Low-rank sparse matrix decomposition echo enhancement method, system, medium and equipment

Abstract

The invention provides a low-rank sparse matrix decomposition echo enhancement method and system, a medium and equipment, and the method comprises the steps: S1, carrying out the beam forming of active sonar echo data, and obtaining an azimuth distance map; s2, flattening each frame of azimuth distance map into vectors, and stacking the vectors into a matrix; s3, constructing an augmented Lagrange function; step S4, initializing parameters; step S5, based on an augmented Lagrange function, adopting an alternating direction multiplier method to solve sub-problems; and S6, repeating the step S5 until algorithm convergence is carried out to obtain enhanced active sonar echo data. According to the method, the low-rank characteristic of reverberation in multi-frame echo data and the sparse characteristic of target echoes are fully utilized, and the target echo enhancement problem is converted into the low-rank sparse matrix decomposition problem. Through the method, the target echo can be efficiently and accurately extracted from the strong reverberation background, and then the detection capability of the active sonar is improved.

Description

Technical Field

[0001] The present invention relates to the field of sonar technology in underwater acoustic engineering, and in particular to a low-rank sparse matrix decomposition echo enhancement method, system, medium and equipment. Background Art

[0002] In the field of active sonar technology, ocean environmental noise and reverberation are the two main interference factors. Among them, reverberation has unique characteristics. It is formed by the superposition of scattered waves from many scatterers. It is close to the transmitted signal in the time domain, coherent in the frequency domain, and its intensity often far exceeds the target echo. What is more tricky is that due to the relative motion between the scatterers and the active sonar carrier, the reverberation will be accompanied by Doppler frequency deviation. The Doppler frequency deviation of the reverberation is also different due to the difference in relative motion speed of scatterers in different directions, which ultimately makes the reverberation spectrum widely distributed to form a reverberation band.

[0003] When active sonar emits Doppler sensitive signals and the carrier and the target have a large relative motion, the Doppler frequency shift of the target echo is large, which can avoid the influence of the reverberation band; otherwise, the target echo will fall into the reverberation band and the detection capability will be greatly reduced. This shows that reverberation has always been a severe challenge for active sonar, and enhancing the target echo under the reverberation background has always been a difficult point in underwater acoustic signal processing.

[0004] Traditional target echo enhancement methods only focus on single-frame echo data and fail to fully tap the value of multi-frame echo data. In fact, the ocean environment has a slowly time-varying characteristic, and the reverberation in multi-frame echo data is correlated and exhibits low rank. At the same time, due to the relative motion between the active sonar carrier and the target, the target echoes in the multi-frame echo data are in different spatial positions, showing sparsity.

[0005] Therefore, if we can break through the traditional limitations and effectively utilize the low-rank and sparse characteristics of multi-frame echo data to accurately decompose the echo data into low-rank reverberation and sparse target echoes, we can achieve the enhancement of target echoes.

[0006] Through searching patent documents, it was found that the invention patent with publication number CN116012264B discloses an image restoration method based on sparse constraints. The method constructs a matrix M from the image I to be restored containing n×m pixels; assumes that the matrix M can be decomposed into a low-rank matrix L with the real structure of the matrix M and a noise matrix E with sparse representation; uses a method based on sparse constraints to replace the rank function and the matrix l0 norm with the nuclear norm and sparse constraints; uses the alternating direction method to fix other parameters and iterate to solve subproblems L and E respectively; subproblem L uses the singular value threshold method to equally shrink the singular values, and subproblem E uses the generalized threshold function to solve; after a certain number of iterations or when the error is small enough, the low-rank approximate matrix L is obtained, which is the restored image. This patent is limited to image restoration, dealing with the problem of separating low-rank and sparse components in sonar signals to enhance target echoes, and has a narrow scope of application.

[0007] In summary, in response to the above-mentioned problems of the prior art, studying a low-rank sparse matrix decomposition echo enhancement method, system, medium and equipment has become a key task that needs to be solved urgently. Summary of the invention

[0008] In view of the defects in the prior art, the object of the present invention is to provide a low-rank sparse matrix decomposition echo enhancement method, system, medium and equipment.

[0009] A low-rank sparse matrix decomposition echo enhancement method provided by the present invention comprises the following steps:

[0010] Step S1, performing beamforming on active sonar echo data to obtain a azimuth range map;

[0011] Step S2, flattening the azimuth distance map of each frame into vectors, and stacking the vectors into a matrix;

[0012] Step S3, constructing a convex optimization problem based on the matrix, and constructing an augmented Lagrangian function based on the convex optimization problem;

[0013] Step S4, initializing parameters;

[0014] Step S5, solving the subproblem by using the alternating direction multiplier method based on the augmented Lagrangian function;

[0015] Step S6, repeating step S5 until the algorithm converges to obtain enhanced active sonar echo data.

[0016] Preferably, step S1 comprises: performing a processing on m frames of active sonar echo data s i Perform beamforming to obtain the m-frame azimuth distance map D i , where i=1,…,m.

[0017] Preferably, step S2 comprises: converting each frame azimuth distance map D i Flatten into vectors of dimension n and stack the vectors into a matrix M of dimension m×n.

[0018] Preferably, step S3 includes the following sub-steps:

[0019] Step S3.1, express the matrix M as the sum of the low-rank component X and the sparse component S, and construct a convex optimization problem. The formula is as follows:

[0020]

[0021] stX+S=M (2)

[0022] Among them, μ>0 represents the sparse regularization parameter; X is the low-rank reverberation, and S is the sparse target echo.

[0023] Step S3.2, based on the convex optimization problem, construct the augmented Lagrangian function, the formula is as follows:

[0024]

[0025] Among them, ρ>0 represents the penalty factor, Y represents the Lagrange multiplier, <·,·> represents the matrix inner product, ||·|| F Represents the norm of the matrix F.

[0026] Preferably, step S4 includes: initializing S, Y, ρ to S 0 , Y 0 , ρ 0 , let k = 0; where S 0 =0, Y 0 =M / ||M|| 1 ,ρ 0 =ρ, ρ is an arbitrary value.

[0027] Preferably, step S5 includes the following sub-steps:

[0028] Step S5.1, based on S k and Y k Update to get X subproblems, update to get X k+1 , the formula is as follows:

[0029]

[0030] in, UDiag(σ(A))V T represents the reduced singular value decomposition of A, Diag(·) represents the operation of converting a vector into a diagonal matrix, sign(·) represents the sign function, max{·,·} represents the maximum value, and σ(A) is the singular value vector of A;

[0031] Step S5.2, based on X k+1 and Y k Update to get S subproblems, update to get S k+1 , the formula is as follows:

[0032]

[0033] Step S5.3, based on X k+1 and S k+1 Update the Lagrange multiplier Y subproblem, the formula is as follows:

[0034] Y k+1 =Y k +ρ k (X k+1 +S k+1 -M) (6)

[0035] Step S5.4, based on the update factor τ, update the penalty factor ρ sub-problem, the formula is as follows:

[0036] ρ k+1 =τρ k (7)

[0037] Preferably, in step S6, the algorithm convergence includes: when When , the algorithm converges, and gate is the convergence threshold.

[0038] The present invention also provides a low-rank sparse matrix decomposition echo enhancement system, comprising:

[0039] Module M1, performs beamforming on active sonar echo data to obtain a azimuth range map;

[0040] Module M2, flattens the azimuth distance map of each frame into vectors, and stacks the vectors into a matrix;

[0041] Module M3, constructs a convex optimization problem based on a matrix, and based on the convex optimization problem, constructs an augmented Lagrangian function;

[0042] Module M4, initialization parameters;

[0043] Module M5, based on the augmented Lagrangian function, uses the alternating direction multiplier method to solve the subproblems;

[0044] Module M6, repeating module M5 until the algorithm converges to obtain enhanced active sonar echo data.

[0045] The present invention also provides a computer-readable storage medium storing a computer program, and when the computer program is executed by a processor, the steps of the above-mentioned low-rank sparse matrix decomposition echo enhancement method are implemented.

[0046] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the computer program is executed by the processor, the steps of the above-mentioned low-rank sparse matrix decomposition echo enhancement method are implemented.

[0047] Compared with the prior art, the present invention has the following beneficial effects:

[0048] 1. The method of the present invention makes full use of the low-rank characteristics of reverberation in multi-frame echo data and the sparse characteristics of target echoes, and transforms the target echo enhancement problem into a low-rank sparse matrix decomposition problem. Through this method, the target echo can be accurately extracted from the strong reverberation background efficiently, thereby improving the detection capability of active sonar.

[0049] 2. The alternating direction multiplier method adopted in the present invention has the advantages of relatively loose requirements on hyperparameters and relatively small amount of calculation, and is easy to implement in engineering practice. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Other features, objects and advantages of the present invention will become more apparent from the detailed description of non-limiting embodiments made with reference to the following drawings:

[0051] Figure 1 A flowchart of a low-rank sparse matrix decomposition target echo enhancement method in an embodiment of the present invention;

[0052] Figure 2 An azimuth distance diagram of the first frame echo in an embodiment of the present invention;

[0053] Figure 3 The target echo enhanced by the PCA algorithm in the embodiment of the present invention;

[0054] Figure 4 Target echo enhanced by the algorithm in the embodiment of the present invention. DETAILED DESCRIPTION

[0055] The present invention is described in detail below in conjunction with specific embodiments. The following embodiments will help those skilled in the art to further understand the present invention, but are not intended to limit the present invention in any form. It should be noted that, for those of ordinary skill in the art, several changes and improvements can also be made without departing from the concept of the present invention. These all belong to the protection scope of the present invention.

[0056] The present invention mainly solves the problem of enhancing target echo under reverberation background.

[0057] Embodiment 1:

[0058] This embodiment provides a low-rank sparse matrix decomposition target echo enhancement method, including the following steps:

[0059] Step S1, beamforming is performed on active sonar echo data to obtain a azimuth range map.

[0060] Specifically, for m frames of active sonar echo data s i Perform beamforming to obtain the m-frame azimuth distance map D i ;

[0061] Among them, i=1,…,m.

[0062] Step S2: Flatten the azimuth distance map of each frame into vectors, and stack the vectors into a matrix.

[0063] Specifically, the azimuth distance map D of each frame i Flatten into vectors of dimension n and stack the vectors into a matrix M of dimension m×n.

[0064] Step S3, constructing a convex optimization problem based on the matrix, and constructing an augmented Lagrangian function based on the convex optimization problem.

[0065] Specifically, step S3 includes the following sub-steps:

[0066] Step S3.1, express the matrix M as the sum of the low-rank component X and the sparse component S, and construct a convex optimization problem. The formula is as follows:

[0067]

[0068] stX+S=M (2)

[0069] Among them, μ>0 represents the sparse regularization parameter; X is the low-rank reverberation, and S is the sparse target echo; by solving S, the purpose of enhancing the target echo can be achieved.

[0070] Step S3.2, based on the convex optimization problem, construct the augmented Lagrangian function, the formula is as follows:

[0071]

[0072] Among them, ρ>0 represents the penalty factor, Y represents the Lagrange multiplier, <·,·> represents the matrix inner product, ||·|| F Represents the norm of the matrix F.

[0073] Step S4, initializing parameters.

[0074] Specifically, initialize S, Y, ρ to S 0 , Y 0 , ρ 0 , let k = 0; where S 0 =0, Y 0 =M / ||M||1 , ρ 0 =ρ, ρ is an arbitrary value.

[0075] Step S5, based on the augmented Lagrangian function, the alternating direction multiplier method is used to solve the sub-problem.

[0076] Specifically, step S5.1, based on S k and Y k Update to get X subproblems, update to get X k+1 , the formula is as follows:

[0077]

[0078] in, UDiag(σ(A))V T represents the reduced singular value decomposition of A, Diag(·) represents the operation of converting a vector into a diagonal matrix, sign(·) represents the sign function, max{·,·} represents the maximum value, and σ(A) is the singular value vector of A.

[0079] Step S5.2, based on X k+1 and Y k Update to get S subproblems, update to get S k+1 , the formula is as follows:

[0080]

[0081] Step S5.3, based on X k+1 and S k+1 Update the Lagrange multiplier Y subproblem, the formula is as follows:

[0082] Y k+1 =Y k +ρ k (X k+1 +S k+1 -M) (6)

[0083] Step S5.4, based on the update factor τ, update the penalty factor ρ sub-problem, the formula is as follows:

[0084] ρ k+1 =τρ k (7)

[0085] Step S6, repeating step S5 until the algorithm converges to obtain enhanced active sonar echo data.

[0086] Specifically, the algorithm convergence includes: When , the algorithm converges, gate is the convergence threshold, and gate is set according to the actual data. After the algorithm converges, the low-rank component X and the sparse component S are obtained. The sparse component S is the result after echo enhancement.

[0087] Embodiment 2:

[0088] Figure 2 An azimuth distance diagram of the first frame echo in an embodiment of the present invention; Figure 3 The target echo enhanced by the PCA algorithm in the embodiment of the present invention; Figure 4 Target echo enhanced by the algorithm in the embodiment of the present invention.

[0089] The following is a specific embodiment of the present invention:

[0090] In multi-frame echo data, the target angle is:

[0091] [120,118,116,114,112,110,108,106,103,100,96],

[0092] The target distance is: [200,196,192,188,184,180,176,172,168,164,160]. The azimuth distance diagram of the first frame of echo data is shown in the figure below. Figure 2 As shown in the figure, it can be seen that the target echo is submerged by the reverberation. Figure 3 As shown, the target echo reference after the algorithm of the present invention is enhanced Figure 4 As shown, through comparison, it is found that the algorithm proposed in the present invention can more effectively decompose the target echo and effectively suppress the reverberation interference, thereby improving the detection capability of the active sonar.

[0093] Embodiment 3:

[0094] The present invention also provides a low-rank sparse matrix decomposition echo enhancement system. The low-rank sparse matrix decomposition echo enhancement system can be implemented by executing the process steps of a low-rank sparse matrix decomposition echo enhancement method, that is, those skilled in the art can understand the low-rank sparse matrix decomposition echo enhancement method as a preferred implementation of the low-rank sparse matrix decomposition echo enhancement system.

[0095] Specifically, the low-rank sparse matrix decomposition echo enhancement system includes:

[0096] Module M1, performs beamforming on active sonar echo data to obtain a azimuth range map;

[0097] Module M2, flattens the azimuth distance map of each frame into vectors, and stacks the vectors into a matrix;

[0098] Module M3, constructs a convex optimization problem based on a matrix, and based on the convex optimization problem, constructs an augmented Lagrangian function;

[0099] Module M4, initialization parameters;

[0100] Module M5, based on the augmented Lagrangian function, uses the alternating direction multiplier method to solve the subproblems;

[0101] Module M6, repeating module M5 until the algorithm converges to obtain enhanced active sonar echo data.

[0102] Embodiment 4:

[0103] This embodiment provides a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, the steps of a low-rank sparse matrix decomposition echo enhancement method in the above-mentioned embodiment 1 are implemented.

[0104] Embodiment 5:

[0105] This embodiment provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the computer program is executed by the processor, the steps of a low-rank sparse matrix decomposition echo enhancement method in the above-mentioned embodiment 1 are implemented.

[0106] Those skilled in the art know that, in addition to realizing the system and its various devices, modules, and units provided by the present invention in a purely computer-readable program code, it is entirely possible to realize the same functions in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers by logically programming the method steps. Therefore, the system and its various devices, modules, and units provided by the present invention can be considered as a hardware component, and the devices, modules, and units included therein for realizing various functions can also be regarded as structures within the hardware component; the devices, modules, and units for realizing various functions can also be regarded as both software modules for realizing the method and structures within the hardware component.

[0107] The above describes the specific embodiments of the present invention. It should be understood that the present invention is not limited to the above specific embodiments, and those skilled in the art can make various changes or modifications within the scope of the claims, which does not affect the essence of the present invention. In the absence of conflict, the embodiments of the present application and the features in the embodiments can be combined with each other arbitrarily.

Claims

1. A low-rank sparse matrix decomposition echo enhancement method, characterized in that: The steps include: Step S1, performing beamforming on active sonar echo data to obtain a azimuth range map; Step S2, flattening the azimuth distance graphs of each frame into vectors, and stacking the vectors into a matrix; Step S3, constructing a convex optimization problem based on the matrix, and constructing an augmented Lagrangian function based on the convex optimization problem; Step S4, initializing parameters; Step S5, solving the subproblem by using the alternating direction multiplier method based on the augmented Lagrangian function; Step S6, repeating step S5 until the algorithm converges to obtain enhanced active sonar echo data.

2. The low-rank sparse matrix decomposition echo enhancement method according to claim 1, characterized in that: The step S1 comprises: performing a search on m frames of active sonar echo data s i Perform beamforming to obtain the m-frame azimuth distance map D i , where i=1,…,m.

3. The low-rank sparse matrix decomposition echo enhancement method according to claim 2, characterized in that: The step S2 comprises: i Flatten into vectors of dimension n, and stack the vectors into a matrix M of dimension m×n.

4. The low-rank sparse matrix decomposition echo enhancement method according to claim 3, characterized in that: The step S3 includes the following sub-steps: Step S3.1, the matrix M is expressed as the sum of the low-rank component X and the sparse component S, and a convex optimization problem is constructed, and the formula is as follows: stX+S=M (2) Where, μ>0 represents the sparse regularization parameter; X is the low-rank reverberation, and S is the sparse target echo; Step S3.2, based on the convex optimization problem, construct an augmented Lagrangian function, the formula is as follows: Among them, ρ>0 represents the penalty factor, Y represents the Lagrange multiplier, <·,·> represents the matrix inner product, ||·|| F Represents the norm of the matrix F.

5. The low-rank sparse matrix decomposition echo enhancement method according to claim 4, characterized in that: The step S4 includes: initializing S, Y, ρ to S 0 , Y 0 , ρ 0 , let k = 0; where S 0 =0, Y 0 =M / ||M||1,ρ 0 =ρ, ρ is an arbitrary value.

6. The low-rank sparse matrix decomposition echo enhancement method according to claim 5, characterized in that: The step S5 includes the following sub-steps: Step S5.1, based on S k and Y k Update to get X subproblems, update to get X k+1 , the formula is as follows: in, UDiag(σ(A))V T represents the reduced singular value decomposition of A, Diag(·) represents the operation of converting a vector into a diagonal matrix, sign(·) represents the sign function, max{·,·} represents the maximum value, and σ(A) is the singular value vector of A; Step S5.2, based on X k+1 and Y k Update to get S subproblems, update to get S k+1 , the formula is as follows: Step S5.3, based on X k+1 and S k+1 Update the Lagrange multiplier Y subproblem, the formula is as follows: Y k+1 =Y k +ρ k (X k+1 +S k+1 -M) (6) Step S5.4, based on the update factor τ, update the penalty factor ρ sub-problem, the formula is as follows: r k+1 =tr k (7) 7. The low-rank sparse matrix decomposition echo enhancement method according to claim 5, characterized in that: In step S6, the algorithm convergence includes: when When , the algorithm converges, and gate is the convergence threshold.

8. A low-rank sparse matrix decomposition echo enhancement system, characterized in that: include: Module M1, performs beamforming on active sonar echo data to obtain a azimuth range map; Module M2, flattens the azimuth distance map of each frame into vectors, and stacks the vectors into a matrix; Module M3, constructing a convex optimization problem based on the matrix, and constructing an augmented Lagrangian function based on the convex optimization problem; Module M4, initialization parameters; Module M5, based on the augmented Lagrangian function, using the alternating direction multiplier method to solve the sub-problem; Module M6, repeating module M5 until the algorithm converges to obtain enhanced active sonar echo data.

9. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the steps of a low-rank sparse matrix decomposition echo enhancement method described in any one of claims 1 to 7 are implemented.

10. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the computer program is executed by a processor, the steps of a low-rank sparse matrix decomposition echo enhancement method described in any one of claims 1 to 7 are implemented.

Images