Fixed-time neural dynamics sparse signal reconstruction method based on non-convex norm

Abstract

The present invention discloses a fixed-time neural dynamics sparse signal reconstruction method based on non-convex norm, the steps are as follows: S1, establishing an L0 norm minimization optimization model; S2, using L 1‑μ2 The hybrid norm optimization model is used to approximate the L0 norm minimization optimization model; S3, L 1‑μ2 The minimum solution of the hybrid norm optimization model is equivalent to the equilibrium point of the corresponding proximal neural dynamics optimization model, and the optimal solution is solved; S4, establish a fixed-time proximal neural dynamics optimization model; S5, set the initial parameters, and find the optimal solution of the fixed-time proximal neural dynamics optimization model within the upper limit of the convergence time; S6, continuously iterate the model to achieve sparse signal reconstruction within a fixed time. Under the same conditions, the present invention has higher accuracy in restoring sparse signals and smaller relative errors; within the same time, the present invention performs sparse signal recovery to obtain better recovery results and higher image quality.

Description

Technical Field

[0001] The present invention relates to the technical field of sparse signal reconstruction, and in particular to a fixed-time neural dynamics sparse signal reconstruction method based on non-convex norm. Background Art

[0002] Sparse reconstruction technology has attracted much attention for its wide application in many fields, including but not limited to signal processing, target detection, radar detection, and electronic engineering. In the engineering and scientific communities, scholars have a strong interest in the study of sparse reconstruction problems. The core challenge is to infer unknown sparse signals from underdetermined linear systems with noise. Compared with the traditional method based on Nyquist sampling theorem, the sparse reconstruction process based on compressed sensing principle has more relaxed requirements on sampling speed, such as Figure 6 In-depth analysis from theoretical and practical perspectives shows that proposing an efficient sparse reconstruction method is one of the key issues to be solved in this field.

[0003] Currently, compressed sensing tends to be biased towards incoherent systems, where any two observation matrices are as little correlated as possible. However, in reality, many sampled matrices are highly correlated, and traditional methods, such as L1-norm minimization, do not perform well in recovery. Recently, different mixed norms constraining the L1 and L2 norms, denoted as L1-L2, have been shown to outperform the classical L1 method, but their computational cost is high. Since the emergence of the unconstrained L1-L2 model, the convex difference method is generally used to solve it. Numerical experiments have shown that the L1-l2 model is a useful sparse recovery model. Mixed norm models have been widely studied in sparse signal recovery research, especially the L1 and l2 norms.

[0004] In recent years, a large number of sparse optimization problems are based on big data, and the real-time requirements for data processing are getting higher and higher. For example, in satellite communications, when the captured video images are transmitted from the satellite to the ground terminal, they need to be presented to people after a short period of noise reduction processing. At present, the data types are increasing day by day, and the data dimensions are also increasing. This urgently requires the development of an efficient optimization method to solve the sparse optimization problem. Although the existing numerical optimization methods still have room for improvement in terms of convergence speed, and there are deficiencies in real-time performance, there is still potential for improvement. This requires researchers to continuously explore new methods or improve existing methods to meet the needs of high-speed and real-time processing. For example, the patent application number is 200910023785.3, and the invention name is a sparse signal reconstruction method; the patent application number is 201210290161.X, and the invention name is a sparse sampling and signal compression sensing reconstruction method. Fast convergence speed, high calculation accuracy, and strong anti-interference ability are important indicators of efficient optimization methods. Different from iterative optimization methods and intelligent optimization methods, the neural dynamics optimization method uses the activity principle of neurons and has unique advantages.

[0005] At present, there are some neurodynamic optimization methods with asymptotic or exponential convergence to deal with the problem of sparse signal reconstruction. For example, the invention with application number 2021110095037.7 is called a sparse signal reconstruction method based on IPNN and compressed sensing; in order to further improve the convergence speed of the neurodynamic method, a finite time method is proposed. The upper bound of the convergence time of the finite time neurodynamic method is often related to the initial state of the method. Therefore, some relevant scholars have studied the sparse signal reconstruction method based on neurodynamic optimization that is independent of the initial state.

[0006] The existing sparse signal reconstruction methods may have the following problems: First, most of the existing numerical iterative methods are based on digital computer implementation, which is not conducive to the real-time characterization of the methods; Second, most of the existing sparse signal recovery problems use convex approximate sampling. When the sampling matrix is ​​highly correlated, the sparse signal recovery effect is not good; Third, most of the existing neurodynamic methods are asymptotically convergent or exponentially convergent. In theory, when time tends to infinity, the trajectory of the neurodynamic optimization method can achieve complete sparse signal reconstruction; Fourth, the upper bound of the convergence time of the finite-time sparse signal reconstruction method is related to the initial state. In some cases, the initial state of the system may be unknown, which is not conducive to the characterization of the upper bound of the convergence time. Summary of the invention

[0007] The object of the present invention is to provide a non-convex 1-μ2 The fixed-time neural dynamics sparse signal reconstruction method based on norm can solve the sparse signal reconstruction problem in a fixed time.

[0008] To achieve the above object, the present invention provides the following technical solutions:

[0009] A non-convex L 1-μ2 The fixed-time neural dynamics sparse signal reconstruction method based on the norm includes the following steps:

[0010] S1. According to the needs of the restored signal (such as an image), the signal is converted into a digital form and an L0 norm minimization optimization model for sparse signal reconstruction is established;

[0011] S2, through the Lagrange multiplier with L 1-μ2 The hybrid norm optimization model is used to approximate the L0 norm minimization optimization model;

[0012] S3, make L 1-μ2 The minimum solution of the hybrid norm optimization model is equivalent to the equilibrium point of the corresponding proximal neurodynamic optimization model. Combined with the explicit expression of the neurodynamic optimization model, the optimal solution of the proximal neurodynamic optimization model is solved.

[0013] S4, establish a fixed-time proximal neural dynamics optimization model through adaptive functions;

[0014] S5, set initial parameters and find the optimal solution of the fixed-time proximal neural dynamics optimization model within the upper bound of the convergence time;

[0015] S6. Continuously iterate the fixed-time proximal neural dynamics optimization model to achieve sparse signal reconstruction within a fixed time.

[0016] In some embodiments, in step S1, the L0 norm minimization optimization model is:

[0017]

[0018] Where σ is the regularization coefficient, σ>0, which is used to weigh the accuracy and sparsity of the estimated signal; is the signal data that needs to be reconstructed; is an N-dimensional real Euclidean space; the matrix is the observation matrix, is a known observation vector; ∥x∥0 is the L0 norm used to calculate the number of non-zero elements in the vector x.

[0019] In some embodiments, in step S2, the minimization problem of the L0 norm minimization optimization model which is originally difficult to handle is transformed into a model which is easier to operate by using Lagrange multipliers. 1-μ2 The mixed norm optimization model is:

[0020]

[0021] in,

[0022]

[0023] in,

[0024]

[0025] f(·)=σ(∥·∥1-μ∥·∥2);

[0026] In the formula, is the gradient operator; f(·) is the regularization term; η is an adjustable constant coefficient step size, η>0; μ is the non-convex model coefficient, μ∈(0,1]; x is the sparse signal to be restored.

[0027] In some embodiments, in step S3, the terminal neural dynamics optimization model is:

[0028]

[0029] in,

[0030]

[0031] Where k is an adjustable parameter, k>0; B T is the transpose of the observation matrix B; prox ηf(·) is the proximal operator;

[0032] The explicit expression of the neural dynamics optimization model is:

[0033]

[0034] in,

[0035] z=sign(x)*max{|x|-ση,0};

[0036] Wherein, sign(x) is a sign function, x>0, returns 1, x<0, returns -1, x=0, returns 0. The end neural dynamics optimization model has asymptotic exponential convergence and realizes sparse signal reconstruction.

[0037] In some embodiments, in step S4, the adaptive function is:

[0038]

[0039] In the formula, is the set of equilibrium points, and to simplify the notation, ψ(x)=B T (Bx-b) is the difference between the observed vector and the measured vector; Ψ(x) is the main part of the iteration;

[0040] The fixed-time proximal neural dynamics optimization model is:

[0041]

[0042] Where k1, k2, k3, β1, β2 are all adjustable parameters and are constants, k1, k2, k3>0, β1∈(0,1), β2>1.

[0043] In some embodiments, in step S5, it is assumed that the measurement matrix B satisfies the 2s RIP condition, and The trajectory of the fixed-time proximal neural dynamics optimization model converges to the optimal solution within a fixed time, where the fixed-time convergence upper bound T is:

[0044]

[0045] in,

[0046]

[0047] In the formula, is the coefficient of the restricted equidistant condition, RIP is the restricted equidistant condition for sampling required for the sparse recovery problem, Γ is the corresponding coefficient of the estimated convergence time, and Λ is the corresponding coefficient of the estimated convergence time.

[0048] In some embodiments, the iteration in step S6 includes the following steps:

[0049] S61. Input parameters and set the maximum number of iterations k <T / △t;

[0050] S62, setting iteration time k△t;

[0051] S63, calculate And assign it to ψ(x);

[0052] S64, through the adaptive function k(x), is the value of the kth iteration, calculate the value of the kth iteration;

[0053] S65. Calculate the value of the next iteration

[0054] S66: Update the next cycle.

[0055] Compared with the prior art, the present invention has the following beneficial effects:

[0056] The present invention solves the sparse signal reconstruction problem in a fixed time by introducing a mixed norm of a non-convex L1 norm and an L2 norm to approximate the L0 sparse operator and by using a sparse signal reconstruction method of proximal neural dynamics optimization with fixed-time convergence.

[0057] Under the same conditions, the present invention has higher accuracy in restoring sparse signals and smaller relative errors; within the same time, the present invention performs sparse signal restoration to obtain better restoration results and higher image quality. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 It is a schematic diagram of the process of the present invention;

[0059] FIG2( a ) is a trajectory diagram of different methods under an orthogonal Gaussian matrix according to an embodiment of the present invention;

[0060] FIG2( b ) is a graph showing sparse signal recovery using different methods under an orthogonal Gaussian matrix according to an embodiment of the present invention;

[0061] FIG2( c ) is an error response diagram of different methods under an orthogonal Gaussian matrix according to an embodiment of the present invention;

[0062] FIG3( a ) is a trajectory diagram of different methods under the DCT matrix of an embodiment of the present invention;

[0063] Figure 3(b) is the sparse signal recovery diagram of different methods under the DCT matrix of the embodiment of the present invention;

[0064] Figure 3(c) is the error response diagram of different methods under the DCT matrix of the embodiment of the present invention;

[0065] Figure 4 It is a schematic diagram of the comparison effect between the embodiment of the present invention and the prior art;

[0066] Figure 5 It is a comparison diagram of the PSNR values of the embodiment of the present invention and the prior art at T = 2;

[0067] Figure 6 It is a schematic diagram of the signal processing process based on the traditional compressive sensing theory in the prior art. Detailed implementation manners

[0068] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments; based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0069] Please refer to Figure 1 , a fixed-time neural dynamics sparse signal reconstruction method based on non-convex L 1-μ2 norm, comprising the following steps:

[0070] S1. According to the requirements of the recovered signal (such as an image), convert the signal into a digital form and establish an L0 norm minimization optimization model for sparse signal reconstruction;

[0071] Sparse signal reconstruction refers to recovering the signal x using the known observation vector and measurement matrix based on limited observation data. This process is essentially to solve the best sparse solution of an underdetermined linear equation system. Set the linear equation:

[0072] Bx = b (1);

[0073] In the formula, is the signal data to be reconstructed, the matrix is the observation matrix, is the known observation vector, is the M×N-dimensional real Euclidean space.

[0074] If M << N, then the linear equation (1) is ill-conditioned and may have infinitely many solutions. The sparse optimization problem of the underdetermined linear equation system can be constructed in the following form:

[0075]

[0076] Where ∥x∥0 is the number of non-zero elements in the signal x, and st is the constraint condition.

[0077] For sparse optimization problems, the regularization method is a common and effective method, which can transform the sparse optimization problem into an unconstrained optimization problem, also known as a regularization problem. The L0 norm minimization optimization model can be expressed by L0 regularization as:

[0078]

[0079] Where σ is the regularization coefficient, σ>0, which is used to weigh the accuracy and sparsity of the estimated signal; is the signal data that needs to be reconstructed; is an N-dimensional real Euclidean space; the matrix is the observation matrix, is a known observation vector; ∥x∥0 is the L0 norm used to calculate the number of non-zero elements in the vector x.

[0080] However, the L0 regularization problem is non-convex and non-Lipschitz continuous. Although it can provide an optimal sparse solution in theory, it belongs to the category of NP-hard problems, so it is difficult to solve the problem directly.

[0081] S2. In order to solve the L0 minimization problem of the above-mentioned accurate sparse reconstruction, the Lagrange multiplier method is used to transform the originally difficult L0 minimization problem into a more easily operable model. When the observation matrix B satisfies the restricted isometry condition (RIP), L 1-μ2 The hybrid norm optimization model is used to approximate the L0 norm minimization optimization model.

[0082] Specifically, the above expression (3) can be transformed into solving the following calculation expression (L 1-μ2 Optimization problem of mixed norm optimization model):

[0083]

[0084] According to the KKT point theory, expression (4) is equivalent to solving the optimal value point that satisfies the following calculation expression;

[0085]

[0086] in,

[0087]

[0088] f(·)=σ(∥·∥1-μ∥·∥2);

[0089] In the formula, is the gradient operator; f(·) is the regularization term; η is an adjustable constant coefficient step size, η>0; μ is the relaxation coefficient of the non-convex model, μ∈(0,1]; x is the sparse signal to be restored.

[0090] S3, make L 1-μ2 The minimum solution of the hybrid norm optimization model is equivalent to the equilibrium point of the corresponding proximal neurodynamic optimization model. Combined with the explicit expression of the neurodynamic optimization model, the optimal solution of the proximal neurodynamic optimization model is solved.

[0091] The L for the sparse signal reconstruction problem with non-convex approximation 1-μ2 The optimal point of the mixed norm optimization model is the same as the equilibrium point of the following proximal neural dynamics optimization model:

[0092]

[0093] in,

[0094]

[0095] Where k is an adjustable parameter, k>0; B T is the transpose of the observation matrix B; prox ηf(·) is the proximal operator;

[0096] The explicit expression of the neural dynamics optimization model is:

[0097]

[0098] in,

[0099] z=sign(x)*max{|x|-ση,0};

[0100] Where sign(x) is the sign function. If x>0, it returns 1; if x<0, it returns -1; and if x=0, it returns 0.

[0101] According to the prior art, the proximal neural dynamics optimization model has asymptotic exponential convergence, which means that when time t tends to infinity, x(t) converges to L 1-μ2 The optimal solution of the hybrid norm optimization model (calculation expression (4)) is to achieve sparse signal reconstruction. The x(t) refers to the sparse signal recovered at time t during the sparse signal recovery process, that is, the iteration time is long enough to recover the original signal.

[0102] S4. In order to quickly find the L of the non-convex approximation sparse signal reconstruction problem 1-μ2 The solution of the mixed norm optimization model is used to establish a fixed-time proximal neural dynamics optimization model through an adaptive function.

[0103] Based on the theoretical basis of the proximal operator, the adaptive function is as follows:

[0104]

[0105] In the formula, is the set of equilibrium points, and to simplify the notation, ψ(x)=B T (Bx-b) is the difference between the observed vector and the measured vector; Ψ(x) is the main part of the iteration;

[0106] In order to solve L 1-μ2 The hybrid norm optimization model establishes a fixed-time proximal neural dynamics optimization model as follows:

[0107]

[0108] Where k1, k2, k3, β1, β2 are all adjustable parameters and are constants, k1, k2, k3>0, β1∈(0,1), β2>1.

[0109] Since the fixed-time proximal neural dynamics optimization model has a fixed-time convergence property, and the equilibrium point of the fixed-time proximal neural dynamics optimization model (Formula 7) is equivalent to that of the proximal neural dynamics optimization model (Formula 6), then based on the discussion in step S2, solving L 1-μ2 The mixed norm optimization model (Formula 4) is equivalent to solving the equilibrium point of the fixed-time proximal neural dynamics optimization model (Formula 7). Therefore, the equilibrium point of the fixed-time proximal neural dynamics optimization model (Formula 7) is also the solution to the sparse signal recovery problem.

[0110] S5. Set the initial parameters and find the optimal solution of the fixed-time proximal neural dynamics optimization model within the upper bound of the convergence time.

[0111] As long as L 1-μ2 The measurement matrix B of the hybrid norm optimization model (Formula 4) satisfies the 2s RIP condition, so the gradient (The purpose is to find the iterative descent direction of the method) is a strongly monotone mapping and also a Lipschitz mapping, where the strongly monotone coefficient The Lipschitz constant is

[0112] Assume that the measurement matrix B satisfies the 2s RIP condition and The trajectory of the fixed-time proximal neural dynamics optimization model converges to the optimal solution within a fixed time, where the fixed-time convergence upper bound T is:

[0113]

[0114] Among them,

[0115]

[0116] In the formula, is the coefficient for the restricted isometry condition, RIP is the restricted isometry condition for the sampling required for the sparse recovery problem, Γ is the corresponding coefficient for estimating the convergence time, and Λ is the corresponding coefficient for estimating the convergence time.

[0117] The fixed-time convergence upper bound T is a general convergence upper bound. For different parameter selections, different convergence time upper bounds can be obtained. For the observation matrix that satisfies the restricted isometry condition, using the L 1-μ2 mixed-norm optimization model to solve the corresponding coefficient signal recovery problem can be recovered within the fixed-time convergence upper bound T, and the fixed-time convergence upper bound T is a relatively low recovery time upper bound.

[0118] S6. Continuously iterate the fixed-time proximal neural dynamics optimization model to achieve sparse signal reconstruction within a fixed time.

[0119] It includes the following steps:

[0120] S61. Input parameters: proximal operator prox ηf(·) , step size △t, number of iterations k, design parameters k1, k2, k3, β1, β2, initial value Set the maximum number of iterations k < T / △t, and set the termination condition (the maximum number of iterations, or the difference between the k-th iteration value and the (k + 1)-th iteration value, that is, the precision value). For example, the termination condition can be set to

[0121] S62. Set the iteration time to k△t;

[0122] S63. Calculate and assign it to Ψ(x);

[0123] S64. Through the adaptive function k(x), being the value of the k-th iteration, calculate the value of the k-th iteration;

[0124] S65. Calculate the value of the next iteration

[0125] S66. Update the next loop.

[0126] In a specific embodiment, the present invention verifies the beneficial effects of the present invention through sparse signal recovery experiments and face compression recovery experiments.

[0127] 1. Sparse signal reconstruction experiment

[0128] In order to verify the effectiveness of the present invention, a sparse signal recovery experiment is used, that is, the recovered signal is recorded as This experiment uses two measurement matrices, namely the orthogonal Gaussian random measurement matrix B and the oversampled DCT matrix as the sensing matrix, m = 20, n = 100. The oversampled DCT matrix is ​​used definition The parameters are used to determine the coherence of the matrix, is a random vector.

[0129] First, an orthogonal Gaussian random matrix b is used to perform a signal recovery experiment, generating a sparse signal where n = 100, s = 5, where s represents sparsity. The non-zero elements of x are generated by a normal Gaussian distribution. Using the measurement matrix and m = 20. The measurement vector is Where ε is Gaussian noise and the standard deviation is ε=0.01. Set the threshold Among them v=0.005, μ=0.5, σ=0.02, Then, for the sparse signal reconstruction problem, the present invention (FxPNA) is compared with the methods in the prior art:

[0130] CAPPA: Fixed-time proximal neural dynamics approach;

[0131] FxLCA: a fixed-time local competition neural dynamics approach;

[0132] FxTFNN: a fixed-time time-invariant neural dynamics approach;

[0133] SNNL1q: Smooth neural network L1-2;

[0134] SIPNNLpq: Smoothed Neural Dynamics with Inertia Term;

[0135] FTSNF: Fixed-Time Neural Dynamics Method;

[0136] Take n = 100, m = 20, s = 5. As can be seen from Figure 2 (a), Figure 2 (b), and Figure 2 (c), compared with other methods such as FTSNF, the convergence speed of the present invention (FxPNA) and FxLCA is faster. At the same time, under the same conditions, the present invention (FxPNA) has a higher accuracy in recovering sparse signals and a smaller relative error. Therefore, in the same time, the present invention (FxPNA) can obtain better recovery results for sparse signal recovery.

[0137] The experiment was conducted under the condition of oversampled sensing matrix B, where F = 6, m = 20, n = 100, s = 5. Similarly, the present invention (FxPNA) is compared with CAPPA, FxLCA, FxTFNN, SNNL1q, SIPNNLpq and FTSNF to converge in a fixed time.

[0138] From Figure 3(a), Figure 3(b), and Figure 3(c), we can see that the present invention has a better ability to recover sparse signals than other models. While other methods cannot recover the true sparse signal results, the present invention (FxPNA) can still recover the sparse signal under this measurement matrix. Under the same conditions, the present invention (FxPNA) has better recovery ability.

[0139] 2. Face reconstruction experiment:

[0140] In order to verify the performance of the present invention, we considered the application of face reconstruction, taking into account the problems of image compression and reconstruction that are often encountered in real life. The present invention FxPNA (7) was compared with LCA, CAPPA, FTSNF and SNNL1 methods.

[0141] By reconstructing a 112×92 image from the ORL dataset, the image is sparsely represented using wavelet transform. The measurement matrix is ​​a standard orthogonal Gaussian random matrix. The higher the PSNR, the better the image quality. In order to intuitively illustrate the restoration performance of the FxPNA of the present invention, Figure 5 The PSNR values ​​corresponding to the recovery states of each method are included.

[0142] Under the same recovery time constraint, it is obvious that Figure 4 As can be seen from , facial features can generally be restored. Figure 5 It can be quantitatively seen that compared with the LCA, CAPPA, FTSNF and SNNL12 methods, the FxPNA of the present invention exhibits superior recovery performance.

Claims

1. A fixed-time neural dynamics sparse signal reconstruction method based on non-convex norm, characterized by: The following steps are involved: S1. Establish sparse signal reconstruction according to the needs of the restored signal Norm minimization optimization model: (3)； In the formula, is the regularization coefficient, , used to balance the accuracy and sparsity of the estimated signal; is the signal data that needs to be reconstructed; for Dimensional Euclidean space; matrix is the observation matrix, is a known observation vector; for The norm is used to calculate the vector The number of non-zero elements in ; S2, through the Lagrange multiplier Hybrid norm optimization model to approximate Norm minimization optimization model; The mixed norm optimization model is: (4)； in, (5)； in, ； ； In the formula, is the gradient operator; is the regularization term; is an adjustable constant coefficient step size, ; are the non-convex model coefficients, , is the sparse signal to be recovered; S3. The minimum solution of the hybrid norm optimization model is equivalent to the equilibrium point of the corresponding proximal neurodynamic optimization model. Combined with the explicit expression of the neurodynamic optimization model, the optimal solution of the proximal neurodynamic optimization model is solved; the proximal neurodynamic optimization model is: (6)； in, ； In the formula, is an adjustable parameter. ; is the observation matrix The transpose of is the proximal operator; The explicit expression of the neural dynamics optimization model is: ； in, ； In the formula, is the symbolic function, , returns 1, , returns -1, , returns 0; is an adjustable constant coefficient step size, ; for A portion of the displayed form solved for the proximal operator; S4, establish a fixed-time proximal neural dynamics optimization model through adaptive functions; The adaptive function is: ； In the formula, is the set of equilibrium points, and to simplify the notation, ; is the difference between the observed vector and the measured vector value; It is the main part of the iteration; The fixed-time proximal neural dynamics optimization model is: (7)； In the formula, are all adjustable parameters, are constants, , , ; S5. Set the initial parameters and find the optimal solution of the fixed-time proximal neural dynamics optimization model within the upper bound of the convergence time; assume that the measurement matrix The 2s RIP condition is met, and , the trajectory of the fixed-time proximal neural dynamics optimization model converges to the optimal solution within a fixed time, where the fixed-time convergence upper bound T is: (8)； in, ； ； In the formula, is the coefficient of the isometry constraint, RIP is the isometry constraint for sampling of sparse problems, is the corresponding coefficient for estimating the convergence time, is the corresponding coefficient for estimating the convergence time; S6. Continuously iterate the fixed-time proximal neural dynamics optimization model to achieve sparse signal reconstruction within a fixed time.

2. The method for reconstructing fixed-time neural dynamics sparse signals based on non-convex norm according to claim 1, characterized in that: The iteration in S6 includes the following steps: S61, input parameters and set the maximum number of iterations; S62, setting iteration time; S63, calculate And assign it to ; S64, through adaptive function , is the value of the kth iteration, calculate the value of the kth iteration; S65. Calculate the value of the next iteration ; S66. Update the next cycle.

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