Signal robust sparse time-frequency analysis method, terminal device and storage medium

Abstract

The present invention relates to a signal robust sparse time-frequency analysis method, a terminal device, and a storage medium. The method includes: S1: constructing a signal impulse noise removal model based on morphological component analysis, sparse time-frequency analysis, and frame wavelet transform; S2: using the forward decomposition method for the signal impulse noise removal model to calculate the texture component y of the signal after impulse noise removal T and the cartoon component y C ; S3: according to the texture component y of the signal T and the cartoon component y C , using the backward decomposition method for the signal impulse noise removal model to calculate the spectral sparse solution x of the signal after impulse noise removal i . The present invention introduces the morphological component analysis algorithm to decompose the signal to be processed into a low-frequency cartoon component, a high-frequency texture component, and a noise component, and further introduces a stationary frame wavelet regularization term on the basis of morphological component analysis to fully exploit the difference between the effective component and the noise component of the signal, so as to achieve the purpose of suppressing noise and robust time-frequency analysis.

Description

Technical Field

[0001] The present invention relates to the field of signal processing, and in particular to a signal robust sparse time-frequency analysis method, terminal equipment and storage medium. Background Art

[0002] Time-frequency analysis methods can effectively reflect the spectral distribution of signals in local time. They are an important research branch in the field of signal processing and are widely used in many fields such as geophysical exploration, radar imaging, mechanical vibration signal analysis, biomedical signal analysis, and power signal analysis. However, traditional time-frequency analysis methods have problems such as insufficient resolution and cross-term interference.

[0003] In recent years, with the rise of sparse representation and the continuous maturity and improvement of optimization theory, sparse time-frequency analysis methods based on sparse representation have begun to appear, which has solved the problem of insufficient resolution of time-frequency analysis to a certain extent. Although the sparse time-frequency analysis method accurately depicts the spectrum of the effective signal, it cannot accurately reflect the spectrum distribution of the effective signal under noise interference, especially under impulse noise interference. Summary of the invention

[0004] In order to solve the above problems, the present invention proposes a signal robust sparse time-frequency analysis method, a terminal device and a storage medium.

[0005] The specific plan is as follows:

[0006] A signal robust sparse time-frequency analysis method comprises the following steps:

[0007] S1: Construct a signal impulse noise removal model based on morphological component analysis, sparse time-frequency analysis and frame wavelet transform:

[0008]

[0009] Among them, MCA(.) represents the morphological component analysis algorithm, y T Represents signal y n The texture component, y C Represents signal y n Cartoon composition, y iT Indicates that the signal y T The i-th sub-signal after segmentation, y iC Indicates that the signal y C The i-th sub-signal after segmentation, g represents the sliding window, Θ = SF -1 represents a sparse transformation matrix, S = [I|O] represents a truncated matrix, I represents an identity matrix, O represents a matrix with all elements zero, and F represents a Fourier transform matrix. represents the L2 norm, represents the Lp pseudo-norm, p is the control parameter of the sparsity of the sparse variables in the LP pseudo-norm, x i represents the sparse solution of the signal spectrum, μ represents the balance parameter;

[0010] S2: Use the forward decomposition method to calculate the texture component y of the signal after the impulse noise is removed. T and cartoon ingredients C ;

[0011] S3: According to the texture component y of the signal T and cartoon ingredients C , the backward decomposition method is used for the signal impulse noise removal model to calculate the spectral sparse solution x after the signal impulse noise is removed i .

[0012] Furthermore, step S2 specifically includes the following steps:

[0013] S21: Use the forward decomposition method to obtain the texture component y of the signal after the impulse noise is removed T and cartoon ingredients C The solution model is:

[0014]

[0015] Among them, α 0 represents the fidelity balance parameter, α 1 and α 2 represents the balance parameter of the regularization term, Both represent Lp pseudo-norm, p 0 、p 1 、p 2 are the control parameters of the sparsity of sparse variables in the LP pseudo-norm, D(.) represents the first-order stationary frame wavelet positive transform, and m represents the mask vector;

[0016] S22: Using the alternating multiplier iteration method, introduce the intermediate auxiliary variable q 0 ,q 1 ,q 2 The corresponding Lagrange multiplier Secondary Penalty and the quadratic penalty coefficient λ 0 , 1 , 2 After that, the texture component y T and cartoon ingredients C The solution of q is converted into 0 ,q 1 ,q 2 , The solution is:

[0017]

[0018]

[0019] S23: Calculate texture component y through iterative training T and cartoon ingredients C .

[0020] Furthermore, in step S23, the texture component y is calculated by iterative training. T and cartoon ingredients C The specific process includes: initial setting y C ,y T ,q 0 ,q 1 ,q 2 , are all 0, set the number of iterations k = 0, the number of iterations threshold K; in each iteration, by 0 ,q 1 ,q 2 , The update to calculate the updated y C and T When the number of iterations k = K, stop the iteration and output y at this time C and T As the final texture component y after the impact noise is removed T and cartoon ingredients C .

[0021] Furthermore, q 0 ,q 1 ,q 2 , The update formulas are:

[0022]

[0023]

[0024]

[0025]

[0026]

[0027]

[0028] Wherein, the superscripts (k) and (k+1) represent the kth and k+1th iterations respectively, and γ represents the learning rate parameter.

[0029] Furthermore, step S3 specifically includes the following steps:

[0030] S31: The sparse spectrum solution x after the signal impulse noise is removed using the backward decomposition method i The solution model is:

[0031]

[0032] S32: Represented as sub-signal s i , introduce the intermediate variable z = x i Its dual variable Then the spectral sparse solution x i The augmented Lagrangian function of the solution model is:

[0033]

[0034] Among them, β represents the coefficient of the quadratic penalty term;

[0035] S33: Through iterative training, x i , z and Update to get the final spectral sparse solution x i .

[0036] Furthermore, the specific process of iterative training in step S33 is as follows: initially set x i ,z, are all 0, set the number of iterations k = 0, the number of iterations threshold K; in each iteration, according to the x before the iteration i ,z, Update the iterative x i ,z, When the number of iterations k = K, stop the iteration and output x at this time i As the final spectral sparse solution x i .

[0037] Furthermore, x i ,z, The update formulas are:

[0038]

[0039]

[0040]

[0041] Among them, shrink p represents the contraction operator, Θ H represents the conjugate transposed matrix of Θ.

[0042] Furthermore, at each iteration, x iAfter updating according to the update formula, it also needs to be centralized.

[0043] A signal robust sparse time-frequency analysis terminal device comprises a processor, a memory and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the above-mentioned method in an embodiment of the present invention when executing the computer program.

[0044] A computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps of the method described above in an embodiment of the present invention are implemented.

[0045] The present invention adopts the above technical solution and has the following beneficial effects:

[0046] (1) The strategy of “detection first, imaging later” is adopted. The amplitude characteristics of the impact noise are used to locate the “position information” of the impact noise in advance. Then, the “sparse prior” statistical characteristics of the noise are combined to effectively remove the noise.

[0047] (2) Morphological component analysis is introduced into the time-frequency analysis algorithm to decompose the signal into low-frequency cartoon components and high-frequency texture components. The frame wavelet regularization technology is used to reconstruct the low-frequency and high-frequency components of the signal in the frame wavelet transform domain, and sparse time-frequency imaging is performed on this basis.

[0048] (3) The forward-backward decomposition method and ADMM are combined to effectively solve the proposed model.

[0049] (4) In order to reduce the complexity of the algorithm, an optimization algorithm is proposed based on the unique matrix structure of the flat matrix in the model to accelerate the inversion operation in the algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 FIG. 4 is a schematic diagram of sliding window weighted sub-signals in Embodiment 1 of the present invention.

[0051] Figure 2 FIG. 1 is a schematic diagram of the first-order stationary frame wavelet transform and inverse transform in this embodiment, wherein: Figure 2 (a) is a schematic diagram of the first-order stationary frame wavelet forward transform. Figure 2 (b) is a schematic diagram of the first-order stationary frame wavelet inverse transform.

[0052] Figure 3 Schematic diagram of various norms in this embodiment is shown, where: Figure 3 (a) is a schematic diagram of the L2 norm contour line. Figure 3 (b) is a schematic diagram of the L1 norm contour line. Figure 3 (c) is a schematic diagram of the Lp pseudo-norm contour lines.

[0053] Figure 4Shown is a flow chart of Embodiment 1 of the present invention.

[0054] Figure 5 FIG. 4 shows the application of the method in this embodiment in the spectrum analysis of seismic signals, wherein: Figure 5 (a) is the seismic signal not contaminated by the impact signal. Figure 5 (b) is the seismic signal contaminated by the impact signal. Figure 5 (c) is the seismic signal recovered by the method of this embodiment, Figure 5 (d) is the sparse time-frequency distribution of the seismic signal without impact noise interference, Figure 5 (e) is the time-frequency distribution of the seismic signal disturbed by the impact noise. Figure 5 (f) is the robust time-frequency distribution obtained by the method of this embodiment.

[0055] Figure 6 FIG. 4 shows the test result of the method in this embodiment for a single component signal, wherein: Figure 6 (a) is the original signal, Figure 6 (b) is the signal interfered by impulse noise, Figure 6 (c) is the ideal time-frequency distribution, Figure 6 (d) is the result of direct time-frequency analysis of the interference signal. Figure 6 (e) is the time-frequency analysis result obtained by the method of this embodiment, Figure 6 (f) is the signal restored by the method of this embodiment, Figure 6 (g) is the low-frequency component restored by the method of this embodiment, Figure 6 (h) is the high frequency component restored by the method of this embodiment.

[0056] Figure 7 FIG. 4 shows the test results of the method in this embodiment for multi-component signals, wherein: Figure 7 (a) is the original signal, Figure 7 (b) is the signal interfered by impulse noise, Figure 7 (c) is the ideal time-frequency distribution, Figure 7 (d) is the result of direct time-frequency analysis of the interference signal. Figure 7 (e) is the time-frequency analysis result obtained by the method of this embodiment, Figure 7 (f) is the signal restored by the method of this embodiment, Figure 7 (g) is the low-frequency component restored by the method of this embodiment, Figure 7 (h) is the high frequency component restored by the method of this embodiment. DETAILED DESCRIPTION

[0057] To further illustrate various embodiments, the present invention provides drawings. These drawings are part of the disclosure of the present invention, which are mainly used to illustrate the embodiments and can be used in conjunction with the relevant descriptions in the specification to explain the operating principles of the embodiments. With reference to these contents, ordinary technicians in this field should be able to understand other possible implementations and advantages of the present invention.

[0058] The present invention will now be further described with reference to the accompanying drawings and specific implementation methods.

[0059] Embodiment 1:

[0060] First, preliminary knowledge related to this embodiment is introduced.

[0061] (1) Sparse time-frequency analysis model

[0062] Figure 1 The process of short-time Fourier transform weighting sub-signals using a sliding window is demonstrated. Figure 1 medium signal sub-signal Sliding Window The signal can be decomposed through a short-time sliding window to obtain the local time spectrum distribution of the signal.

[0063] Figure 1 In, order Represents the weighted sub-signal. The starting point of sparse time-frequency analysis is to find a sparse solution of the spectrum in the frequency domain. The spectrum satisfies the following formula:

[0064]

[0065] in, is the sparse transformation matrix, S = [I|O] is the truncation matrix, which is used to obtain the inversion signal The first M points of is the identity matrix, represents a matrix with all elements equal to zero, represents the Fourier transform matrix, represents the L2 norm, represents the Lp pseudo-norm, p is the control parameter of the sparsity of the sparse variables in the LP pseudo-norm, and μ represents the balance parameter.

[0066] It can be seen from formula (1) that the inverted time domain signal After truncation operation Indicates obtaining the first M points of the inverted time domain signal so that y i ≈Θx i , while using the sparse regularization term Characterize the sparsity of the spectrum.

[0067] (2) Morphological Component Analysis (MCA)

[0068] The basic idea of ​​morphological component analysis is to decompose the processed signal into cartoon components containing low-frequency information, texture components containing high-frequency information, and impact noise components.

[0069] (3) First-order stationary frame wavelet transform

[0070] The schematic diagram of the first-order stationary frame wavelet transform and its inverse transform is as follows Figure 2 shown. Figure 2 middle, represents a low-pass analysis filter, and is a high-pass analysis filter, represents a low-pass synthesis filter, and It indicates a high-pass integrated filter. From the schematic diagram of frame wavelet transform and inverse transform, it can be concluded that the frame wavelet transform and its inverse transform algorithm do not have the downsampling and upsampling operations of the Mallat algorithm, so there is no need to fill the data with zeros, and it has translation invariance. Compared with the traditional wavelet transform, the frame wavelet transform adds a high-pass filter, which can separate and process the signal more effectively.

[0071] (4) Lp pseudo-norm

[0072] Due to the presence of noise, the fidelity term There will be some interference, such as Figure 3 As shown by the dotted line in . Figure 3 (a) shows the intersection of the contour line of the L2 norm and the data fidelity term. Obviously, the intersection is not on the coordinate axis, which shows that the L2 norm is not very effective in promoting sparsity. Figure 3 As shown in (b), the contour lines based on the L1 norm intersect with the perturbed data fidelity term near the coordinate axis, indicating that the L1 norm has a stronger ability to promote sparsity than the L2 norm. However, the L1 norm is still susceptible to noise interference. Figure 3 As shown in (c), the contour lines of the Lp pseudo-norm intersect the data fidelity term at the point on the coordinate axis. It can be seen that the Lp pseudo-norm inherits the advantage of the L1 norm in promoting sparsity and is more robust to noise interference.

[0073] Based on the above preliminary knowledge, the embodiment of the present invention takes the sparse time-frequency analysis of seismic signals as an example and proposes a signal robust sparse time-frequency analysis method, such as Figure 4 As shown, the method comprises the following steps:

[0074] S1: Construct a signal impulse noise removal model based on morphological component analysis, sparse time-frequency analysis and frame wavelet transform:

[0075]

[0076] Among them, MCA(.) represents the morphological component analysis algorithm, y T Represents signal y n The texture component, y C Represents signal y n Cartoon composition, y iT Indicates that the signal y T The i-th sub-signal after segmentation, y iC Indicates that the signal y C The i-th sub-signal after segmentation.

[0077] S2: Use the forward decomposition method to calculate the texture component y of the signal after the impulse noise is removed. T and cartoon ingredients C .

[0078] In this embodiment, step S2 specifically includes the following steps:

[0079] S21: Use the forward decomposition method to obtain the texture component y of the signal after the impulse noise is removed T and cartoon ingredients C The solution model is:

[0080]

[0081] Among them, α 0 represents the fidelity balance parameter, α 1 and α 2 represents the balance parameter of the regularization term, Both represent Lp pseudo-norm, p 0 、p 1 、p 2 are all control parameters of the sparsity of sparse variables in the LP pseudo-norm, D(.) represents the first-order stationary frame wavelet positive transform, and m represents the mask vector.

[0082] S22: Using the alternating multiplier iteration method, introduce the intermediate auxiliary variable q 0 ,q 1 ,q 2 The corresponding Lagrange multiplier Secondary Penalty and the quadratic penalty coefficient λ 0 , 1 , 2 After that, the texture component y T and cartoon ingredients C The solution of q is converted into 0 ,q1 ,q 2 , The solution is to transform equation (3) into the following augmented Lagrangian function:

[0083]

[0084] To solve the above augmented Lagrangian function, it is necessary to solve the sub-problem of each variable separately.

[0085] (1)y C Solve the subproblem and fix other variables, then we can get:

[0086]

[0087] Square the above equation, then y C The sub-problem is transformed into:

[0088]

[0089] make have to:

[0090]

[0091] Arranged:

[0092]

[0093] Also because Then the above formula (8) can be rearranged as:

[0094]

[0095] Solved using the Conjugate Gradient Method (CGM) The CGM algorithm is shown in Algorithm 1 in Table 1.

[0096] Table 1

[0097]

[0098] (2)y T Sub-problem solving:

[0099]

[0100] With y C The sub-problem is solved similarly, and the matching method is adopted to obtain:

[0101]

[0102] Similarly, have to:

[0103]

[0104] Solving using the conjugate gradient method

[0105] (3)q 0 Sub-problem solving:

[0106]

[0107] Square the above formula to get:

[0108]

[0109] have to:

[0110]

[0111] (4)q 1 Sub-problem solving:

[0112]

[0113] After squaring, we get:

[0114]

[0115] have to:

[0116]

[0117] (5)q 2 Sub-problem solving:

[0118]

[0119] After squaring, we get:

[0120]

[0121] have to:

[0122]

[0123] (6) Sub-problem solving:

[0124]

[0125] Using the gradient ascent method, we get:

[0126]

[0127] (7) Sub-problem solving:

[0128]

[0129] Using the gradient ascent method, we get:

[0130]

[0131] (8) Sub-problem solving:

[0132]

[0133] Using the gradient ascent method, we get:

[0134]

[0135] S23: Calculate texture component y through iterative training T and cartoon ingredients C .

[0136] The overall process of the iterative training process in this embodiment is as follows:

[0137] S231: Initial setting C ,y T ,q 0 ,q 1 ,q 2 , All are 0; set the number of iterations k = 0, the number of iterations threshold K;

[0138] S232: Solve equations (9) and (12) respectively according to the conjugate gradient algorithm, and update the cartoon part of the signal at the k+1th iteration and texture part

[0139] S233: Update the intermediate auxiliary variables at the k+1th iteration according to equations (15), (18), and (21) respectively

[0140] S234: Update the intermediate auxiliary variables at the k+1th iteration according to equations (23), (25), and (27) respectively The corresponding Lagrange multiplier

[0141] S235: Determine whether k=K. If yes, proceed to S236; otherwise, increment k by 1 and return to S232;

[0142] S236: Output the cartoon part of the signal at the k+1th iteration and texture part As the final texture component y after the impact noise is removed T and cartoon ingredients C.

[0143] S3: According to the texture component y of the signal T and cartoon ingredients C , the backward decomposition method is used for the signal impulse noise removal model to calculate the spectral sparse solution x after the signal impulse noise is removed i .

[0144] In this embodiment, step S3 specifically includes the following steps:

[0145] S31: The sparse spectrum solution x after the signal impulse noise is removed using the backward decomposition method i The solution model is:

[0146]

[0147] S32: Represented as sub-signal s i , introduce the intermediate variable z = x i Its dual variable Then the spectral sparse solution x i The augmented Lagrangian function of the solution model is:

[0148]

[0149] Among them, β represents the coefficient of the quadratic penalty term.

[0150] To solve the above augmented Lagrangian function, it is necessary to solve the sub-problem of each variable separately.

[0151] (1) Fix other variables and obtain x by formula i The objective function of the subproblem is:

[0152]

[0153] The solution is:

[0154]

[0155] in, are all unit matrices, Θ H represents the conjugate transposed matrix of Θ.

[0156] Furthermore, the calculated spectrum needs to be centralized, namely:

[0157]

[0158] Among them, fftshif represents the centering operator, which swaps the first half and the second half of the vector.

[0159] (2) The objective function of the z subproblem is:

[0160]

[0161] The closed-form solution of formula (33) is:

[0162]

[0163] in, Denotes the Lp contraction operator.

[0164] (3) The objective function of the subproblem is:

[0165]

[0166] Then we have:

[0167]

[0168] S33: Through iterative training, x i , z and Update to get the final spectral sparse solution x i .

[0169] The overall process of iterative training in this embodiment is as follows:

[0170] S331: Initial setting x i ,z, All are 0; set the number of iterations k = 0, the number of iterations threshold K;

[0171] S332: Update the spectral sparse solution at the k+1th iteration according to equation (32)

[0172] S333: Update the intermediate variables at the k+1th iteration according to formula (34)

[0173] S334: Update the dual variable of the intermediate variable at the k+1th iteration according to formula (36)

[0174] S335: Determine whether k=K. If yes, proceed to S336; otherwise, increment k by 1 and return to S332;

[0175] S336: Output the spectral sparse solution at the k+1th iteration As the final spectral sparse solution x i .

[0176] Experimental analysis

[0177] In this embodiment, actual seismic signal data is selected for experiment to reflect the correctness of the proposed method. The experimental results are as follows: Figure 5 shown. Figure 5 (b) Subjected to 20% impact noise interference, Figure 5 (c) It can be seen that this embodiment proposes to effectively restore the time domain information of the seismic signal. Figure 5 (e) It can be seen that if the impulse noise is not suppressed, the obtained time-frequency diagram will be severely interfered, and the true spectrum of the seismic signal cannot be effectively obtained. The time-frequency diagram obtained by the robust time-frequency analysis method proposed in this embodiment is basically consistent with the time-frequency diagram of the seismic signal without impulse noise interference. It can be seen that the proposed method effectively suppresses the interference spectrum brought by the impulse noise to the time-frequency diagram.

[0178] In addition, this embodiment is also tested on different theoretical signals, and a series of indicators are used to objectively evaluate and compare the method proposed in this article with other time-frequency analysis methods.

[0179] (1) Single-component signal time-frequency imaging

[0180] A single-component sinusoidal signal y=0.8sin(πt) is used as a test signal. To verify the effectiveness of the proposed method, a 10% impulse signal is applied to the test signal to interfere with the test signal. Then, the method of this embodiment is used to perform time-frequency imaging on the interfered signal. Figure 6 shown.

[0181] from Figure 6 It can be seen that when the signal is contaminated by impulse noise, a large number of interference frequencies will appear when the contaminated signal is directly subjected to time-frequency analysis. The robust time-frequency analysis algorithm proposed in this embodiment can accurately obtain the local spectrum of the signal, and the proposed MCA framework can effectively remove the interference of impulse noise.

[0182] (2) Time-frequency imaging of multi-component signals

[0183] The multi-component signal y=0.5sin(πt)+0.25sin(8πt) is used as the test signal, and a 10% impulse signal is used to interfere with the test signal. Then, the method proposed in this embodiment is used to perform time-frequency imaging on the interfered signal. Figure 7 shown.

[0184] from Figure 7 It can be seen that the proposed MCA framework can better separate the low-frequency components and high-frequency components, and restore the time domain signal while removing the impulse noise. At the same time, the proposed method can obtain a robust time-frequency distribution, which is close to the standard time-frequency distribution.

[0185] The embodiment of the present invention introduces a morphological component analysis algorithm to decompose the signal to be processed into a low-frequency cartoon component, a high-frequency texture component and a noise component. In addition, considering that the spectrum of the impact noise also has the characteristics of sparsity to a certain extent, the sparse time-frequency analysis method cannot effectively distinguish the signal component from the noise component. Noise is random and lacks good structural similarity compared to the effective signal, so it cannot be sparsely represented by a dictionary composed of atoms such as wavelets and frame wavelets. Taking this characteristic of noise into consideration, the embodiment of the present invention intends to further introduce a stationary frame wavelet regularization term on the basis of morphological component analysis to fully explore the differences between the effective components of the signal and the noise components, so as to achieve the purpose of suppressing noise and highlighting signals.

[0186] The embodiment of the present invention uses the alternating multiplier iteration method to decompose the proposed model into several simple sub-problems for solution. Finally, the effectiveness of the proposed method is reflected by the signal time-frequency imaging under the Gaussian noise background. From the subsequent experiments, it can be seen that this processing method will effectively suppress the noise spectrum and protect the frequency components of the signal.

[0187] Embodiment 2:

[0188] The present invention also provides a signal robust sparse time-frequency analysis terminal device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps in the above-mentioned method embodiment of embodiment 1 of the present invention when executing the computer program.

[0189] Further, as an executable solution, the signal robust sparse time-frequency analysis terminal device can be a computing device such as a desktop computer, a notebook, a PDA, and a cloud server. The signal robust sparse time-frequency analysis terminal device may include, but is not limited to, a processor and a memory. Those skilled in the art can understand that the composition structure of the above-mentioned signal robust sparse time-frequency analysis terminal device is only an example of a signal robust sparse time-frequency analysis terminal device, and does not constitute a limitation on the signal robust sparse time-frequency analysis terminal device. It may include more or less components than the above, or a combination of certain components, or different components. For example, the signal robust sparse time-frequency analysis terminal device may also include input and output devices, network access devices, buses, etc., and the embodiments of the present invention do not limit this.

[0190] Further, as an executable solution, the processor may be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor or any conventional processor, etc. The processor is the control center of the signal robust sparse time-frequency analysis terminal device, and uses various interfaces and lines to connect the various parts of the entire signal robust sparse time-frequency analysis terminal device.

[0191] The memory can be used to store the computer program and / or module, and the processor realizes various functions of the signal robust sparse time-frequency analysis terminal device by running or executing the computer program and / or module stored in the memory, and calling the data stored in the memory. The memory can mainly include a program storage area and a data storage area, wherein the program storage area can store an operating system and at least one application required for a function; the data storage area can store data created according to the use of the mobile phone, etc. In addition, the memory can include a high-speed random access memory, and can also include a non-volatile memory, such as a hard disk, a memory, a plug-in hard disk, a smart memory card (Smart Media Card, SMC), a secure digital (Secure Digital, SD) card, a flash card (Flash Card), at least one disk storage device, a flash memory device, or other volatile solid-state storage devices.

[0192] The present invention also provides a computer-readable storage medium, wherein the computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps of the above method in the embodiment of the present invention are implemented.

[0193] If the module / unit integrated in the signal robust sparse time-frequency analysis terminal device is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the present invention implements all or part of the processes in the above-mentioned embodiment method, and can also be completed by instructing the relevant hardware through a computer program. The computer program can be stored in a computer-readable storage medium, and the computer program can implement the steps of the above-mentioned various method embodiments when executed by the processor. Among them, the computer program includes computer program code, and the computer program code can be in source code form, object code form, executable file or some intermediate form. The computer-readable medium may include: any entity or device capable of carrying the computer program code, recording medium, U disk, mobile hard disk, disk, optical disk, computer memory, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory) and software distribution medium, etc.

[0194] Although the present invention has been specifically shown and described in conjunction with the preferred embodiments, it should be understood by those skilled in the art that various changes may be made to the present invention in form and details without departing from the spirit and scope of the present invention as defined by the appended claims, all of which are within the scope of protection of the present invention.

Claims

1. A robust sparse time-frequency analysis method for signals, It is characterized in that The following steps are involved: S1: Construct a signal impulse noise removal model based on morphological component analysis, sparse time-frequency analysis and frame wavelet transform: Among them, MCA(.) represents the morphological component analysis algorithm, y T Represents signal y n The texture component, y C Represents signal y n Cartoon composition, y iT Indicates that the signal y T The i-th sub-signal after segmentation, y iC Indicates that the signal y C The i-th sub-signal after segmentation, g represents the sliding window, Θ = SF -1 represents a sparse transformation matrix, S = [I|O] represents a truncated matrix, I represents an identity matrix, O represents a matrix with all elements zero, and F represents a Fourier transform matrix. represents the L2 norm, represents the Lp pseudo-norm, p is the control parameter of the sparsity of the sparse variables in the LP pseudo-norm, x i represents the sparse solution of the signal spectrum, μ represents the balance parameter; S2: Use the forward decomposition method to calculate the texture component y of the signal after the impulse noise is removed. T and cartoon ingredients C ; Specifically including the following steps: S21: Use the forward decomposition method to obtain the texture component y of the signal after the impulse noise is removed T and cartoon ingredients C The solution model is: Among them, α 0 represents the balance parameter of the fidelity term, α 1 and α 2 represent the balance parameters of the regularization term, both represent the Lp pseudo-norm, p 0 、p 1 、p 2 are all control parameters for the sparsity degree of the sparse variables in the LP pseudo-norm. D(.) represents the first-order stationary frame wavelet forward transform, and m represents the mask vector; S22: Introduce intermediate auxiliary variables q using the alternating direction method of multipliers 0 and q 1 and q 2 and their corresponding Lagrange multipliers the quadratic penalty term and the quadratic penalty coefficient λ 0 and λ 1 and λ 2 After that, the solution of the texture component y T and the cartoon component y C is transformed into the solution of q 0 and q 1 and q 2 and That is: Wherein, the superscripts (k) and (k+1) represent the kth and k+1th iterations, respectively; S23: Calculate texture component y through iterative training T and cartoon ingredients C ; S3: According to the texture component y of the signal T and cartoon ingredients C , the backward decomposition method is used for the signal impulse noise removal model to calculate the spectral sparse solution x after the signal impulse noise is removed i ; Specifically including the following steps: S31: The sparse spectrum solution x after the signal impulse noise is removed using the backward decomposition method i The solution model is: S32: Represented as sub-signal s i , introduce the intermediate variable z = x i Its dual variable Then the spectral sparse solution x i The augmented Lagrangian function of the solution model is: Among them, β represents the coefficient of the quadratic penalty term; S33: Through iterative training, x i , z and Update to get the final spectral sparse solution x i .

2. The signal robust sparse time-frequency analysis method according to claim 1, Features: In step S23, the texture component y is calculated by iterative training T and cartoon ingredients C The specific process includes: initial setting y C ,y T ,q 0 ,q 1 ,q 2 , are all 0, set the number of iterations k = 0, the number of iterations threshold K; in each iteration, by 0 ,q 1 ,q 2 , The update to calculate the updated y C and T When the number of iterations k = K, stop the iteration and output y at this time C and T As the final texture component y after the impact noise is removed T and cartoon ingredients C .

3. The signal robust sparse time-frequency analysis method according to claim 2, Features: q 0 ,q 1 ,q 2 , The update formulas are: Among them, γ represents the learning rate parameter.

4. The signal robust sparse time-frequency analysis method according to claim 1, Features: The specific process of iterative training in step S33 is as follows: Initially set x i ,z, are all 0, set the number of iterations k = 0, the number of iterations threshold K; in each iteration, according to the x before the iteration i ,z, Update the iterative x i ,z, When the number of iterations k = K, stop the iteration and output x at this time i As the final spectral sparse solution x i .

5. The signal robust sparse time-frequency analysis method according to claim 4, Features: x i ,z, The update formulas are: Among them, shrink p represents the contraction operator, Θ H represents the conjugate transposed matrix of Θ.

6. The signal robust sparse time-frequency analysis method according to claim 5, Features: At each iteration, x i After updating according to the update formula, it also needs to be centralized.

7. A signal robust sparse time-frequency analysis terminal device, Features: The method comprises a processor, a memory and a computer program stored in the memory and running on the processor, wherein the processor implements the steps of the method according to any one of claims 1 to 6 when executing the computer program.

8. A computer-readable storage medium storing a computer program. Features: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 6 are implemented.

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