A magnetic resonance sounding signal denoising method based on backtracking generalized OMP

Abstract

The application belongs to the field of magnetic resonance sounding signal noise filtering, and particularly relates to a magnetic resonance sounding signal denoising method based on backtracking generalized OMP. A magnetic resonance sounding water detector is used to sample a sparse signal at a frequency lower than a Nyquist frequency to obtain a noisy MRS signal. The noisy MRS signal is converted into a two-dimensional matrix signal. A KSVD algorithm is used to learn a dictionary from the two-dimensional matrix signal, and an updated dictionary is obtained after iteration. An independently distributed Gaussian random matrix is used to calculate a recovery matrix and measurement data. A backtracking generalized orthogonal matching pursuit algorithm is used to iteratively operate on the measurement data, and an atom sequence with the maximum projection of the measurement data and the recovery matrix is selected to obtain a sparse coefficient matrix of the measurement data under the recovery matrix. A recovery signal is calculated according to the dictionary and the sparse coefficient matrix of the measurement data under the recovery matrix.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of magnetic resonance sounding signal noise filtering, and particularly relates to a magnetic resonance sounding signal denoising method based on backtracking generalized OMP. BACKGROUND

[0002] Magnetic resonance sounding (MRS) is a promising geophysical method for direct and quantitative detection of groundwater. The technology collects the induced magnetic field of the excited hydrogen protons in groundwater, analyzes the characteristics and occurrence state of groundwater quantitatively according to the relaxation characteristics. MRS is an efficient geophysical detection technology with the advantages of non-invasiveness and high sensitivity, and is widely used in water resource investigation, environmental monitoring, soil research, geological survey and earthquake research.

[0003] The MRS signal obtained in the process of ground magnetic resonance detection is extremely weak, and the MRS signal is very weak, usually in nanovolt level, and is often submerged in environmental noise. During the detection process, external environmental interference factors cannot be completely shielded, resulting in that the MRS signal is affected by random noise, power harmonic and spike noise, the quality of the signal is reduced, the extraction of MRS signal parameters and inversion is hindered, and finally the inaccuracy of regional water resource content evaluation is caused. In order to solve the problems of noise suppression and effective signal extraction, domestic and foreign scholars have carried out related research. However, the noise suppression method at the present stage has great limitations, and has good denoising performance under certain conditions, but for various uncertain noises in the MRS signal, noise suppression and effective extraction of the MRS signal are still technical problems in the field. SUMMARY

[0004] The embodiment of the application provides a magnetic resonance sounding signal denoising method based on backtracking generalized OMP, which solves the problem that the MRS signal is easily interfered by random noise and spike noise in the measurement process.

[0005] According to the magnetic resonance sounding signal denoising method based on backtracking generalized OMP, the method comprises the following steps:

[0006] A magnetic resonance sounding water detector is used to sample a sparse signal at a frequency lower than the Nyquist frequency, and a noisy MRS signal is obtained;

[0007] After removing the power harmonic noise in the noisy MRS signal by using a harmonic modeling method, the noisy MRS signal is converted into a two-dimensional matrix signal;

[0008] KSVD algorithm is used for dictionary learning of the two-dimensional matrix signal, a random matrix is used as an initial dictionary, the two-dimensional matrix signal is used as original data, and an updated dictionary is obtained after iteration;

[0009] The recovery matrix and the measurement data are calculated using independent distributed Gaussian random matrix;

[0010] The measurement data is iteratively operated using the backtracking generalized orthogonal matching pursuit algorithm, an atomic sequence of a modulus maximum projection of the measurement data and the recovery matrix is selected, and a sparse coefficient matrix of the measurement data under the recovery matrix is obtained;

[0011] The recovery signal is calculated according to a product of the dictionary and the sparse coefficient matrix of the measurement data under the recovery matrix, and a first row of the recovery signal is restored to a one-dimensional signal.

[0012] Further, the recovery matrix is , the measurement data is , wherein is the recovery matrix, is the Gaussian random matrix, is the two-dimensional matrix signal, is the dictionary, is the measurement data.

[0013] Further, the calculation formula of the recovery signal is: , is the sparse coefficient matrix of the measurement data under the recovery matrix, is the recovery signal, is the dictionary.

[0014] Further, the dictionary learning is performed on the two-dimensional matrix signal by using the KSVD algorithm, the random matrix is used as an initial dictionary, the two-dimensional matrix signal is used as original data, and the updated dictionary is obtained after iteration, including: the sparse coefficient matrix of the two-dimensional matrix signal under the current dictionary is calculated using the backtracking generalized orthogonal matching pursuit algorithm;

[0015] The dictionary learning is performed, and the first column of the dictionary is updated, and the formula used is:

[0016] , is the first column vector of the dictionary, is the first row vector of the sparse coefficient matrix of the two-dimensional matrix signal under the current dictionary, is the signal residual, represents the square of the F norm, is the first column vector of the dictionary, is the first row vector of the sparse coefficient matrix of the two-dimensional matrix signal under the current dictionary, is the two-dimensional matrix signal, is the dictionary, is the dictionary, is the first row vector of the sparse coefficient matrix of the two-dimensional matrix signal under the current dictionary, is the two-dimensional matrix signal, is the dictionary, ​This is the sparse coefficient matrix of the current dictionary;

[0017] Extract the sparse coefficient matrix of the corresponding two-dimensional matrix signal in the current dictionary from the signal residual. The column vectors whose row vectors are not zero form the new signal residual. Singular value decomposition is then performed on the new signal residual to obtain the first column of the left singular vector, which replaces the dictionary. Column vector;

[0018] Repeat the process the same number of times as the number of atoms in the dictionary to obtain the updated dictionary.

[0019] Furthermore, the singular value decomposition of the new signal residual includes: transforming the new signal residual into a singular value decomposition. The product of three matrices, It is an orthogonal matrix with the same number of rows as the residual of the new signal, and its column vectors are called left singular vectors. It is a rectangular diagonal matrix of the same size as the residual of the new signal, with the non-negative elements on the diagonal arranged in descending order being the singular values. It is an orthogonal matrix with the same column number as the residual of the new signal, and its row vectors are right singular vectors.

[0020] Furthermore, the sparse coefficient matrix of the two-dimensional matrix signal under the current dictionary is calculated using the backtracking generalized orthogonal matching pursuit algorithm, including:

[0021] Input the number of atoms in the dictionary, and generate an initialized dictionary;

[0022] The sparse coefficient matrix of the two-dimensional matrix signal under the current dictionary is calculated using the backtracking generalized orthogonal matching pursuit algorithm. The inputs are the initial dictionary, the two-dimensional matrix signal, and the first atomic constraint degree. Sparse coding is performed by iteratively calculating the column vectors of the two-dimensional matrix signal, with the initial residuals as follows: , For a two-dimensional matrix signal, the column vectors are... The first residual;

[0023] Calculate the projection of the transpose of the current dictionary onto the current residual: , The projection of the current residual. For the transpose of the current dictionary, select the index with the largest projection and add it to the index set;

[0024] The least squares method is used to solve for the sparse coefficient atoms of the column vector corresponding to the index of the two-dimensional matrix signal in the current loop.

[0025] Update the first residual based on the sparse coefficient atoms;

[0026] repeat Next, fill the sparse coefficient atoms into the first sparse coefficient matrix A( ), Indicates the length of the signal. The position of each signal is used to process all column vectors of the two-dimensional matrix signal, and finally the sparse coefficient matrix of the two-dimensional matrix signal under the current dictionary is obtained.

[0027] Furthermore, the first residual is updated based on the sparse coefficient atoms, expressed as: ,in, For the first residual, For sparse coefficient atoms, , This is the pseudo-inverse operation of the sub-dictionary set corresponding to the index set of the dictionary. This represents the set of sub-dictionaries corresponding to the index set of the dictionary.

[0028] Furthermore, the backtracking generalized orthogonal matching pursuit algorithm is used to iteratively calculate the measurement data, selecting the atomic sequence that projects the measurement data onto the maximum magnitude of the recovery matrix, thus obtaining the sparse coefficient matrix of the measurement data under the recovery matrix, including:

[0029] Input recovery matrix, measurement data, second atomic constraint degree And select the number of atoms S, perform iterative calculations on the column vector of the measurement data, and initialize the second residual to be equal to the column vector of the measurement data;

[0030] Calculate the modulus of the projection of the current second residual onto the transpose of the recovery matrix, and select the indices of the S largest moduli to add to the index set;

[0031] Select a sub-dictionary set of the index set corresponding to the recovery matrix, and use pseudo-inverse operation to solve for the first coefficient;

[0032] Update the second residual based on the first coefficient;

[0033] repeat Next, fill the first coefficient into the second sparse coefficient matrix. ( ), Indicates the length of the signal. The position of each signal is used to process all atoms of the measurement data and obtain the sparse coefficient matrix of the measurement data under the recovery matrix.

[0034] Furthermore, the second residual is updated based on the first coefficient, expressed as: , A column vector representing the measurement data. This represents a set of sub-dictionaries corresponding to the index set of the recovery matrix. As the first coefficient, This is the second residual.

[0035] Compared with the prior art, the advantages of this application are as follows:

[0036] The present application is significantly better than the traditional OMP (orthogonal matching pursuit) and other sparse signal reconstruction in performance. The block atomic selection mechanism selects multiple candidate atoms in each iteration, greatly reduces the number of iterations, thereby accelerating the convergence speed and improving the efficiency in high-dimensional or high sparsity scenarios. Through the dynamic backtracking mechanism, the atomic set is optimized to eliminate redundant or noise interference atoms, significantly improving the reconstruction accuracy and noise immunity, and avoiding the problem of cumulative error caused by early misselection in the traditional OMP method. In addition, in terms of computational complexity, although the pseudo-inverse calculation of a single iteration increases the computational complexity, by reducing the number of iterations, the overall efficiency is still better than the traditional OMP method, especially when processing large-scale data or high sparse signals. While maintaining low computational complexity, the reconstruction accuracy, convergence speed and robustness are significantly improved, and it is suitable for sparse representation tasks in complex environments, such as non-stationary signal processing, image recovery and low sampling rate compressed sensing scenarios. BRIEF DESCRIPTION OF DRAWINGS

[0037] Figure 1 A flow chart of a magnetic resonance sounding signal denoising method based on backtracking generalized OMP provided by an embodiment of the present application;

[0038] Figure 2 Ideal MRS signals and spectra provided by an embodiment of the present application, (A) is a time-amplitude graph, and (B) is a frequency-amplitude graph;

[0039] Figure 3 Original MRS signals, denoised signals, and spectra of ideal MRS signals provided by an embodiment of the present application, (A) is a time-amplitude graph, and (B) is a frequency-amplitude graph;

[0040] Figure 4 Spectra of measured noisy MRS signals and denoised signals provided by an embodiment of the present application, (A) is a time-amplitude graph, and (B) is a frequency-amplitude graph. DETAILED DESCRIPTION

[0041] In order to make the purpose, technical scheme and advantages of the present application more clear and explicit, the following will further describe the present application in combination with embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and do not limit the present application.

[0042] In order to make the purpose, technical scheme and advantages of the present application more clear and explicit, the following will further describe the present application in combination with embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and do not limit the present application.

[0043] Reference should be made to Figure 1The method for removing noise from a magnetic resonance sounding signal based on a backtracking generalized OMP, comprising:

[0044] S1 uses a magnetic resonance sounding instrument to sample a sparse signal at a frequency lower than the Nyquist frequency to obtain a noisy MRS signal; the number of sampling points is , wherein the Nyquist frequency refers to the highest frequency at which the signal can be effectively restored in the sampled signal, and should be greater than or equal to twice the highest frequency of the effective signal.

[0045] S2 uses a harmonic modeling method to remove power harmonic noise in the noisy MRS signal, and then converts the noisy MRS signal into a two-dimensional matrix signal; wherein the sampling order is set to ;

[0046] The harmonic modeling method considers electromagnetic field distribution and electromagnetic induction phenomena, establishes an electromagnetic model through electromagnetic theory such as Maxwell's equations, analyzes the generation mechanism of harmonics, and removes power harmonic noise according to the generation mechanism of harmonics.

[0047] The two-dimensional matrix signal is represented as:

[0048] , wherein is the two-dimensional matrix signal, which is related to the number of sampling points and the sampling order, represents the element of the first row and the first column, represents the element of the first row and the first column, represents the element of the first row and the first column, and other elements have similar meanings, the value of P is the sampling order, and the value of P is the sampling point number. S3 performs dictionary learning on the two-dimensional matrix signal through the KSVD algorithm (K times iteration singular value decomposition), uses a random matrix as the initial dictionary, and uses the two-dimensional matrix signal as the original data to obtain an updated dictionary after iteration;

[0049] S4 uses an independently distributed Gaussian random matrix to calculate a recovery matrix and measurement data, wherein the recovery matrix is calculated as and the measurement data is calculated as

[0050] , wherein is the recovery matrix, is the Gaussian random matrix, is the two-dimensional matrix signal, is the dictionary, and the measurement data; , wherein the Gaussian random matrix is a matrix related to the sampling order and the parameter

[0051] . ​​For a number much lower than the Nyquist frequency, the Gaussian random matrix also begins to be expressed as .

[0052] S5 uses the backtracking generalized orthogonal matching pursuit algorithm to perform iterative operation on the measurement data, selects an atomic sequence of a projection of the measurement data and the recovery matrix with the maximum modulus, and obtains a sparse coefficient matrix of the measurement data under the recovery matrix;

[0053] S6 calculates a recovery signal according to the dictionary and the sparse coefficient matrix of the measurement data under the recovery matrix, and restores the first row of the recovery signal to a one-dimensional signal, wherein the recovery signal , is the sparse coefficient matrix of the measurement data under the recovery matrix, is the recovery signal.

[0054] In an embodiment, dictionary learning is performed on a two-dimensional matrix signal by using the KSVD algorithm, a random matrix is used as an initial dictionary, the two-dimensional matrix signal is used as original data, and an updated dictionary is obtained after iteration, including: using the backtracking generalized orthogonal matching pursuit algorithm to calculate a sparse coefficient matrix of the two-dimensional matrix signal under a current dictionary;

[0055] Dictionary learning is performed, and a first column of the dictionary is updated, and a formula used is:

[0056] , is a first column vector of the dictionary, is a first row vector of the sparse coefficient matrix of the two-dimensional matrix signal under the current dictionary, is a signal residual, represents a square of the F norm, is a first column vector of the dictionary, is a first row vector of the sparse coefficient matrix of the two-dimensional matrix signal under the current dictionary, is the sparse coefficient matrix under the current dictionary; wherein the signal residual refers to a difference between the noisy signal Y and a signal restored by the current dictionary and the sparse coefficient matrix under the current dictionary, A column vector group, in which a first row vector of the sparse coefficient matrix of the two-dimensional matrix signal under the current dictionary is not 0, is extracted from the signal residual to form a new signal residual, and singular value decomposition is performed on the new signal residual, including: singular value decomposition is performed on the new signal residual to be converted into a product of three matrices,

[0057]

[0058] singular value decomposition is performed on the new signal residual to be converted into a product of three matrices, ​​​​​​is an orthogonal matrix with the same number of columns as the new signal residual, whose column vectors are called left singular vectors, is a rectangular diagonal matrix with the same size as the new signal residual, whose non-negative elements arranged in descending order on the diagonal are singular values, is an orthogonal matrix with the same number of columns as the new signal residual, whose row vectors are right singular vectors, and the first column left singular vector replaces the first column vector of the dictionary, The column vector of the dictionary is obtained.

[0059] Repeat the same number of times as the number of dictionary atoms to obtain the updated dictionary.

[0060] When obtaining the updated dictionary, it is necessary to calculate the sparse coefficient matrix under the current dictionary. In an embodiment, the backtracking generalized orthogonal matching pursuit algorithm is used to calculate the sparse coefficient matrix of the two-dimensional matrix signal under the current dictionary, including:

[0061] Input the number of dictionary atoms, and use to represent, generate the initialized dictionary, and the dictionary is related to the number of dictionary atoms and the sampling order, which can be represented as , in order to facilitate the following is used to represent;

[0062] The backtracking generalized orthogonal matching pursuit algorithm is used to calculate the sparse coefficient matrix of the two-dimensional matrix signal under the current dictionary, and the initial dictionary, the two-dimensional matrix signal and the atomic constraint degree are input to perform sparse coding, and the column vectors of the two-dimensional matrix signal are calculated in a loop, and the initialized residual is: , is the column vector of the two-dimensional matrix signal, is the first residual;

[0063] Calculate the projection of the transpose of the current dictionary and the current residual: , is the projection of the current residual, is the transpose of the current dictionary, and the index of the maximum projection is selected and added to the index set, which is represented by , is a number from 1 to , which is the current loop number;

[0064] The least square method is used to solve the sparse coefficient atom corresponding to the index of the column vector of the two-dimensional matrix signal under the current loop;

[0065] Update the first residual according to the sparse coefficient atom: , wherein is the first residual, is the sparse coefficient atom, , is the pseudo-inverse operation of the dictionary corresponding to the index set sub-dictionary set, This represents the set of sub-dictionaries corresponding to the index set of the dictionary;

[0066] repeat The order, which is related to the atomic constraint degree, involves filling the sparse coefficient atoms into the first sparse coefficient matrix A. ), Indicates the length of the signal. The position of each signal is determined by processing all column vectors of the two-dimensional matrix signal, ultimately obtaining the sparse coefficient matrix of the two-dimensional matrix signal under the current dictionary. The sparse coefficient matrix under the current dictionary is the first sparse coefficient matrix A obtained at the end. ).

[0067] In one embodiment, calculating the recovered signal also requires an important parameter: the sparse coefficient matrix of the measurement data under the recovery matrix. The sparse coefficient matrix of the measurement data under the recovery matrix is ​​similar to the sparse coefficient matrix under the current dictionary; both are calculated iteratively using the backtracking generalized orthogonal matching pursuit algorithm. The difference lies in:

[0068] The measurement data is iteratively processed using the backtracking generalized orthogonal matching pursuit algorithm. The atom sequence with the largest projection of the measurement data onto the modulus of the recovery matrix is ​​selected to obtain the sparse coefficient matrix of the measurement data under the recovery matrix. ,include:

[0069] Input recovery matrix, measurement data, second atomic constraint degree And select the number of atoms S, perform iterative calculations on the column vector of the measurement data, and initialize the second residual to be equal to the column vector of the measurement data;

[0070] The modulus of the projection of the current second residual onto the transpose of the recovery matrix is ​​calculated using the following formula: , For the second residual, To recover the projection of the matrix transpose, Indicates modulo, This indicates restoring the transpose of the matrix, selecting the indices of the S largest moduli and adding them to the index set;

[0071] Select a sub-dictionary set corresponding to the index set of the recovery matrix, and use pseudo-inverse operation to solve for the first coefficient, expressed as: , For the column vector of measurement data, This indicates a pseudo-inverse operation. This represents a set of sub-dictionaries representing the index set corresponding to the recovery matrix;

[0072] Update the second residual based on the first coefficient: ;

[0073] repeat Next, fill the first coefficient into the second sparse coefficient matrix. ( ), Indicates the length of the signal. The position of each signal is determined, and all atoms of the measurement data are processed to obtain the sparse coefficient matrix of the measurement data under the reconstruction matrix. That is, the final second sparse coefficient matrix ( ).

[0074] Simulation experiments were conducted on the method described in this application.

[0075] This embodiment is a simulation experiment of the method of this application conducted in the MATLAB R2023b programming environment.

[0076] According to mathematical formulas Construct a pure MRS signal, amplitude 200nV, Larmor frequency The frequency is 2325Hz, and the relaxation time is... It takes 0.25 seconds. For the length of time, ,like Figure 2 As shown. Among them, Figure 2 (A) in the graph is a time-amplitude plot. Figure 2 (B) in the diagram is a frequency-amplitude graph. The signal sampling frequency... Length of time The number of sampling points is P.

[0077] Set the standard deviation to Random noise is added to the MRS signal. Power frequency harmonic noise is removed from the signal using harmonic modeling methods. The sampling order is set. =2000, converting the signal into a two-dimensional matrix signal, setting the number of measurement points M=6000, generating independently distributed Gaussian random matrices for calculating the reconstruction matrix and measurement data. Comparative analysis of the time and frequency domain information of the original MRS signal, the ideal MRS signal, and the denoised signal (reconstructed signal), such as... Figure 3 As shown, where Figure 3 (A) in the graph is a time-amplitude plot. Figure 3 (B) in the diagram is a frequency-amplitude diagram. Calculations show that the initial amplitude error is -0.4043%, the relaxation time error is -2.2084%, and the SNR is 23.4293dB. The obtained parameter errors all meet the application requirements.

[0078] In another embodiment of this application, measured data collected on-site at Changchun Cultural Square is used as the processing object of the method of this application. To verify the effectiveness of the method of this application, as follows... Figure 4The measured noise-containing MRS signal is compared with the de-noised signal (restored signal) in time domain and frequency domain, wherein Figure 4 (A) is a time-amplitude graph, Figure 4 (B) is a frequency-amplitude graph. After de-noising, the measured data is calculated, and the parameter fitting is good under different signal-to-noise ratios, the signal-to-noise ratio is improved to more than 23 dB. The error of the obtained key parameters meets the application requirements.

[0079] The above only describes the preferred embodiments of the present application and is not intended to limit the present application. Any modification, equivalent replacement and improvement made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A method for magnetic resonance sounding signal denoising based on backtracking generalized OMP, characterized in that, The method comprises the following steps: A magnetic resonance depth sounder is used to sample sparse signals at a frequency lower than the Nyquist frequency to obtain a noisy MRS signal; A harmonic modeling method is used to remove power harmonic noise in the noisy MRS signal, and the noisy MRS signal is converted into a two-dimensional matrix signal; A KSVD algorithm is used to learn a dictionary from the two-dimensional matrix signal, a random matrix is used as an initial dictionary, and the two-dimensional matrix signal is used as original data, and an updated dictionary is obtained after iteration; An independent distributed Gaussian random matrix is used to calculate a recovery matrix and measurement data; A backtracking generalized orthogonal matching pursuit algorithm is used to iteratively operate on the measurement data, an atom sequence with the maximum projection of the measurement data and the recovery matrix is selected, and a sparse coefficient matrix of the measurement data under the recovery matrix is obtained; A recovery signal is calculated according to the product of the dictionary and the sparse coefficient matrix of the measurement data under the recovery matrix, and the first row of the recovery signal is restored to a one-dimensional signal; The recovery matrix is , the measurement data is , wherein is the recovery matrix, is a Gaussian random matrix, is a two-dimensional matrix signal, is a dictionary, is the measurement data.

2. The method according to claim 1, wherein, The calculation formula of the recovery signal is: , is the sparse coefficient matrix of the measurement data under the recovery matrix, is the recovery signal, is the dictionary.

3. The method of claim 2, wherein, The KSVD algorithm is used to learn a dictionary from the two-dimensional matrix signal, a random matrix is used as an initial dictionary, and the two-dimensional matrix signal is used as original data, and an updated dictionary is obtained after iteration, including: a backtracking generalized orthogonal matching pursuit algorithm is used to calculate a sparse coefficient matrix of the two-dimensional matrix signal under the current dictionary; The dictionary learning is performed, and the first column of the dictionary is updated The formula used is: , is the i-th column vector of the dictionary D, is the i-th column vector of the dictionary D, is the i-th column vector of the dictionary D, is the i-th column vector of the dictionary D, is the signal residual, denotes the square of the F-norm, is the i-th column vector of the dictionary D, is the i-th column vector of the dictionary D, is the i-th column vector of the dictionary D, is the i-th column vector of the dictionary D, is the two-dimensional matrix signal, is the dictionary, is the sparse coefficient matrix under the current dictionary; extracting the first column of the sparse coefficient matrix of the corresponding two-dimensional matrix signal in the signal residual under the current dictionary The column vector with a row vector of 0 forms a new signal residual, and singular value decomposition is performed on the new signal residual to obtain the first column left singular vector to replace the first column vector of the dictionary The column vector with a row vector of 0 forms a new signal residual, and singular value decomposition is performed on the new signal residual to obtain the first column left singular vector to replace the first column vector of the dictionary The above steps are repeated the same number of times as the number of dictionary atoms to obtain the updated dictionary.

4. The method of claim 3, wherein, The singular value decomposition of the new signal residual includes: a product of three matrices, is an orthogonal matrix with the same number of rows as the new signal residual, and its column vectors are called left singular vectors, is a rectangular diagonal matrix with the same size as the new signal residual, and the non-negative elements arranged in descending order on the diagonal are singular values, is an orthogonal matrix with the same number of columns as the new signal residual, and its row vectors are right singular vectors.

5. The method of claim 3, wherein, The backtracking generalized orthogonal matching pursuit algorithm is used to calculate the two-dimensional matrix signal under the current dictionary, including: The number of dictionary atoms is inputted to generate an initialized dictionary; calculating a sparse coefficient matrix of a two-dimensional matrix signal under a current dictionary using a backtracking generalized orthogonal matching pursuit algorithm, inputting an initial dictionary, the two-dimensional matrix signal and a first atom constraint degree performing sparse coding, cyclically calculating column vectors of the two-dimensional matrix signal, initializing a residual error: , column vectors of the two-dimensional matrix signal, is a first residual error; Compute the projection of the current dictionary transpose with the current residual: , is the projection of the current residual, is the transpose of the current dictionary, select the index of the maximum projection to add to the index set; A least square method is used to solve sparse coefficient atoms corresponding to the index of the column vector of the two-dimensional matrix signal in the current cycle; The first residual is updated according to the sparse coefficient atoms; repeat Next, fill the sparse coefficient atoms into the first sparse coefficient matrix A( ), Indicates the length of the signal. The position of each signal is used to process all column vectors of the two-dimensional matrix signal, and finally the sparse coefficient matrix of the two-dimensional matrix signal under the current dictionary is obtained.

6. The method according to claim 5, wherein, The first residual is updated according to the sparse coefficient atom, denoted as: wherein, is the first residual, is the sparse coefficient atom, , is a pseudo-inverse operation of the dictionary corresponding index set sub-dictionary set, denotes the dictionary corresponding index set sub-dictionary set.

7. The method of claim 1, wherein, The backtracking generalized orthogonal matching pursuit algorithm is used to iteratively operate on the measurement data, an atom sequence with the maximum projection of the measurement data and the recovery matrix is selected, and a sparse coefficient matrix of the measurement data under the recovery matrix is obtained, including: inputting a recovery matrix, measurement data, and a second atomic constraint degree and selecting an atomic number S, performing loop calculation on a column vector of the measurement data, and initializing a second residual error to be equal to the column vector of the measurement data; The modulus of the projection of the current second residual and the transpose of the recovery matrix is calculated, and the indexes of the maximum S modulus are added to the index set; A sub-dictionary set corresponding to the index set of the recovery matrix is selected, and a pseudo-inverse operation is used to solve the first coefficient; The second residual is updated according to the first coefficient; repetition second sparse coefficient matrix with the first coefficient ( ), denotes the position of the atom, all atoms of the measurement data are processed to obtain a sparse coefficient matrix of the measurement data under the recovery matrix.

8. The method according to claim 7, wherein, updating the second residual according to the first coefficient, denoted as: , denotes a column vector of the measurement data, denotes a sub-dictionary set of the recovery matrix corresponding to the index set, is the first coefficient, is the second residual.

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