Towed sonar space-time reverberation suppression method based on knowledge prior and auxiliary sample

Abstract

The invention discloses a towed sonar space-time reverberation suppression method based on knowledge priori and an auxiliary sample. The method comprises the steps that the auxiliary sample and a to-be-tested sample are acquired based on a sonar array; uniformly dividing a space-time plane along a space frequency axis and a Doppler axis and then constructing a space-time steering vector set; screening vectors in a reverberation energy concentration area according to the space-time steering vector set to obtain a first set; performing energy analysis and effective vector screening according to the auxiliary sample and the first set to obtain a second set; distributing a sparse penalty weight for each vector in the second set; constructing an optimization model containing a data fitting item and a weighted sparse constraint item according to the second set; solving the optimization model to obtain a reverberation sparse coefficient vector; obtaining a reconstructed reverberation component according to the reverberation sparse coefficient vector and the second set; and subtracting the reconstructed reverberation component from the to-be-detected sample to complete reverberation suppression.

Description

Technical Field

[0001] This invention relates to the field of underwater acoustic signal processing, and in particular to a method for suppressing spatiotemporal reverberation of towed sonar based on prior knowledge and auxiliary samples. Background Technology

[0002] In active sonar systems, sonar transmits acoustic signals and processes the echo signals to detect and estimate the parameters of underwater targets. In shallow seas and complex marine environments, sonar echo signals typically contain a large number of reverberation components caused by the seabed, sea surface, and inhomogeneous media of the water body. Reverberation is characterized by high energy, long duration, and complex statistical characteristics, often drowning out weak target echoes and severely affecting the detection performance and parameter estimation accuracy of the sonar system.

[0003] Existing sonar reverberation suppression typically employs the STAP (Space-Time Adaptive Processing) method. STAP suppresses reverberation and interference by constructing a space-time filter, achieving good performance under ideal conditions. However, in real-world shallow-sea environments, reverberation often exhibits significant non-stationary characteristics. The limited number of training samples and the mismatch between statistical characteristics and the test data can easily lead to biased covariance matrix estimation and even rank deficiency, thus affecting the algorithm's stability and robustness. Furthermore, traditional STAP methods usually require global filtering across the entire angle-Doppler domain, failing to fully utilize the structured distribution characteristics of reverberation in the space-time domain, and the target echo may also be simultaneously weakened during filtering. In recent years, sparse representation and compressed sensing theory have been introduced into sonar signal processing. By constructing a space-time steering vector dictionary, reverberation and the target signal are represented as a linear combination of a small number of dictionary atoms, thereby achieving reverberation suppression. This type of method alleviates, to some extent, the difficulty of covariance matrix estimation under small sample conditions. However, existing sparse constraint methods typically impose a uniform sparsity penalty on all dictionary atoms, failing to fully utilize the prior information contained in the auxiliary training data. When reverberation energy exhibits a significant concentrated distribution in the spatiotemporal domain, uniform sparse constraints struggle to effectively distinguish between reverberant and non-reverberant atoms, resulting in limited reverberation suppression performance. In practical sonar reverberation suppression, it is necessary to fully utilize the structured distribution characteristics of reverberation in the spatiotemporal domain and combine this with statistical information from the auxiliary training data to apply differentiated constraints to different spatiotemporal steering vectors, thereby improving the accuracy and robustness of reverberation suppression. However, existing methods still fall short in utilizing reverberation structure and incorporating training information, making it difficult to achieve stable and effective reverberation suppression under complex environments and limited training sample conditions.

[0004] Therefore, a new technical solution is urgently needed to address the technical problem of effectively suppressing reverberation interference in sonar echo signals under complex reverberation backgrounds. Summary of the Invention

[0005] This invention provides a towed sonar spatiotemporal reverberation suppression method based on prior knowledge and auxiliary samples, which solves the technical problem of how to effectively suppress reverberation interference in sonar echo signals under complex reverberation backgrounds.

[0006] To achieve the above objectives, this invention provides a method for suppressing spatiotemporal reverberation of towed sonar based on prior knowledge and auxiliary samples, comprising: Auxiliary samples and test samples are acquired based on a sonar array; a set of space-time steering vectors is constructed by uniformly dividing the space-time plane along the spatial frequency axis and the Doppler axis; vectors located in the reverberant energy concentration region are selected based on the set of space-time steering vectors to obtain the first set; energy analysis and effective vector selection are performed based on the auxiliary samples and the first set to obtain the second set; sparse penalty weights are assigned to each vector in the second set. An optimization model containing data fitting terms and weighted sparse constraints is constructed based on the second set; the reverberation sparse coefficient vector is obtained by solving the optimization model; the reconstructed reverberation component is obtained based on the reverberation sparse coefficient vector and the second set; the reconstructed reverberation component is subtracted from the sample to be tested to complete the reverberation suppression.

[0007] Preferably, constructing a set of spacetime steering vectors by uniformly dividing the spacetime plane along the spatial frequency axis and the Doppler axis includes: Based on the motion parameters and array parameters of the sonar platform, the space-time plane is uniformly divided along the spatial frequency axis and the Doppler axis, and a space-time steering vector is constructed for each grid point to obtain a set of space-time steering vectors; the space-time steering vector is composed of the Kronecker product of the spatial steering component and the temporal steering component.

[0008] Preferably, the vectors located in the reverberant energy concentration region are filtered according to the set of space-time steering vectors to obtain the first set, which includes: Based on the sonar platform's speed and yaw angle, transmitted signal frequency, and speed of sound, a geometric relationship model between the reverberation center frequency and the angle is established. For a given angle... The geometric relationship model is represented as follows: ; in, The speed of the ship; Yaw angle; The frequency of the transmitted signal; Speed ​​of sound; and These represent the port reverberation center frequency and the starboard reverberation center frequency, respectively. Based on a geometric model, the reverberation energy concentration region is defined within the angle-Doppler plane. ,include: ; in, For the spatial frequency axis The discrete angles corresponding to each grid. , The number of spatial frequency axis grids in a space-time plane; For the Doppler axis The Doppler frequencies corresponding to each grid. , The number of Doppler axis grids in the empty-time plane; To preset the reverberation range; Based on the set of space-time steering vectors, regions located in the reverberation energy concentration area are selected. The vectors are used to obtain the first set.

[0009] Preferably, based on the auxiliary samples and the first set, energy analysis and effective vector screening are performed to obtain the second set, which includes: Based on the auxiliary samples, the matching energy of each vector in the first set is analyzed, and the energy statistics are obtained: ; in, Represents the first set The Middle Energy statistics of each vector; Represents the first set The first in One vector; Indicates the first Frame-assisted samples; This indicates the total number of auxiliary sample frames; Indicates conjugate transpose; The second set is obtained by filtering vectors from the first set whose energy statistics are greater than or equal to the reverberation energy threshold: ; in, The reverberation energy threshold; This is the second set.

[0010] Preferably, assigning sparsity penalty weights to each vector in the second set includes: The sparse penalty weights assigned to each vector in the second set Represented as: ; in, For smoothing parameters; This is the weight adjustment parameter.

[0011] Preferably, constructing an optimization model containing data fitting terms and weighted sparse constraint terms based on the second set includes: Based on the second set and the sparse penalty weights, an optimization model containing data fitting terms and weighted sparse constraint terms is constructed for the test samples, as follows: ; in, Let be the second matrix, representing the matrix corresponding to the second set; Indicates the sample to be tested; Represents the reverberation sparse coefficient vector; For regularization parameters; Indicates the first The values ​​of the elements of the reverberation sparse coefficient vector.

[0012] Preferably, the reverberation sparse coefficient vector obtained by solving the optimization model includes: The optimization model is solved using the alternating direction multiplier method, including: Introducing auxiliary variables The optimization model is transformed into an optimization problem with equality constraints: ; in, , express The first in One component; This represents the square of the L2 norm of a vector; Auxiliary variables The update is based on the soft threshold shrinkage operator, expressed as: ; in, For the first Next iteration update The value; For the first Next iteration update The value, For the dual variable vector, , for The corresponding number in the middle The components of the reverberation sparse coefficient constraint term; For the first Next iteration update The value; For soft threshold shrinkage operators, ; For penalty parameters; This is the sparse penalty weight vector; For the Auxiliary variables in the next iteration update The Each component The calculation method is as follows: ; ; in, for The corresponding shrinkage threshold; To prevent extremely small positive numbers from being divided by zero; for The One component; for The One component; for The update methods include: ; in, For the first Next iteration update The value; Dual variable vector To perform consistency adjustments, update methods include: ; in, For the first Next iteration update The value; right , and Perform alternating updates in a loop until the original variable is updated. with auxiliary variables The errors between them satisfy the convergence condition, thus yielding the reverberation sparse coefficient vector. .

[0013] Preferably, the reconstructed reverberation component is obtained based on the reverberation sparse coefficient vector and the second set; the reconstructed reverberation component is subtracted from the sample to be tested to complete the reverberation suppression, which includes: The reverberation sparsity coefficient vector The matrix corresponding to the second set is the second matrix. Multiplying them together yields the reconstructed reverberation components. ; the sample to be tested Subtract the reconstructed reverberation component The residual signal after reverberation suppression is obtained. , is represented as: ; The present invention has the following beneficial effects: The present invention provides a towed sonar spatiotemporal reverberation suppression method based on prior knowledge and auxiliary samples. By fully utilizing the structured distribution characteristics of reverberation in the spatiotemporal domain, it can achieve accurate modeling and effective suppression of reverberation components under complex reverberation backgrounds and limited training samples. This significantly improves the discriminability and signal-to-noise ratio of target components in the residual signal, thus providing a more reliable data foundation for sonar target detection, parameter estimation, or imaging processing. Reverberation component elimination based on the method of this invention can effectively suppress the dominant reverberation component in the original sonar received data, reduce the masking effect of reverberation on target echoes, and thereby relatively increase the energy proportion of target components in the residual signal.

[0014] In addition to the objectives, features, and advantages described above, the present invention has other objectives, features, and advantages. The invention will now be described in further detail with reference to the accompanying drawings. Attached Figure Description

[0015] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings: Figure 1 This is the schematic diagram of the method flow of a preferred embodiment of the present invention.

[0016] Figure 2 This is a schematic diagram of the spatiotemporal spectrum (two-dimensional view) of the original test data in a preferred embodiment of the present invention.

[0017] Figure 3 This is a schematic diagram of the spatiotemporal spectrum (three-dimensional view) of the original test data in a preferred embodiment of the present invention.

[0018] Figure 4 This is a schematic diagram of the spatiotemporal spectrum (two-dimensional view) after processing by the method of the present invention according to a preferred embodiment of the present invention.

[0019] Figure 5 This is a schematic diagram of the spatiotemporal spectrum (three-dimensional view) after processing by the method of the present invention according to a preferred embodiment of the present invention. Detailed Implementation

[0020] The embodiments of the present invention will be described in detail below with reference to the accompanying drawings, but the present invention can be implemented in many different ways as defined and covered by the claims.

[0021] See Figure 1 In a preferred embodiment of the present invention, a method for suppressing spatiotemporal reverberation of towed sonar based on prior knowledge and auxiliary samples is provided, comprising: S1. Acquire auxiliary samples and test samples based on sonar array; construct a set of space-time steering vectors by uniformly dividing the space-time plane along the spatial frequency axis and Doppler axis.

[0022] In a preferred embodiment of the present invention, auxiliary samples are constructed based on acoustic sampling data acquired by a sonar array. and the sample to be tested ,in, , Total number of auxiliary sample frames; The number of array elements. The number of time-domain sampling points. Sampling rate, This refers to the signal pulse width.

[0023] In a preferred embodiment of the present invention, constructing a set of spacetime steering vectors by uniformly dividing the spacetime plane along the spatial frequency axis and the Doppler axis includes: Based on the motion parameters and array parameters of the sonar platform, the spacetime plane is uniformly divided along the spatial frequency axis and the Doppler axis. A set of space-time steering vectors is obtained by constructing a space-time steering vector for each grid point; the space-time steering vector is composed of the Kronecker product of the spatial steering component and the temporal steering component. The number of grid cells for the spatial frequency axis of the spacetime plane. ; The number of Doppler axis grids in the spacetime plane. ;parameter and These represent the spatial frequency axis resolution and the Doppler axis resolution, respectively. Each spatial frequency axis grid corresponds to a discrete angle, and each Doppler axis grid corresponds to a Doppler frequency.

[0024] In a preferred embodiment of the present invention, the signal pulse width =12s, number of array elements The sampling rate is 5000Hz. Regarding spatial Doppler frequencies, 180 angles from 0 to 180° are divided using equal angular resolution. Because the signal pulse width was relatively long in this experiment, only two frames of data were selected as auxiliary samples. .

[0025] In a preferred embodiment of the present invention, for any spatial frequency-Doppler frequency grid point Construct the corresponding space-time steering vector include: ; ; ; in, It is a spatial guiding vector; Time-oriented vector; This is the Kronecker product operator; It is the spatial frequency, which is related to the target incident angle, the spacing between array elements, and the speed of sound. The frequency is the Doppler frequency. The sampling time interval, The sampling frequency; Indicates the transpose operation; The natural base, This is a virtual part unit.

[0026] The set of spacetime steering vectors consists of the spacetime steering vectors corresponding to all spatial frequency-Doppler frequency grid points. : ; S2. Based on the set of space-time guiding vectors, filter the vectors located in the region of concentrated reverberation energy to obtain the first set.

[0027] In a preferred embodiment of the present invention, S2 specifically includes: Under active sonar operating conditions, seabed or surface reverberation typically exhibits an energy-concentrated structure distributed along a specific geometric relationship in the angle-Doppler domain, with the corresponding Doppler frequency varying with the incident angle. Based on the sonar platform's speed and yaw angle, transmitted signal frequency, and sound speed, a geometric relationship model between the reverberation center frequency and angle is established. For a given angle... The geometric relationship model is represented as follows: ; in, The speed of the ship; Yaw angle; The frequency of the transmitted signal; Speed ​​of sound; and These represent the port reverberation center frequency and the starboard reverberation center frequency, respectively. Based on a geometric model, the reverberation energy concentration region is defined within the angle-Doppler plane. ,include: ; in, For the spatial frequency axis The discrete angles corresponding to each grid. , The number of spatial frequency axis grids in a space-time plane; For the Doppler axis The Doppler frequencies corresponding to each grid. , The number of Doppler axis grids in the empty-time plane; To preset the reverberation extension range, 0.4Hz was selected based on empirical values.

[0028] Based on the set of space-time steering vectors, regions located in the reverberation energy concentration area are selected. The vectors are used to obtain the first set.

[0029] S3. Perform energy analysis and effective vector screening based on auxiliary samples and the first set to obtain the second set; assign sparsity penalty weights to each vector in the second set.

[0030] In a preferred embodiment of the present invention, energy analysis and effective vector screening are performed based on auxiliary samples and a first set to obtain a second set, which includes: The matching energy of each vector in the first set is analyzed based on auxiliary samples to characterize the energy contribution of different spatiotemporal steering vectors in the training data, and the energy statistics are obtained: ; in, Represents the first set The Middle Energy statistics of each vector; Represents the first set The first in One vector; Indicates the first Frame-assisted samples; This indicates the total number of auxiliary sample frames; Indicates conjugate transpose; The second set is obtained by filtering vectors from the first set whose energy statistics are greater than or equal to the reverberation energy threshold: ; in, The reverberation energy threshold; This is the second set.

[0031] In a preferred embodiment of the present invention, assigning sparsity penalty weights to each vector in the second set includes: The sparse penalty weights assigned to each vector in the second set Represented as: ; in, For smoothing parameters; This is the weight adjustment parameter.

[0032] S4. Construct an optimization model containing data fitting terms and weighted sparse constraint terms based on the second set; solve the optimization model to obtain the reverberation sparse coefficient vector.

[0033] In a preferred embodiment of the present invention, constructing an optimization model containing data fitting terms and weighted sparse constraint terms based on the second set includes: Based on the second set and the sparse penalty weights, an optimization model containing data fitting terms and weighted sparse constraint terms is constructed for the test samples, as follows: ; in, Let be the second matrix, representing the matrix corresponding to the second set; Indicates the sample to be tested; Represents the reverberation sparse coefficient vector; For regularization parameters; Indicates the first The values ​​of the elements of the reverberation sparse coefficient vector.

[0034] In a preferred embodiment of the present invention, solving the optimization model to obtain the reverberation sparse coefficient vector includes: The optimization model is solved using the alternating direction multiplier method, including: Introducing auxiliary variables The optimization model is transformed into an optimization problem with equality constraints: ; in, , express The first in One component; This represents the square of the L2 norm of a vector; Auxiliary variables The update is based on the soft threshold shrinkage operator, expressed as: ; in, For the first Next iteration update The value; For the first Next iteration update The value, For the dual variable vector, , for The corresponding number in the middle The components of the reverberation sparse coefficient constraint term; For the first Next iteration update The value; For soft threshold shrinkage operators, ; For penalty parameters; This is the sparse penalty weight vector; For the Auxiliary variables in the next iteration update The Each component The calculation method is as follows: ; ; in, for The corresponding shrinkage threshold; To prevent extremely small positive numbers from being divided by zero; for The One component; for The One component; for The update methods include: ; in, For the first Next iteration update The value; Dual variable vector To perform consistency adjustments, update methods include: ; in, For the first Next iteration update The value; right , and Perform alternating updates in a loop until the original variable is updated. with auxiliary variables The errors between them satisfy the convergence condition, thus yielding the reverberation sparse coefficient vector. .

[0035] S5. Obtain the reconstructed reverberation component based on the reverberation sparse coefficient vector and the second set; subtract the reconstructed reverberation component from the sample to be tested to complete the reverberation suppression.

[0036] In a preferred embodiment of the present invention, S5 specifically includes: The reverberation sparsity coefficient vector The matrix corresponding to the second set is the second matrix. Multiplying them together yields the reconstructed reverberation components. ; the sample to be tested Subtract the reconstructed reverberation component The residual signal after reverberation suppression is obtained. , is represented as: ; The present invention provides a towed sonar spatiotemporal reverberation suppression method based on prior knowledge and auxiliary samples. By fully utilizing the structured distribution characteristics of reverberation in the spatiotemporal domain, it can achieve accurate modeling and effective suppression of reverberation components under complex reverberation backgrounds and limited training samples. This significantly improves the discriminability and signal-to-noise ratio of target components in the residual signal, thus providing a more reliable data foundation for sonar target detection, parameter estimation, or imaging processing. Reverberation component elimination based on the method of this invention can effectively suppress the dominant reverberation component in the original sonar received data, reduce the masking effect of reverberation on target echoes, and thereby relatively increase the energy proportion of target components in the residual signal.

[0037] Verification section: Simulated sea trials were conducted to acquire sea trial data. The transmitted signal pulse width was included in this sea trial data. ,frequency The array has 64 elements, the target is a transponder-simulated target with a frequency shift of approximately -0.2 Hz, and the target is located around 90°. Since the signal pulse width is long, one frame of data before and after the data to be measured is selected as auxiliary samples.

[0038] Figure 2 It is the spatiotemporal spectrum (two-dimensional view) of the original data to be tested. Figure 3 This is the original spatiotemporal spectrum (3D view) of the data to be measured. As can be seen, the target is located near 90°, with a frequency shift of about -0.2Hz. The reverberation and ship noise interference are obvious, resulting in a weak target signal that is almost invisible. Figure 4 This is the spatiotemporal spectrum (two-dimensional view) after processing according to an embodiment of the present invention. Figure 5 This is the spatiotemporal spectrum (3D view) after processing according to the embodiments of the present invention. After processing according to the embodiments of the present invention, the target bright spot is clearly visible, and most of the reverberation and ship noise interference are suppressed, proving that the method in this respect is practical.

[0039] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for suppressing spatiotemporal reverberation of towed sonar based on prior knowledge and auxiliary samples, characterized in that, include: Auxiliary samples and test samples are acquired based on sonar arrays; A set of spacetime steering vectors is constructed by uniformly dividing the spacetime plane along the spatial frequency axis and the Doppler axis; Vectors located in the reverberant energy concentration region are filtered according to the space-time steering vector set to obtain a first set; energy analysis and effective vector filtering are performed according to the auxiliary sample and the first set to obtain a second set; sparse penalty weights are assigned to each vector in the second set. An optimization model containing data fitting terms and weighted sparse constraints is constructed based on the second set; the reverberation sparse coefficient vector is obtained by solving the optimization model. The reconstructed reverberation component is obtained based on the reverberation sparse coefficient vector and the second set; the reconstructed reverberation component is subtracted from the sample to be tested to complete the reverberation suppression.

2. The towed sonar spatiotemporal reverberation suppression method based on prior knowledge and auxiliary samples according to claim 1, characterized in that, After uniformly dividing the spacetime plane along the spatial frequency axis and the Doppler axis, a set of spacetime steering vectors is constructed, including: Based on the motion parameters and array parameters of the sonar platform, the space-time plane is uniformly divided along the spatial frequency axis and the Doppler axis, and a space-time steering vector is constructed for each grid point to obtain a set of space-time steering vectors; the space-time steering vector is composed of the Kronecker product of the spatial steering component and the temporal steering component.

3. The towed sonar spatiotemporal reverberation suppression method based on prior knowledge and auxiliary samples according to claim 2, characterized in that, Based on the set of space-time steering vectors, vectors located in the reverberant energy concentration region are filtered to obtain a first set including: Based on the sonar platform's speed and yaw angle, transmitted signal frequency, and speed of sound, a geometric relationship model between the reverberation center frequency and the angle is established. For a given angle... The geometric relationship model is represented as follows: ； in, The speed of the ship; Yaw angle; The frequency of the transmitted signal; Speed ​​of sound; and These represent the port reverberation center frequency and the starboard reverberation center frequency, respectively. Based on the aforementioned geometric model, a reverberation energy concentration region is defined within the angle-Doppler plane. ,include: ； in, For the spatial frequency axis The discrete angles corresponding to each grid. , The number of spatial frequency axis grids in a space-time plane; For the Doppler axis The Doppler frequencies corresponding to each grid. , The number of Doppler axis grids in the empty-time plane; To preset the reverberation range; Based on the set of space-time steering vectors, the region located in the reverberation energy concentration area is selected. The vectors are used to obtain the first set.

4. The towed sonar spatiotemporal reverberation suppression method based on prior knowledge and auxiliary samples according to claim 3, characterized in that, Based on the auxiliary samples and the first set, energy analysis and effective vector screening are performed to obtain the second set, which includes: Based on the auxiliary samples, the matching energy of each vector in the first set is analyzed to obtain the energy statistics: ； in, Represents the first set The Middle Energy statistics of each vector; Represents the first set The first in One vector; Indicates the first Frame-assisted samples; This indicates the total number of auxiliary sample frames; Indicates conjugate transpose; By filtering the vectors in the first set whose energy statistics are greater than or equal to the reverberation energy threshold, a second set is obtained: ； in, The reverberation energy threshold; This is the second set.

5. The towed sonar spatiotemporal reverberation suppression method based on prior knowledge and auxiliary samples according to claim 4, characterized in that, Assigning sparsity penalty weights to each vector in the second set includes: The sparse penalty weights assigned to each vector in the second set Represented as: ； in, For smoothing parameters; This is the weight adjustment parameter.

6. The towed sonar spatiotemporal reverberation suppression method based on prior knowledge and auxiliary samples according to claim 5, characterized in that, The optimization model constructed based on the second set, including data fitting terms and weighted sparse constraint terms, includes: Based on the second set and the sparse penalty weights, an optimization model containing data fitting terms and weighted sparse constraint terms is constructed for the test samples, as follows: ； in, Let be the second matrix, representing the matrix corresponding to the second set; Indicates the sample to be tested; Represents the reverberation sparse coefficient vector; For regularization parameters; Indicates the first The values ​​of the elements of the reverberation sparse coefficient vector.

7. The towed sonar spatiotemporal reverberation suppression method based on prior knowledge and auxiliary samples according to claim 6, characterized in that, Solving the optimization model yields the reverberation sparse coefficient vector, including: The optimization model is solved using the alternating direction multiplier method, including: Introducing auxiliary variables The optimization model is then transformed into an optimization problem with equality constraints: ； in, , express The first in One component; This represents the square of the L2 norm of a vector; The auxiliary variable The update is based on the soft threshold shrinkage operator, expressed as: ； in, For the first Next iteration update The value; For the first Next iteration update The value, For the dual variable vector, , for The corresponding number in the middle The components of the reverberation sparse coefficient constraint term; For the first Next iteration update The value; For soft threshold shrinkage operators, ; For penalty parameters; This is the sparse penalty weight vector; For the Auxiliary variables in the next iteration update The Each component The calculation method is as follows: ； ； in, for The corresponding shrinkage threshold; To prevent extremely small positive numbers from being divided by zero; for The One component; for The One component; for The update methods include: ； in, For the first Next iteration update The value; For the dual variable vector To perform consistency adjustments, update methods include: ； in, For the first Next iteration update The value; right , and Perform alternating updates in a loop until the original variable is updated. with auxiliary variables The errors between them satisfy the convergence condition, thus yielding the reverberation sparse coefficient vector. .

8. The towed sonar spatiotemporal reverberation suppression method based on prior knowledge and auxiliary samples according to claim 7, characterized in that, The reconstructed reverberation components are obtained based on the reverberation sparse coefficient vector and the second set; Subtracting the reconstructed reverberation component from the sample to be tested to complete reverberation suppression includes: The reverberation sparse coefficient vector The matrix corresponding to the second set is the second matrix. Multiplying them together yields the reconstructed reverberation components. The sample to be tested Subtract the reconstructed reverberation component The residual signal after reverberation suppression is obtained. , is represented as: 。

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