Tensor robust principal component analysis-based reverberation suppression method and device

Abstract

The invention relates to the technical field of underwater target detection, and discloses a reverberation suppression method and device based on tensor robust principal component analysis. The method comprises the following steps: arranging frame signals received by a sonar receiving array according to a time sequence to obtain a distance-azimuth echo sequence; performing histogram matching processing on the distance-azimuth echo sequence, aligning the intensity distribution of each frame to a reference frame, and obtaining a distance-azimuth echo sequence after matching processing; after the distance-azimuth echo sequence after matching processing is preprocessed, low-rank component estimation initialization processing is executed; and after the initialization processing is completed, executing an adaptive threshold iterative optimization process, and iteratively solving an iterative formula by using a scale gradient descent method to obtain a low-rank component and a target component. By applying the method, the problems of high target false alarm rate and insufficient detection precision caused by reverberation interference in a complex environment can be solved.

Description

Technical Field

[0001] This invention relates to the field of sonar underwater target detection technology, and in particular to a reverberation suppression method and apparatus based on tensor robust principal component analysis. Background Technology

[0002] Active sonar target detection relies on periodically emitting active pulse signals and acquiring target echoes to detect moving targets such as unmanned underwater vehicles. However, the current operating environment of active platforms is complex and variable. Complex factors such as the sea surface, seabed, and media impurities lead to strong reverberation components. The echoes of moving targets are often submerged in strong reverberation, causing strong false alarms and making it impossible to correctly identify moving targets from multi-frame sonar range-azimuth echo sequences.

[0003] Existing technologies have presented various reverberation suppression methods. For example, one method for anti-reverberation target detection based on a stochastic algorithm extracts the low-rank structure of a matrix through joint processing of multiple frames of data to suppress the reverberation background, and achieves moving target detection based on the assumption of strong reverberation correlation. Another example is a reverberation suppression method based on frequency-filtered tensor robust principal component analysis, which uses tensor modeling to preserve the three-dimensional structure of the echo sequence, constrains the low-rank characteristics of steady-state reverberation through the frequency-filtered nuclear norm, and combines weighted spatiotemporal density differences to suppress reverberation fluctuations.

[0004] The aforementioned existing technologies all rely on manual parameter adjustment and the parameters are fixed, making it difficult to adapt to complex and ever-changing real-world scenarios. At the same time, the non-stationarity of the sonar range-azimuth echo sequence may lead to a decrease in the accuracy of low-rank modeling or tensor decomposition, thereby affecting the effectiveness of background suppression and target separation.

[0005] Therefore, how to develop a reverberation suppression method that is adaptable to complex and ever-changing scenarios and has high precision has become a technical problem that needs to be solved. Summary of the Invention

[0006] The purpose of this invention is to provide a reverberation suppression method and apparatus based on tensor robust principal component analysis, in order to solve the problems of high false alarm rate and insufficient detection accuracy caused by reverberation interference in complex environments.

[0007] To achieve the above objectives, the present invention provides the following technical solution: According to one aspect of the present invention, a reverberation suppression method based on tensor robust principal component analysis is provided, comprising the following steps: Based on the signals received by the sonar receiving array, the range-azimuth echo sequence is obtained by arranging them in chronological order. Histogram matching is performed on the range-azimuth echo sequence to align the intensity distribution of each frame to the reference frame, resulting in the matched range-azimuth echo sequence. After preprocessing the range-azimuth echo sequence after matching, low-rank component estimation initialization is performed. After initialization, an adaptive threshold iterative optimization process is executed, using the scale gradient descent method to iteratively solve the iterative equation and obtain the low-rank component and the target component.

[0008] According to an embodiment of the present invention, the step of arranging the range-azimuth echo sequence according to the time sequence of each frame of signals received by the sonar receiving array includes performing beamforming, matched filtering, and normalization processing on each frame of signals received by the sonar receiving array, and then arranging them according to the time sequence to obtain the range-azimuth echo sequence.

[0009] According to an embodiment of the present invention, histogram matching processing is performed on the range-azimuth echo sequence to align the intensity distribution of each frame to a reference frame, thereby obtaining a matched range-azimuth echo sequence, specifically including: A reference frame is selected from the range-azimuth echo sequence, and the cumulative distribution function of the reference frame is obtained based on the intensity histogram of the reference frame. For each frame in the range-azimuth echo sequence, the cumulative distribution function of each frame is obtained based on the intensity histogram of each frame; By performing an inverse mapping operation on the cumulative distribution function of each frame using the cumulative distribution function of the reference frame, each pixel in each frame is identical to the cumulative distribution function of the reference frame, thus achieving intensity alignment. After performing intensity alignment processing on all frames, a range-azimuth echo sequence with consistent background intensity distribution is obtained.

[0010] According to an embodiment of the present invention, the preprocessing of the matched range-azimuth echo sequence includes: performing nonlinear constraint optimization on the matched range-azimuth echo sequence using a soft threshold operator; and using the difference between the unoptimized matched range-azimuth echo sequence and the optimized matched range-azimuth echo sequence as the preprocessed sequence. The low-rank component estimation initialization process includes: Preprocessed sequences Perform higher-order singular value decomposition: The specific expansion form corresponding to this decomposition is: ,in, For higher-order singular value decomposition operators, It is a multilinear rank. For the initial factor matrix, For the initial core tensor, express Modular multiplication.

[0011] According to an embodiment of the present invention, the initial factor matrix is ​​obtained by adjusting the initial factor matrix. The initial factor matrix is ​​obtained by performing singular value decomposition on each expansion mode. Each contains The former There are singular value vectors; where... refer to Along Tensor matrix form of the order mode, The three dimensions of a tensor. .

[0012] According to an embodiment of the present invention, in the step of performing the adaptive threshold iterative optimization process and iteratively solving the optimization function using the scaling gradient descent method to obtain the low-rank component and the target component, the optimization function is: This minimizes the optimization function to obtain the low-rank component and the target component; where... for , To estimate the target component values, the iterative process includes the following steps: Based on the initialized components Initiate the iterative process; The preprocessed sequence is updated by modifying the threshold of the soft threshold operator during each iteration. Update; The threshold of the soft threshold operator is expressed as follows: ,in For the first The low-rank components estimated in the next iteration For decay rate parameters, This represents the current iteration number; Passing the threshold soft threshold operator Filter outliers, separate target components, and obtain the first... The estimated target component value at the next iteration is ; Update the factor matrix using the scaled gradient descent method. The aim is to improve the convergence speed, and the update iterative formula is... ;in, , , , For Kronecker product, For learning rate, The three dimensions of a tensor. ; Update core tensor The updated formula is ,in ; After the iteration is complete, the final low-rank components are obtained. and target components .

[0013] According to an embodiment of the present invention, the reference frame is the first frame in the range-azimuth echo sequence.

[0014] On the other hand, the present invention also provides a reverberation suppression device based on tensor robust principal component analysis for implementing the above-described method, the device comprising: The receiving unit is configured to obtain a range-azimuth echo sequence by arranging the signals received by the sonar receiving array in chronological order. The matching unit is configured to perform histogram matching processing on the range-azimuth echo sequence, aligning the intensity distribution of each frame to the reference frame, to obtain the matched range-azimuth echo sequence. The initialization unit is configured to perform low-rank component estimation initialization processing after preprocessing the range-azimuth echo sequence following the matching process; The iterative processing unit is configured to perform an adaptive threshold iterative optimization process after initialization, using the scale gradient descent method to iteratively solve the iterative equation to obtain the low-rank component and the target component.

[0015] On the other hand, the present invention also provides a computer storage medium storing instructions that, when executed, implement the reverberation suppression method based on tensor robust principal component analysis.

[0016] On the other hand, the present invention also provides a computing device, including a processor and a communication interface coupled to the processor; the processor is used to run computer programs or instructions to implement the reverberation suppression method based on tensor robust principal component analysis.

[0017] The present invention discloses a reverberation suppression method and apparatus based on tensor robust principal component analysis. After beamforming and matched filtering the sonar range-azimuth echo sequence, the intensity distribution of each frame is aligned by histogram matching to achieve background stabilization. The low-rank component is initialized by high-order singular value decomposition, and the threshold is dynamically adjusted by adaptive threshold iteration optimization combined with scale gradient descent method to separate the low-rank reverberation from the target component.

[0018] Compared with the prior art, the beneficial effects of the present invention are as follows: (1) This invention overcomes the limitations of traditional fixed thresholds by using histogram matching preprocessing and threshold exponential decay mechanism, and maintains stable convergence even when the reverberation intensity changes abruptly, which significantly improves the target separation accuracy.

[0019] (2) Experimental results show that the method of the present invention can effectively suppress reverberation interference and reduce false alarm rate in complex environments, and is suitable for underwater moving target detection in complex marine environments. Attached Figure Description

[0020] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this invention, illustrate exemplary embodiments of the invention and are used to explain the invention, but do not constitute an undue limitation of the invention. In the drawings: Figure 1 This is a flowchart of a reverberation suppression method based on tensor robust principal component analysis; Figure 2 This is a schematic diagram of a reverberation suppression device based on tensor robust principal component analysis; Figure 3 This is a schematic diagram of the original sonar range-azimuth echo sequence; Figure 4 This is a schematic diagram of the first frame after processing using the existing Alternating Direction Multiplier (ADMM) method; Figure 5 This is a schematic diagram of the first frame after processing using the existing Gaussian mixture robust principal component analysis (MOG-RPCA) method; Figure 6 This is a schematic diagram of the first frame after processing by the reverberation suppression process based on tensor robust principal component analysis of the present invention. Figure 7 This is a schematic diagram comparing the sparsity coefficients of the target matrix in each frame using different processing methods; Figure 8 This is a schematic diagram comparing the average sparsity coefficients of the target matrices in each frame using different processing methods; Figure 9 This is a schematic diagram comparing the ROC curves of the target detection after using different processing methods. Detailed Implementation

[0021] To facilitate a clear description of the technical solutions in the embodiments of the present invention, the terms "first" and "second" are used to distinguish identical or similar items with essentially the same function and effect. For example, the first threshold and the second threshold are merely used to distinguish different thresholds and do not limit their order. Those skilled in the art will understand that the terms "first" and "second" do not limit the quantity or execution order, and that the terms "first" and "second" are not necessarily different.

[0022] It should be noted that in this invention, the terms "exemplary" or "for example" are used to indicate examples, illustrations, or descriptions. Any embodiment or design described as "exemplary" or "for example" in this invention should not be construed as being more preferred or advantageous than other embodiments or designs. Specifically, the use of terms such as "exemplary" or "for example" is intended to present the relevant concepts in a concrete manner.

[0023] In this invention, "at least one" refers to one or more, and "more than one" refers to two or more. "And / or" describes the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A alone, A and B simultaneously, or B alone, where A and B can be singular or plural. The character " / " generally indicates that the preceding and following related objects are in an "or" relationship. "At least one" or similar expressions refer to any combination of these items, including any combination of singular or plural items. For example, "at least one of a, b, or c" can represent: a, b, c, a combination of a and b, a combination of a and c, a combination of b and c, or a, b, and c, where a, b, and c can be single or multiple.

[0024] like Figure 1 As shown, a flowchart of a reverberation suppression method based on tensor robust principal component analysis is presented. The method includes the following steps: Step S1: Arrange the range-azimuth echo sequence according to the time sequence of the signals received by the sonar receiving array. Step S2: Perform histogram matching processing on the range-azimuth echo sequence to align the intensity distribution of each frame to the reference frame, thereby obtaining the matched range-azimuth echo sequence; Step S3: After preprocessing the range-azimuth echo sequence after matching, perform low-rank component estimation initialization processing; Step S4: After the initialization process is completed, the adaptive threshold iterative optimization process is executed. The iterative equation is solved iteratively using the scale gradient descent method to obtain the low-rank component and the target component.

[0025] In step S1, beamforming, matched filtering, and normalization are performed on each frame of signal received by the sonar receiving array to form a multi-frame echo map. These echo maps are then arranged in chronological order to obtain a range-azimuth echo sequence, denoted as […]. , These represent the magnitudes of the three dimensions of the tensor. The three dimensions of a tensor are respectively ,in Represents the distance dimension. Indicates the direction of the dimension. This represents the total number of frames.

[0026] In step S2, the range-azimuth echo sequence after matching is obtained. The specific implementation steps include: Step S21: Select a reference frame from the range-azimuth echo sequence, for example, select the first frame as the reference frame. , Step S22: Obtain the cumulative distribution function of the reference frame based on the intensity histogram of the reference frame; for example... As a reference frame, its intensity histogram is calculated. Calculate its cumulative distribution function. ; Step S23: For each frame in the range-azimuth echo sequence, obtain the cumulative distribution function of each frame based on the intensity histogram of each frame; for example, for the Frame echo map Calculate the cumulative distribution function of the echo map for this frame. For the first For each pixel of the frame, the cumulative distribution function of the echo map of this frame is the same as the cumulative distribution function of the reference frame; Step S24: Perform an inverse mapping operation on the cumulative distribution function of each frame using the cumulative distribution function of the reference frame, so that each pixel in each frame is the same as the cumulative distribution function of the reference frame, achieving intensity alignment; for example, using inverse mapping Perform the above operations to achieve intensity correction, and compare its intensity histogram with the first frame echo map. Strength alignment.

[0027] By following the steps above, preprocessed data with a consistent background intensity distribution can be obtained. By performing beamforming and matched filtering on the sonar range-azimuth echo sequence, and then using histogram matching to align the intensity distribution of each frame, background stabilization is achieved.

[0028] In step S3, the range-azimuth echo sequence after matching is preprocessed using a soft threshold operator.

[0029] Preprocessed data ; The soft threshold operator is: The low-rank part and elements below a threshold in the data tensor are separated from other parts by nonlinear constraint optimization. This represents a low-rank tensor. Indicates the index number of the tensor. This represents a sign function; the output is 1 when the input is positive, -1 when the input is negative, and 0 when the input is 0.

[0030] in, For the number of iterations, For the first Threshold at the next iteration; initial threshold ,in To obtain the maximum singular value, is the scale factor.

[0031] Then, the preprocessed sequence Perform higher-order singular value decomposition, denoted as For higher-order singular value decomposition operators, we get , For a multilinear rank, the specific expansion form corresponding to this decomposition is: ;in The initial factor matrix contains, respectively The former A singular value vector.

[0032] For the initial factor matrix, This is the initial core tensor.

[0033] in, Tensor Along The tensor matrix form of the order mode (i.e., the dimension of the tensor), the initial factor matrix is ​​a tensor Each expansion mode is obtained by performing singular value decomposition of the matrix.

[0034] In step S4, the optimization function is: This minimizes the optimization function to obtain the low-rank component and the target component; where... for , For the estimated values ​​of the target component, It is the core tensor.

[0035] In step S4, based on the components initialized in S3 In the subsequent In the next iteration, based on the energy of the low-rank component, the formula is used. Update. For the first The soft threshold operator threshold at the next iteration is an adjustable training hyperparameter, denoted as... The threshold sequence up to the Tth iteration is optimized using a grid search method. For the first The low-rank components estimated in the next iteration This is the decay rate parameter.

[0036] Passing the threshold soft threshold operator Filter outliers, separate target components, and obtain the first... The estimated target component value at the next iteration is .

[0037] Update the factor matrix using the scaled gradient descent method. The aim is to improve the convergence speed, and the update iterative formula is... ;in, , , , For Kronecker product, Let be the learning rate, and be an adjustable training hyperparameter. We used a grid search method to perform combined optimization.

[0038] Then, update the core tensor. The updated formula is ,in .

[0039] In the above method, histogram matching preprocessing is used to smooth the background of each frame of echo image, improving the stability of the sonar range-azimuth echo sequence. This significantly improves the accuracy of low-rank modeling or tensor decomposition, enhancing the background suppression and target separation effects. Threshold exponential decay allows for dynamic adjustment of the threshold, overcoming the dependence on traditional fixed thresholds. Stable convergence is maintained even with abrupt changes in reverberation intensity, resulting in more accurate target extraction and improved robustness of target detection in complex marine environments. This overcomes the limitations of existing technologies that rely on manual parameter tuning and fixed parameters, making them difficult to adapt to complex and changing real-world scenarios. Finally, applying the tensor decomposition-based reverberation suppression method of this invention can solve the problems of reverberation fluctuations and high false alarm rates in current active underwater target detection.

[0040] like Figure 2 The diagram shows a reverberation suppression device based on tensor robust principal component analysis. The device includes: The receiving unit is configured to obtain a range-azimuth echo sequence by arranging the signals received by the sonar receiving array in chronological order. The matching unit is configured to perform histogram matching processing on the range-azimuth echo sequence, aligning the intensity distribution of each frame to the reference frame, to obtain the matched range-azimuth echo sequence. The initialization unit is configured to perform low-rank component estimation initialization processing after preprocessing the range-azimuth echo sequence following the matching process; The iterative processing unit is configured to perform an adaptive threshold iterative optimization process after initialization, using the scale gradient descent method to iteratively solve the objective function and obtain the low-rank component and the objective component.

[0041] Example 1: A reverberation suppression method based on tensor robust principal component analysis in shallow water. The received signals from the receiving array are processed by beamforming, matched filtering, and normalization, and then arranged in chronological order to obtain the sonar range-azimuth echo sequence, denoted as . The sonar range-azimuth echo sequence was obtained from real target echo data, sourced from shallow water. The active pulse frequency was a hyperbolic frequency modulated signal with a center frequency of 7250 Hz and a pulse width of 256 ms, totaling 11 frames. The sequence dimension of this data set is [missing information]. The first frame of the sequence summary is shown in the diagram below. Figure 3 As shown.

[0042] Histogram matching was performed on the range-azimuth echo sequence to align the intensity distribution of each frame to the reference frame. The range-azimuth echo sequence after matching is obtained. .

[0043] Select the first frame echo map As a reference frame, its intensity histogram is calculated. Calculate its cumulative distribution function. ; for the first Frame (where, Echo image Calculate its cumulative distribution function. For the first For each pixel of the frame, make it identical to the cumulative distribution function of the reference frame using an inverse mapping. Perform the above operations to achieve intensity correction, and compare its intensity histogram with the first frame echo map. Intensity alignment; perform echo mapping with the first frame on all frames. Intensity alignment operation is performed to obtain preprocessed data with a consistent background intensity distribution. The dimension of the preprocessed data sequence is also 1. .

[0044] The range-azimuth echo sequence after matching is preprocessed, and the low-rank component estimation of the preprocessed sequence is initialized using the higher-order singular value decomposition method.

[0045] First, using Calculate the preprocessed data; in, It is a soft threshold operator, which aims to separate the low-rank part and elements smaller than the threshold in the data tensor from other parts through nonlinear constraint optimization. For the number of iterations, For the first The threshold at the next iteration, in this embodiment; the initial threshold. ,in For the maximum singular value, This is the scaling factor, which is 0.7 in this example.

[0046] Preprocessed sequences Perform higher-order singular value decomposition, denoted as For higher-order singular value decomposition operators, we get , For a multilinear rank, the specific expansion form corresponding to this decomposition is: In this embodiment, the time dimension has a rank of 1, and the spatial dimension has a full rank. in The initial factor matrix contains, respectively The former A singular value vector Let be the initial core tensor; where, Tensor Along The tensor matrix form of the order mode (i.e., the dimension of the tensor), the initial factor matrix is ​​a tensor Each expansion mode is obtained by performing singular value decomposition of the matrix.

[0047] After initialization, the adaptive threshold iterative optimization process begins, using the scale gradient descent method to iteratively solve the problem. To minimize this, i.e., to obtain the low-rank component and the target component, the maximum number of iterations in this embodiment is... =100. After the above iterative solution, the final detection result is as follows: Figure 6 As shown.

[0048] Based on the initialized components In the subsequent In the next iteration, based on the energy of the low-rank component, the formula is used. Update For the first The soft threshold operator threshold at the next iteration is an adjustable training hyperparameter, denoted as... The threshold sequence up to the 100th iteration is optimized using a grid search method. in For the first The low-rank components estimated in the next iteration For the decay rate parameter, in this embodiment Set it to 2.5.

[0049] Passing the threshold soft threshold operator Filter outliers, separate target components, and obtain the first... The estimated target component value at the next iteration is .

[0050] Update the factor matrix using the scaled gradient descent method. The aim is to improve the convergence speed, and the update iterative formula is... ;in, , , , For Kronecker product, Here, is the learning rate, and is an adjustable training hyperparameter, set to 0.7 in this embodiment. We used a grid search method to perform combined optimization.

[0051] Update the core tensor, the update formula is: ,in .

[0052] exist Figure 3 The diagram shows the original sonar range-azimuth echo sequence, including the first frame of the original sequence.

[0053] exist Figure 4 The diagram shows the first frame after processing using the existing ADMM (Alternating Direction Method of Multipliers) method.

[0054] exist Figure 5 The image shows a schematic diagram of the first frame after processing using the existing MOG-RPCA (Mixture of Gaussians-Robust Principal Component Analysis) method.

[0055] exist Figure 6 The document presents a schematic diagram of the first frame after processing using the reverberation suppression process based on tensor robust principal component analysis as described in Example 1. This is achieved through comparison... Figures 3 to 5 It is clearly visible Figure 6 The interference in the areas indicated by the left and right arrows has been suppressed, and the target outlined by the rectangle has been significantly enhanced. Moreover, compared with other methods, the reverberation suppression method based on tensor robust principal component analysis proposed in this invention has a better reverberation suppression effect.

[0056] To quantitatively evaluate the performance of the method in this embodiment, a sparsity coefficient (SC) is introduced as an evaluation metric to quantitatively describe the sparsity of the matrix, defined as follows: ,in This indicates that the pixel intensity in the single-frame matrix obtained after the detection method is higher than... The number of pixels, This represents the total number of pixels in a single frame of data. The threshold value set for calculating the sparsity coefficients. A higher SC indicates weaker reverberation intensity in the frame data and better reverberation suppression. When the smaller value of 10 is taken, the SC of the 10-frame matrix processed by the above method is as follows: Figure 7 As shown, the sparse coefficients of the target tensor matrix extracted by the method proposed in this invention are higher than those of other methods, demonstrating good reverberation suppression performance.

[0057] Subsequently, the sparsity coefficient threshold was adjusted, and the sparse coefficients of each frame were averaged. The result is as follows. Figure 8 As shown, the average sparsity coefficient of the target tensor matrix extracted by the method proposed in this invention is higher than that of other methods.

[0058] ROC curves were used to further quantify and compare the target detection performance of different methods. Given that the target's location in the echo image was known, each frame was divided into target and background regions. Detection probabilities and false alarm probabilities were calculated under different defined detection thresholds, and ROC curves were constructed. The results are as follows: Figure 9 As shown, ADMM, MOG-RPCA, the method proposed in this invention, and pure random detection are respectively. The curves show that the method proposed in this invention can achieve a higher detection probability when the false alarm probability is low, and the AUC value is higher than other comparative methods.

[0059] Although the invention has been described herein in conjunction with various embodiments, those skilled in the art will understand and implement other variations of the disclosed embodiments by reviewing the accompanying drawings, disclosure, and other materials. In this specification, the word "comprising" does not exclude other components or steps, and "a" or "an" does not exclude multiple components. A single processor or other unit can implement several functions listed in the specification. While certain measures are described in different embodiments, this does not mean that these measures cannot be combined to produce good results.

[0060] Although the invention has been described in conjunction with specific features and embodiments, it is obvious that various modifications and combinations can be made therein without departing from the spirit and scope of the invention. Accordingly, this specification and drawings are merely illustrative of the invention and are considered to cover any and all modifications, variations, combinations, or equivalents within the scope of the invention. Clearly, those skilled in the art can make various alterations and modifications to the invention without departing from its spirit and scope. Thus, if such modifications and modifications fall within the scope of the invention and its equivalents, the invention is also intended to include such modifications and modifications.

Claims

1. A reverberation suppression method based on tensor robust principal component analysis, characterized in that, Includes the following steps: Based on the signals received by the sonar receiving array, the range-azimuth echo sequence is obtained by arranging them in chronological order; Histogram matching processing is performed on the range-azimuth echo sequence to align the intensity distribution of each frame to the reference frame, resulting in a matched range-azimuth echo sequence. After preprocessing the range-azimuth echo sequence after matching, low-rank component estimation initialization is performed. After initialization, an adaptive threshold iterative optimization process is executed, using the scale gradient descent method to iteratively solve the iterative equation and obtain the low-rank component and the target component.

2. The reverberation suppression method based on tensor robust principal component analysis according to claim 1, characterized in that, The step of arranging the range-azimuth echo sequence according to the time sequence of each frame of signal received by the sonar receiving array includes beamforming, matched filtering, and normalization of each frame of signal received by the sonar receiving array, and then arranging them according to the time sequence to obtain the range-azimuth echo sequence.

3. The reverberation suppression method based on tensor robust principal component analysis according to claim 1, characterized in that, Histogram matching is performed on the range-azimuth echo sequence to align the intensity distribution of each frame to the reference frame, resulting in a matched range-azimuth echo sequence, specifically including: A reference frame is selected from the range-azimuth echo sequence, and the cumulative distribution function of the reference frame is obtained based on the intensity histogram of the reference frame. For each frame in the range-azimuth echo sequence, the cumulative distribution function of each frame is obtained based on the intensity histogram of each frame; By performing an inverse mapping operation on the cumulative distribution function of each frame using the cumulative distribution function of the reference frame, each pixel in each frame is identical to the cumulative distribution function of the reference frame, thus achieving intensity alignment. After performing intensity alignment processing on all frames, a range-azimuth echo sequence with consistent background intensity distribution is obtained.

4. The reverberation suppression method based on tensor robust principal component analysis according to claim 1, characterized in that, The preprocessing of the matched range-azimuth echo sequence includes: performing nonlinear constraint optimization on the matched range-azimuth echo sequence using a soft threshold operator; and using the difference between the unoptimized matched range-azimuth echo sequence and the optimized matched range-azimuth echo sequence as the preprocessed sequence. The low-rank component estimation initialization process includes: Preprocessed sequences Perform higher-order singular value decomposition: The specific expansion form corresponding to this decomposition is: ,in, For higher-order singular value decomposition operators, It is a multilinear rank. For the initial factor matrix, This is the initial core tensor.

5. The reverberation suppression method based on tensor robust principal component analysis according to claim 4, characterized in that, The initial factor matrix is ​​obtained by... The initial factor matrix is ​​obtained by performing singular value decomposition on each expansion mode. Each contains The former There are singular value vectors; where... refer to Along Tensor matrix form of the order mode, The three dimensions of a tensor. .

6. The reverberation suppression method based on tensor robust principal component analysis according to claim 5, characterized in that, In the step of performing the adaptive threshold iterative optimization process, which uses the scaling gradient descent method to iteratively solve the optimization function to obtain the low-rank component and the target component, the optimization function is: This minimizes the optimization function to obtain the low-rank component and the target component; where... for , To estimate the target component values, the iterative process includes the following steps: Based on the initialized components Initiate the iterative process; The preprocessed sequence is updated by modifying the threshold of the soft threshold operator during each iteration. Update; The threshold of the soft threshold operator is expressed as follows: ,in For the first The low-rank components estimated in the next iteration For decay rate parameters, This represents the current iteration number; Passing the threshold soft threshold operator Filter outliers, separate target components, and obtain the first... The estimated target component value at the next iteration is ; Update the factor matrix using the scaled gradient descent method. The aim is to improve the convergence speed, and the update iterative formula is... ;in, ， ， ， For Kronecker product, For learning rate, The three dimensions of a tensor. ; Update core tensor The updated formula is ,in ; After the iteration is complete, the final low-rank components are obtained. and target components .

7. The reverberation suppression method based on tensor robust principal component analysis according to claim 3, characterized in that, The reference frame is the first frame in the range-azimuth echo sequence.

8. A reverberation suppression device based on tensor robust principal component analysis, for implementing the method according to claims 1 to 7, characterized in that, The device includes: The receiving unit is configured to obtain a range-azimuth echo sequence by arranging the signals received by the sonar receiving array in chronological order. The matching unit is configured to perform histogram matching processing on the range-azimuth echo sequence, aligning the intensity distribution of each frame to the reference frame, to obtain the matched range-azimuth echo sequence. The initialization unit is configured to perform low-rank component estimation initialization processing after preprocessing the range-azimuth echo sequence following the matching process; The iterative processing unit is configured to perform an adaptive threshold iterative optimization process after initialization, using the scale gradient descent method to iteratively solve the iterative equation to obtain the low-rank component and the target component.

9. A computer storage medium, characterized in that, The computer storage medium stores instructions that, when executed, implement the reverberation suppression method based on tensor robust principal component analysis as described in any one of claims 1 to 7.

10. A computing device, characterized in that, It includes a processor and a communication interface coupled to the processor; the processor is used to run computer programs or instructions to implement the reverberation suppression method based on tensor robust principal component analysis as described in any one of claims 1 to 7.

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