 is a comparison of the denoised waveforms of the oscillation signal according to the embodiments of this application. Among them, 3(a) is the original denoised waveform; 3(b) is the waveform after denoising by the algorithm of this application; and 3(c) is the waveform after wavelet denoising.

[0053] Figure 4 shows a comparison of the denoised waveforms of the interrupted signal in the embodiments of this application. Among them, 4(a) is the original denoised waveform; 4(b) is the waveform after denoising by the algorithm of this application; and 4(c) is the waveform after wavelet denoising. Detailed Implementation

[0054] A power grid disturbance signal denoising method based on improved BM3D, the specific implementation of which includes:

[0055] S101, collect the original power grid disturbance signal to obtain a one-dimensional sampling signal X of length N;

[0056] S102, for the sampled signal X, the signal is divided into equal-sized preparatory blocks using a segmentation method. These preparatory blocks are arranged sequentially to form an M×L noisy two-dimensional matrix.

[0057] S103, for each preparatory block of the segmented two-dimensional matrix P, perform a block matching operation within the specified search range. Select the current block p as the execution block, and select a region with diameter R centered on p as the search region. All blocks within the search region are considered as candidate matching blocks. Taking p1 as an example, for each candidate matching block p within the search region... m The condition is that m must be selected within the search range, and the distance d between them and the execution block p1 is calculated using the following formula:

[0058] d(p1,p m)=∑abs(γ(p1)-γ(p m ))

[0059] Where m∈(-R / 2,…,M)∪(1,…,R / 2); γ(p) is the one-dimensional DCT filtering operation performed on the preparatory block within the search range;

[0060] When performing one-dimensional DCT filtering on the execution block and the matching block, assume p m One-dimensional DCT coefficients using Z m Therefore, the threshold can be defined by the following formula:

[0061] α=max{Z m (floor(L / 2)),…,Z m (L)}

[0062] After processing by the above formula, all preparatory blocks in P are filtered to achieve the initial denoising of the noisy two-dimensional matrix P and obtain the two-dimensional matrix P1 after initial denoising. By comparing the average amplitude difference between matrices P and P1 before and after initial denoising, the noise intensity of the original noisy signal can be initially estimated. Using the average amplitude difference, an appropriate residual threshold can be selected as the termination condition of the iteration through the OMP algorithm in the subsequent selection of coefficients.

[0063] S104, for the similar matching block set A p Perform one-dimensional DCT inverse calculation to obtain the two-dimensional coefficient matrix S p Then for S p Perform two-dimensional DCT calculations to obtain the sparse coefficient matrix in the two-dimensional DCT domain.

[0064] S105, using the OMP algorithm to retain the best coefficients, completes the filtering and obtains the coefficient matrix T;

[0065] S106 re-evaluates and weights the signal by integrating overlapping blocks to obtain the final denoised signal.

[0066] S102, S103 and S105 involve five parameters: block sliding block length L, block sliding step size ξ, similar matching block search area R, number of similar matching blocks S and residual threshold ε.

[0067] The selection of ε can be based on the average amplitude difference and residual threshold obtained under different noise intensities, as shown in the table below.

[0068] Table 1: Average amplitude difference and residual threshold selection under different noise intensities

[0069]

[0070] As can be seen from Table 1, under different noise intensities, the average amplitude difference shows obvious differences, and the amplitude difference is also larger when the noise is greater. With the help of this amplitude difference, an appropriate residual threshold can be selected targeted to ensure the efficiency of the OMP algorithm.

[0071] Regarding the selection of parameters L and ξ: Since these two parameters affect the size of the noisy two-dimensional matrix P after segmentation and the running speed of the algorithm, they have little impact on the actual denoising effect.

[0072] In this application, the signal-to-noise ratio (SNR) and mean square error (MSE) after signal denoising are used as the evaluation criteria for the denoising effect. The specific formulas are as follows:

[0073]

[0074]

[0075] In the improved algorithm proposed in this application, it is necessary to select an appropriate similar block search area R and the number of similar block matches S to find the best number and quality of similar blocks. The specific simulation test results are as Figure 2 shown.

[0076] From Figure 2 it can be seen that the selection of R and S is crucial for the final signal denoising effect, and it is necessary to satisfy S < R, that is, to ensure that the number of matching blocks is less than the total number of blocks within the search range. When selecting the parameter S, its value should be ensured to be between 50 and 400 to avoid too few similar blocks due to too small a value, while too large a value will result in too many low-similarity blocks in the similar matching blocks, thus causing greater interference to the result integration. For the parameter R, its value range should be kept within 200 - 913. An overly large search area R will increase the running time cost of the algorithm, while an overly small search range R will result in too few similar matching blocks within the search range.

[0077] To balance the efficiency and quality of denoising, in this application, the values of L, ξ, S, and R are taken as 30, 4, 61, and 313 respectively.

[0078] This application also compares the proposed method with the traditional db5 wavelet denoising algorithm for the noisy oscillating and interrupted signals. The specific waveform results after the two are processed are shown in Figures 3 and 4 respectively.

[0079] As can be seen from Figures 3 and 4, the proposed method differs significantly from traditional wavelet denoising methods in denoising performance. Traditional wavelet denoising methods retain considerable noise during interruptions and oscillations in the processed voltage waveform, resulting in an uneven waveform. Furthermore, this method incorrectly filters out some crucial information in voltage oscillation signals, affecting signal integrity. In contrast, the proposed method demonstrates superior performance in processing these signals. Specifically, this method not only effectively filters out most of the noise and improves the smoothness of the denoised signal waveform, but also better preserves the key feature information of voltage interruptions and oscillations, thus providing more accurate and reliable denoising results. Therefore, this method significantly outperforms traditional wavelet denoising methods in denoising performance, especially in processing power grid disturbance signals with complex noise, where it better preserves the key feature information of the signal.

[0080] To further verify the superiority of this application in denoising, comparative experiments were conducted on different algorithms based on evaluation metrics. A total of three single-frequency disturbance signals (voltage sag, interruption, and oscillation) and harmonic multi-frequency disturbance signals were included. The dB5 and Bior2.2 wavelet denoising algorithms were used to test these signals. During the simulation, Gaussian white noise of 10, 15, 20, 25, and 30 dB was superimposed on the signals. Considering the randomness of the noise, all algorithms underwent 1000 tests to ensure the reliability of the results. Finally, the average SNR and MSE values ​​of the denoised signals obtained by different algorithms were calculated, and the specific results are shown in the table below.

[0081] Table 2: Average SNR and MSE values ​​of the denoised signals obtained by different algorithms

[0082]

[0083] As shown in Table 2, the proposed algorithm outperforms the db5 and bior2.2 wavelet denoising methods in both SNR and MSE under four different perturbation signals and different signal-to-noise ratios. After denoising voltage sag signals, the proposed algorithm achieves an SNR 2 to 6 dB higher than traditional wavelet denoising methods, with a significantly reduced MSE. After denoising voltage interruption signals, the SNR increases by 3 to 4 dB, and the MSE decreases, resulting in more accurate signal recovery. In voltage oscillation signals, although the SNR obtained by the proposed algorithm is slightly higher than the db5 wavelet denoising method under high noise levels, the denoising effect is significantly improved when the original SNR is greater than 15 dB, resulting in a substantial increase in the denoised SNR and a decrease in the MSE. In harmonic signal processing, both the SNR and MSE after denoising are superior to the db5 and bior2.2 wavelet denoising methods, demonstrating stronger denoising capabilities and signal recovery performance.

[0084] Among the evaluation metrics for denoising results, the ability to retain information about abrupt changes is crucial, reflecting the algorithm's capacity to capture and preserve such changes. This metric, expressed as denoising error σ, demonstrates how close the amplitude of the denoised signal at the abrupt change point is to the ideal amplitude. The specific formula for calculating denoising error σ is as follows:

[0085]

[0086] Among them, A x The amplitude at the abrupt change point of the original signal; The amplitude of the abrupt change point in the denoised signal.

[0087] A voltage sag signal with 30dB added noise was selected, with the sag abrupt change occurring at 0.0925s and ending at 0.1425s. Comparative experiments were conducted using this application with the db5 wavelet and the bior2.2 wavelet. The experimental results are shown in the table below.

[0088] Table 3: Comparison experiment between this application and db5 wavelet and bior2.2 wavelet

[0089]

[0090] As shown in Table 3, this application achieves a smaller denoising error when processing the voltage sag signal. This indicates that this application performs best in terms of the ability to restore abrupt change points, and can retain the original information of the signal to the greatest extent, demonstrating superior performance in preserving information at signal abrupt change points.

[0091] In summary, this application, based on the excellent denoising performance of the BM3D algorithm, improves it by leveraging the sparsity of similar matching blocks in the transform domain and employing the OMP algorithm to efficiently retain effective coefficients. The improved BM3D algorithm proposed in this application not only effectively removes noise but also better preserves the detailed information of the original signal. Test results under different power grid disturbance signals and different signal-to-noise ratios (SNRs) demonstrate that this application significantly improves the SNR of the denoised signal and substantially reduces the mean square error. Furthermore, this application exhibits superior performance in preserving the amplitude of abrupt changes, retaining key feature information of the signal in the denoising processing of various power grid disturbance signals.

Claims

1. A method for denoising power grid disturbance signals based on improved BM3D, characterized in that, include: S101, collect the original power grid disturbance signal to obtain a one-dimensional sampling signal X of length N; S102, for the sampled signal X, the signal is divided into equal-sized preparatory blocks using a segmentation method. These preparatory blocks are arranged sequentially to form an M×L noisy two-dimensional matrix. S103, for each preparatory block of the segmented two-dimensional matrix P, perform a block matching operation within the specified search range. Select the current block p as the execution block, and select a region with diameter R centered on p as the search region. All blocks within the search region are considered as candidate matching blocks. Taking p1 as an example, for each candidate matching block p within the search region... m The condition is that m must be selected within the search range, and the distance d between them and the execution block p1 is calculated using the following formula: d(p1,p m )=∑abs(γ(p1)-γ(p m )) Where m∈(-R / 2,…,M)∪(1,…,R / 2); γ(p) is the one-dimensional DCT filtering operation performed on the preparatory block within the search range; When performing one-dimensional DCT filtering on the execution block and the matching block, assume p m One-dimensional DCT coefficients using Z m Therefore, the threshold can be defined by the following formula: α=max{Z m (floor(L / 2)),…,Z m (L)} After processing by the above formula, all preparatory blocks in P are filtered to achieve the initial denoising of the noisy two-dimensional matrix P and obtain the two-dimensional matrix P1 after initial denoising. By comparing the average amplitude difference between matrices P and P1 before and after initial denoising, the noise intensity of the original noisy signal can be initially estimated. Using the average amplitude difference, an appropriate residual threshold can be selected as the termination condition of the iteration through the OMP algorithm in the subsequent selection of coefficients. S104, for the similar matching block set A p Perform one-dimensional DCT inverse calculation to obtain the two-dimensional coefficient matrix S p Then for S p Perform two-dimensional DCT calculations to obtain the sparse coefficient matrix in the two-dimensional DCT domain. S105, using the OMP algorithm to retain the best coefficients, completes the filtering and obtains the coefficient matrix T; S106 re-evaluates and weights the signal by integrating overlapping blocks to obtain the final denoised signal.

2. The method for denoising power grid disturbance signals based on improved BM3D according to claim 1, characterized in that, In step S102, for the one-dimensional power grid disturbance signal X with a length of N, a sliding block Q with a length of L is used, where L < N and the sliding step size is ξ. The signal is segmented from left to right into a total of preliminary blocks of equal size. These preliminary blocks are arranged in order to form a noisy two-dimensional matrix P of M × L.

3. The method for denoising power grid disturbance signals based on improved BM3D according to claim 1, characterized in that, The calculated distances d are sorted from smallest to largest, and the blocks most similar to the execution block are selected sequentially. When determining whether two blocks are similar, the threshold is set to a fixed value S, and the S blocks closest to the execution block p are grouped into a similar matching block set A. P .

4. The method for denoising power grid disturbance signals based on improved BM3D according to claim 1, characterized in that, In step S104, after determining the similar matching blocks of the execution block, it is necessary to perform two-dimensional cooperative transformation and final filtering on the similar matching blocks, which specifically includes the following steps: S201, for similar matching block A P Perform a one-dimensional inverse DCT to obtain the block matrix S P ; S202, perform a two-dimensional DCT on it, that is, first perform a one-dimensional DCT on each row of the matrix, and then perform a one-dimensional DCT on each column to obtain a two-dimensional DCT sparse coefficient matrix. S203, in the two-dimensional transform domain, the OMP algorithm can utilize the block matrix S P The sparsity in the two-dimensional transform domain enables the sparse representation of signals and the selection of appropriate coefficients.

5. The method for denoising power grid disturbance signals based on improved BM3D according to claim 1, characterized in that, In step S105, the specific process of the OMP algorithm is as follows: S301, Initialization: Let the sensing matrix be A, the number of iterations be t1, r0 = y, and the number of iterations t1 = 1. The threshold for terminating the iteration is ε; S302, calculate the inner product and find the corresponding number of atoms to form the support set and calculate θ. i :S i =max(<A,y> ,K),C i =F i-1 ∪S i , S303, backtrack to select the best atoms, form a new support set and recalculate θ. i F = max(abs(θ) i ),K), S304, Calculate the residual: r new =yA F θ i ; S305, if ||r new If -r||≤ε, then let t1=t1+1 and repeat step S302; otherwise, let r=r t Stop the iteration and use the obtained atoms to get the reconstruction coefficients T; In the above process, y is the measurement vector with size M×1; Λ0 is the index set of the 0th iteration; r0, r is the current residual, initialized as r0 = y, and updated in each round; θ i S is the estimate of the sparse coefficients calculated by the least squares method in the i-th iteration; i Let K be the set of candidate atom indices selected from the inner product in step i; K is the sparsity; C i As an intermediate variable, representing a portion of the least squares coefficients; F i-1 A is the support set from the previous iteration; Ci A is a submatrix on the current support set, i.e., the corresponding column is selected from A; A F The submatrix corresponding to the currently updated support set; F is the index of the most relevant atom selected from the projection of the current atom and the residual; r new The residual after the current iteration is the difference between the measurement vector y and the current reconstructed signal.

6. The method for denoising power grid disturbance signals based on improved BM3D according to claim 1, characterized in that, After two-dimensional transform domain filtering in step S106, since there is overlap between blocks and different similar groups may contain the same matching blocks, it is necessary to perform a weighted average of the filtering results from different combinations to obtain the estimated value of the block. The weighted estimation process includes the following steps: S401, Define the base weight W of the current block. P for Where, N P This represents the number of non-zero elements in the matrix coefficients of the current block after two-dimensional transform domain filtering. S402. Since the two-dimensional DCT process may cause boundary effects, a Kaiser window function W is introduced for weighting to reduce its impact. The filtered coefficient matrix T is then subjected to inverse two-dimensional DCT to obtain the reconstructed estimation matrix. S403, the final denoising result of the noisy signal is integrated as follows: in, This is an estimate of the denoised disturbance signal; To reconstruct the estimation matrix; M is the total number of matching blocks; S is the number of similar matching blocks; L is the length of similar matching blocks; is the feature function of similar matching blocks.

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