A signal sparse decomposition and reconstruction system and method based on a learnable fractional wavelet transform

Abstract

The application provides a signal sparse decomposition and reconstruction system and method based on a learnable fractional wavelet transform, constructs training data samples; training signals s(t) are collected for an application scene as training data samples of the network; a learnable fractional wavelet transform deep convolution network is trained; signals to be sparsely decomposed and reconstructed in S1 training data samples are collected; the signals to be sparsely decomposed and reconstructed collected by S1 are input into the S2 trained learnable fractional wavelet transform deep convolution network to be sparsely decomposed and reconstructed; finally, a reconstructed signal is output; preset filter parameters in a convolution cascaded decomposition algorithm and a synthesis algorithm of the fractional wavelet transform are replaced by learnable parameters, and the learnable parameters are updated through a back propagation algorithm, so that the target signal can be sparsely decomposed and reconstructed.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of signal and information processing, and particularly relates to a signal sparse decomposition and reconstruction system and method based on a learnable fractional wavelet transform. BACKGROUND

[0002] In practical applications, the signals encountered are usually non-stationary signals, such as speech, radar signals, biomedical signals, etc. The change of the spectrum with time is a typical characteristic of non-stationary signals. The traditional Fourier transform lays the foundation for the analysis of stationary signals, and is powerless for non-stationary signals.

[0003] In order to process non-stationary signals, a series of new signal processing tools have emerged on the basis of the Fourier transform. Among them, the fractional wavelet transform, as a generalized form of the traditional wavelet transform, can extend the signal analysis method of the wavelet transform in the time-frequency joint domain to the general time-fractional frequency joint domain.

[0004] The fractional wavelet transform not only inherits all the properties of the traditional wavelet transform, but also has unique characteristics that the traditional wavelet transform does not have, and can explain phenomena that the traditional wavelet transform cannot explain. The fractional wavelet transform has a free parameter of rotation angle, and when the rotation angle gradually changes from zero to ninety degrees, it can show the dynamic characteristics of the signal changing from the time domain to the time-frequency joint domain. This provides a powerful tool for fine characterization of the time-varying spectral characteristics of non-stationary signals.

[0005] Figure 1 And Figure 2 The principle diagrams of the decomposition algorithm and the reconstruction algorithm of the fractional wavelet transform are given respectively.

[0006] Although the fractional wavelet transform can perform sparse decomposition and reconstruction of signals to some extent, the fractional wavelet basis function needs to be determined manually for different signal samples, and cannot best match the data to be analyzed. In addition, the selection and optimization of the fractional wavelet transform basis function currently relies on experience and cannot adaptively change according to the changes of the data. SUMMARY

[0007] In view of the above problems, the present application proposes a signal sparse decomposition and reconstruction system and method based on a learnable fractional wavelet transform to solve the phenomenon that the basis function of the fractional wavelet transform needs to be set manually according to experience rather than adaptively adjusted according to the characteristics and corresponding indicators of the input signal. The preset filter parameters in the convolution cascade decomposition algorithm and synthesis algorithm of the fractional wavelet transform are replaced by learnable parameters, which can be updated through the back propagation algorithm, and the sparse decomposition and reconstruction of the target signal can be realized.

[0008] The application realizes the technical solutions in the following aspects:

[0009] A signal sparse decomposition and reconstruction method based on a learnable fractional wavelet transform:

[0010] The method specifically comprises the following steps:

[0011] S1, constructing a training data sample; collecting a training signal s(t) for an application scenario as a training data sample of the network;

[0012] S2, training a learnable fractional wavelet transform deep convolution network;

[0013] S3, collecting a signal to be sparsely decomposed and reconstructed in the training data sample of S1

[0014] S4, collecting the signal to be sparsely decomposed and reconstructed in S1 inputting the learnable fractional wavelet transform deep convolution network trained in S2 for sparse decomposition and reconstruction;

[0015] S5, outputting a reconstructed signal.

[0016] Further,

[0017] In S2, the following steps are included:

[0018] S21, initializing the angle parameter α, the decomposition layer number L and the learnable parameters in the network:

[0019] S22, training the learnable parameters in the network in S1;

[0020] Let v represent the iteration number, and start the loop iteration from v = 1;

[0021] S23, decomposing the input signal to obtain the required decomposition coefficients W = [c L ,d1,d2,…,d L ]:

[0022] S24, using the decomposition coefficients obtained in S23 to reconstruct the signal to obtain a reconstructed signal

[0023] S25, according to the decomposition coefficients output in S23 and the reconstructed signal output in S24, calculating the current objective function value through an objective function, and the objective function is

[0024]

[0025] wherein, all the learnable parameters in the network;

[0026] S26, updating all learnable parameters according to formula (5) according to the value of the objective function;

[0027]

[0028] where v is the current iteration number, represents the i-th learnable parameter in the v-th iteration, μ is the learning rate, the commonly used value is 0.001, λ is the momentum parameter, the commonly used value is 0.9, used to adjust the influence of the gradient generated by the last iteration on the gradient generated by the current iteration, is the objective function the gradient value of ;

[0029] S27, judging whether the maximum iteration number is reached, if yes, the training is completed, otherwise, returning to S23 to continue training.

[0030] Further,

[0031] In S21, the following steps are specifically included:

[0032] S211, initializing the angle parameter α of the network according to the time-frequency characteristics of the input sample;

[0033] S212, initializing the decomposition layer number L in the network according to the length of the training sample and the requirement of the application scenario;

[0034] S213, initializing all convolution kernels in the network, initializing the initial value of the convolution kernel according to the characteristics of the signal, and recommending the initial value to be the scale filter and wavelet filter corresponding to the commonly used wavelet function,

[0035] The commonly used wavelets include Morlet wavelet, Mexoican hat wavelet, and Daubechies series wavelet.

[0036] Further,

[0037] In S23, the following steps are specifically included:

[0038] S231, initializing the input signal, initializing the input in the network using formula ;

[0039] Initializing the layer number L=0, using c 0,n,α to represent the input signal s[n];

[0040] S232, calculating the scale coefficient and wavelet coefficient obtained by the current layer decomposition using formula (1) and formula (2);

[0041] ​

[0042]

[0043] S233, if the decomposition layer has reached the requirement, the decomposition is ended to obtain all the decomposition coefficients W = [c L ,d1,d2,…,d L ];

[0044] Otherwise, return to S232 to output the scale coefficient of the current layer as the input of the next layer.

[0045] Further, in S24, the following steps are specifically included:

[0046] S241, read the decomposition coefficient W = [c L ,d1,d2,…,d L ] obtained in S233;

[0047] S242, use formula (3) to reconstruct;

[0048]

[0049] S243, if the reconstruction is completed, the final output is the reconstructed signal

[0050] Otherwise, use the wavelet coefficient corresponding to the scale coefficient and the decomposition coefficient obtained by the current layer reconstruction as the input of the next layer, and return to S242 to continue the reconstruction.

[0051] A signal sparse decomposition and reconstruction system based on a learnable fractional order wavelet transform:

[0052] The system comprises a data sample training module, a convolution network training module, a signal acquisition module, a sparse decomposition and reconstruction module, and a reconstructed signal output module.

[0053] The data sample training module is configured to construct training data samples; and collect training signals s(t) as the training data samples of the network according to the application scenario.

[0054] The convolution network training module is configured to train a learnable fractional order wavelet transform deep convolution network.

[0055] The signal acquisition module is configured to acquire the signal to be sparsely decomposed and reconstructed in the training data samples.

[0056] The sparse decomposition and reconstruction module is configured to sparsely decompose and reconstruct the signal to be sparsely decomposed and reconstructed acquired by the data sample training module. The trained learnable fractional wavelet transform deep convolutional network performs sparse decomposition and reconstruction.

[0057] The reconstructed signal output module is configured to output a reconstructed signal.

[0058] An electronic device includes a memory storing a computer program and a processor that implements the steps of the above method when executing the computer program.

[0059] A computer-readable storage medium for storing computer instructions that are executed by a processor to implement the steps of the above method.

[0060] Advantages of the present application

[0061] The basis function of the learnable fractional wavelet transform of the present application is updated according to the gradient obtained by the back propagation algorithm of the convolutional neural network based on the set target function, which solves the problem that the basis function of the fractional wavelet transform needs to be set artificially according to experience rather than being adjusted adaptively according to the characteristics of the input signal and the corresponding indicators.

[0062] The learnable fractional wavelet transform of the present application is a completely data-driven signal sparse decomposition and reconstruction method, which can improve the sparsity of signal decomposition coefficients and thus reduce the data volume and improve the computational efficiency of the algorithm while ensuring complete reconstruction of the signal compared with the conventional fractional wavelet transform. BRIEF DESCRIPTION OF DRAWINGS

[0063] Figure 1 The figure is a principle block diagram of the fractional wavelet transform decomposition algorithm.

[0064] Figure 2 The figure is a principle block diagram of the fractional wavelet transform synthesis algorithm.

[0065] Figure 3 The figure is a structure block diagram of the learnable fractional wavelet transform deep convolutional neural network.

[0066] Figure 4 The figure is a step block diagram of the signal sparse decomposition and reconstruction method of the present application.

[0067] Figure 5 The figure is a step block diagram of training the learnable fractional wavelet transform deep convolutional neural network.

[0068] Figure 6 The figure is a step block diagram of the step of training the learnable fractional wavelet transform deep convolutional neural network.

[0069] Figure 7A step block diagram for signal reconstruction in the steps of training the learnable fractional wavelet transform deep convolutional neural network;

[0070] Figure 8 A time domain waveform of the training sample;

[0071] Figure 9 A fractional spectrum of the original signal at α = π / 2;

[0072] Figure 10 A comparison chart of the reconstructed signal obtained by the trained learnable fractional wavelet transform deep convolutional neural network and the original signal. DETAILED DESCRIPTION

[0073] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative work fall within the scope of protection of the present application.

[0074] In combination Figures 1 to 10 .

[0075] To simplify the analysis, first introduce the definition of fractional wavelet transform. For any energy-limited signal f(t) ∈ L 2 (R), the fractional wavelet transform is defined as

[0076]

[0077] In the formula, the scale parameter a and the translation parameter b satisfy: a ∈ R + , b ∈ R. The expression of the kernel function ψ α,a,b (t) is:

[0078]

[0079] In particular, when the angle α = π / 2, the fractional wavelet transform degenerates into the traditional wavelet transform.

[0080] For numerical calculation and simplifying theoretical analysis, it is usually necessary to discretize the scale parameter and the translation parameter, generally taking a = 2 -k , b = n2 -k , so that the kernel function of the fractional wavelet transform becomes

[0081]

[0082] For a given fractional scale function φ(t), denote its corresponding orthogonal fractional wavelet function as ψ(t), and denote the kernel function generated by the fractional wavelet function as ψ k,n,α(t) Fractional wavelet subspace of frame Let

[0083]

[0084] Similarly, let

[0085]

[0086] Fractional scaling subspace of frame Let

[0087]

[0088] For simplicity, let According to the theory of fractional wavelet transform, let 2 The orthogonal fractional multi-resolution analysis of L The fractional scaling equation and the fractional wavelet equation are respectively

[0089]

[0090] where the coefficients h α [n]∈l 2 (Z) and g α [n]∈l 2 (Z) satisfy

[0091]

[0092] For any signal f(t)∈L 2 (R), introduce the notation

[0093]

[0094] are called the fractional scaling coefficients and the fractional wavelet coefficients of the signal f(t) respectively.

[0095] According to the orthogonal direct sum decomposition relation of the fractional scaling subspace and the fractional wavelet subspace

[0096]

[0097] It can be obtained that

[0098]

[0099] If the coefficients {c k,n,α ,k∈Z} are known, the algorithm for calculating the coefficients {c k-1,n,α ,k∈Z} and {d k-1,n,α ,k∈Z} is called the fractional wavelet transform decomposition algorithm, that is

[0100]

[0101]

[0102] For the starting point c of the decomposition algorithm k,n,α , we need to initialize as follows:

[0103]

[0104] where s(t) is the original signal to be decomposed.

[0105] If the coefficients {c k-1,n,α ,k∈Z} and {d k-1,n,α ,k∈Z} are known, the algorithm for calculating the coefficients {c k,n,α ,k∈Z} is called the synthesis algorithm of the fractional wavelet transform, that is,

[0106]

[0107] A signal sparse decomposition and reconstruction method based on a learnable fractional wavelet transform:

[0108] The method specifically comprises the following steps:

[0109] S1, constructing a training data sample; collecting a training signal s(t) for an application scenario as a training data sample of the network;

[0110] S2, training a learnable fractional wavelet transform deep convolutional network as shown in Figure 3 .

[0111] S21, initializing the angle parameter α, the decomposition layer number L and the learnable parameters in the network:

[0112] S21 specifically comprises the following steps:

[0113] S211, initializing the angle parameter α of the network according to the time-frequency characteristics of the input sample;

[0114] S212, initializing the decomposition layer number L in the network according to the length of the training sample and the requirements of the application scenario;

[0115] S213, initializing all the convolution kernels in the network, and setting the initial values of the convolution kernels according to the characteristics of the signal, and the recommended initial values are scale filters and wavelet filters corresponding to commonly used wavelet functions,

[0116] The commonly used wavelets are Morlet wavelets, Mexoican hat wavelets and Daubechies series wavelets.

[0117] S22, training the learnable parameters in the network in S1;

[0118] Let v represent the iteration number, and start the loop iteration from v = 1;

[0119] S23, decompose the input signal to obtain the required decomposition coefficients W = [c L ,d1,d2,…,d L ] :

[0120] S231, initialize the input signal, and use the formula to initialize the input in the network;

[0121] Initialize the layer number L = 0, and let c 0,n,α represent the input signal s[n];

[0122] S232, use formula (1) and formula (2) to calculate the scale coefficients and wavelet coefficients obtained by decomposing the current layer;

[0123]

[0124]

[0125] S233, if the decomposition layer number has reached the required number, the decomposition is completed to obtain all the decomposition coefficients W = [c L ,d1,d2,…,d L ];

[0126] Otherwise, return to S232 to use the scale coefficients output by the current layer as the input of the next layer.

[0127] S24, use the decomposition coefficients obtained in S23 to reconstruct the signal to obtain the reconstructed signal

[0128] S241, read the decomposition coefficients W = [c L ,d1,d2,…,d L ] obtained in S233;

[0129] S242, use formula (3) to reconstruct;

[0130]

[0131] S243, if the reconstruction is completed, the final output is the reconstructed signal

[0132] Otherwise, use the wavelet coefficients corresponding to the scale coefficients and decomposition coefficients obtained by the current layer reconstruction as the input of the next layer, and return to S242 to continue the reconstruction.​

[0133] S25, calculating a current objective function value by an objective function according to the decomposition coefficient output in S23 and the reconstructed signal output in S24, the objective function being

[0134]

[0135] wherein, is all the learnable parameters in the network;

[0136] S26, updating all the learnable parameters according to formula (5) according to the value of the objective function;

[0137]

[0138] wherein, v is the current iteration number, represents the i-th learnable parameter in the v-th iteration, μ is the learning rate, the commonly used value is 0.001, λ is the momentum parameter, the commonly used value is 0.9, used to adjust the influence of the gradient generated by the last iteration on the gradient generated by the current iteration, is the objective function the gradient value of ;

[0139] S27, judging whether the maximum iteration number is reached, if yes, the training is completed, otherwise, returning to S23 to continue the training.

[0140] S3, collecting the signal to be sparsely decomposed and reconstructed in the training data sample of S1

[0141] S4, sparsely decomposing and reconstructing the signal to be sparsely decomposed and reconstructed collected in S1 inputting the learned fractional order wavelet transform deep convolution network into the trained learnable fractional order wavelet transform deep convolution network for sparse decomposition and reconstruction;

[0142] S5, outputting the reconstructed signal.

[0143] A signal sparse decomposition and reconstruction system based on a learnable fractional order wavelet transform:

[0144] The system comprises a data sample training module, a convolution network training module, a signal collecting module, a sparse decomposition and reconstruction module and a reconstructed signal output module.

[0145] The data sample training module is used to construct a training data sample; and a training signal s(t) is collected as the training data sample of the network for an application scenario.

[0146] The convolution network training module is used to train a learnable fractional order wavelet transform deep convolution network.

[0147] The signal collection module is configured to collect a signal to be sparsely decomposed and reconstructed in a training data sample

[0148] The sparse decomposition and reconstruction module is configured to sparsely decompose and reconstruct the signal to be sparsely decomposed and reconstructed collected by the data sample training module The learned fractional wavelet transform deep convolutional network trained by the input convolutional network training module is used for sparse decomposition and reconstruction.

[0149] The reconstructed signal output module is configured to output the reconstructed signal.

[0150] An electronic device includes a memory and a processor, the memory stores a computer program, and the processor implements the steps of the above method when executing the computer program.

[0151] A computer readable storage medium for storing computer instructions, the computer instructions are executed by a processor to implement the steps of the above method.

[0152] The memory in the embodiments of the present application can be a volatile memory or a non-volatile memory, or can include both volatile and non-volatile memories. Among them, the non-volatile memory can be a read only memory (ROM), a programmable ROM (PROM), an erasable programmable ROM (EPROM), an electrically EPROM (EEPROM), or a flash memory. The volatile memory can be a random access memory (RAM) used as an external cache. By way of example, but not limitation, many forms of RAM are available, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDR SDRAM), enhanced SDRAM (ESDRAM), synchlink DRAM (SLDRAM), and direct rambus RAM (DR RAM). It should be noted that the memory of the method described in the present application is intended to include, but not limited to, these and any other suitable types of memory.

[0153] In the above embodiments, all or part of the method can be implemented by software, hardware, firmware or any combination thereof. When implemented by software, all or part of the method can be implemented in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of the present application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable devices. The computer instructions can be stored in a computer-readable storage medium or transferred from one computer-readable storage medium to another computer-readable storage medium, for example, the computer instructions can be transferred from one website, computer, server or data center to another website, computer, server or data center through wired, such as coaxial cable, optical fiber, digital subscriber line (DSL) or wireless, such as infrared, wireless, microwave, etc. The computer-readable storage medium can be any available medium that can be accessed by a computer or a data storage device such as a server, data center, etc. integrated with one or more available media. The available media can be magnetic media, such as floppy disks, hard disks, magnetic tapes, optical media, such as digital video discs (DVD), or semiconductor media, such as solid state discs (SSD), etc.

[0154] In the implementation process, each step of the above method can be completed by integrated logic circuit of hardware in the processor or instruction in the form of software. The steps of the method disclosed in the embodiments of the present application can be directly embodied as hardware processor execution or combined execution by hardware and software modules in the processor. The software module can be located in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, register or other mature storage medium in the art. The storage medium is located in the memory, and the processor reads the information in the memory and combines the hardware to complete the steps of the above method. To avoid repetition, it will not be described in detail here.

[0155] It should be noted that the processor in the embodiments of the present application can be an integrated circuit chip with signal processing capability. In the implementation process, each step of the method embodiments can be completed by integrated logic circuits or instructions in the form of software in the processor. The processor mentioned above can be a general processor, a digital signal processor DSP, an application specific integrated circuit ASIC, a field programmable gate array FPGA or other programmable logic devices, discrete gates or transistor logic devices, discrete hardware components. The disclosed methods, steps and logic block diagrams in the embodiments of the present application can be implemented or executed. The general processor can be a microprocessor or the processor can be any conventional processor. The steps of the method disclosed in combination with the embodiments of the present application can be directly embodied as hardware code processor execution completion, or executed by hardware and software module combination in the code processor. The software module can be located in the random access memory, the flash memory, the read only memory, the programmable read only memory or the electrically erasable programmable memory, the register or other mature storage medium in the art. The storage medium is located in the memory, and the processor reads the information in the memory, and combines the hardware to complete the steps of the above method.

[0156] The above describes the signal sparse decomposition and reconstruction system and method based on the learnable fractional wavelet transform in detail, and the principle and implementation of the present application are described. The above embodiment is only used to help understand the method and core idea of the present application; at the same time, for the general skilled person in the art, according to the idea of the present application, the specific implementation and application range will be changed, and the above description should not be understood as the limitation of the present application.

Claims

1.A method for signal sparse decomposition and reconstruction based on a learnable fractional wavelet transform, characterized in that the method comprises the following steps: S2, training a learnable fractional wavelet transform deep convolutional network; S1, constructing a training data sample; collecting a training signal for an application scenario as a training data sample of the network; S2 comprises the following steps: S25, calculating a current objective function value by an objective function according to the decomposition coefficients output in S23 and the reconstructed signal output in S24, the objective function being S21, angle parameters in the network , decomposition layer number and learnable parameters initialization: S22, learning parameters in the network in S1 are trained; With representing the number of iterations, from start loop iteration; S23, decompose the input signal to obtain the required decomposition coefficients : S24, using the decomposition coefficients obtained in S23 to perform signal reconstruction to obtain a reconstructed signal : S26, updating all learnable parameters according to formula (5) according to the value of the objective function; (4) wherein, are all the learnable parameters in the network; S27, determining whether a maximum number of iterations is reached, if yes, the training is completed, otherwise, returning to S23 for continuing the training; (5) wherein, is the current iteration number, represents the th learnable parameter in the th iteration, is the learning rate, a common value is 0.001, is the momentum parameter, a common value is 0.9, used to adjust the impact of the gradient produced by the last iteration on the gradient produced by the current iteration, is the gradient value of the objective function with respect to ; S5, outputting the reconstructed signal. S3, collecting the signal to be sparsely decomposed and reconstructed in the training data sample S1 ; S4, sparse decomposition and reconstruction of the signal to be collected in S1 input S2 the trained learnable fractional wavelet transform deep convolutional network for sparse decomposition and reconstruction; 2.The method according to claim 1, characterized in that S21 comprises the following steps: The commonly used wavelets include Morlet wavelet, Mexoican hat wavelet and Daubechies series wavelet. 3.The method according to claim 2, characterized in that S23 comprises the following steps: S211. Initialize the angle parameter of the network according to the time-frequency characteristics of the input sample ; S212, initialize the number of decomposition layers in the network according to the length of the training sample and the requirement of the application scenario ; S213、all the convolution kernels in the network are initialized Initialization is performed, and the initial value of the convolution kernel is intuitively set according to the characteristics of the signal. The recommended initial value is the scale filter and wavelet filter corresponding to the commonly used wavelet function. S232, calculating the scale coefficients and the wavelet coefficients obtained by the decomposition of the current layer using formula (1) and formula (2); Otherwise, returning to S232 to take the scale coefficients output by the current layer as the input of the next layer. 4.The method according to claim 3, characterized in that S24 comprises the following steps: S231, initialize the input signal, use the formula for the input in the network initialize; initializing the number of layers L = 0, and representing an input signal ; S242, reconstructing using formula (3); (1) (2) S233, if the decomposition layer number has reached the requirement, the decomposition ends to obtain all decomposition coefficients ; Otherwise, taking the wavelet coefficients corresponding to the scale coefficients and the decomposition coefficients obtained by the reconstruction of the current layer as the input of the next layer, and returning to S242 for continuing the reconstruction. 5.A system for signal sparse decomposition and reconstruction based on a learnable fractional wavelet transform, based on the method for signal sparse decomposition and reconstruction based on a learnable fractional wavelet transform according to any one of claims 1 to 4, characterized in that the system comprises a data sample training module, a convolutional network training module, a signal acquisition module, a sparse decomposition and reconstruction module, and a reconstructed signal output module; The convolutional network training module is configured to train a learnable fractional wavelet transform deep convolutional network; S241, read the decomposition coefficient of S233 ; The reconstructed signal output module is configured to output the reconstructed signal. (3) S243, if the reconstruction is completed, the final output is the reconstructed signal ; The processor executes the computer program to implement the steps of the method according to any one of claims 1 to 4. The computer instructions are executed by the processor to implement the steps of the method according to any one of claims 1 to 4. ​ The data sample training module is configured to construct training data samples; and collect training signals according to application scenarios as network training data samples; ​ The signal collection module is configured to collect a signal to be sparsely decomposed and reconstructed in a training data sample ; The sparse decomposition and reconstruction module is configured to perform sparse decomposition and reconstruction on a signal collected by the data sample training module The trained learnable fractional wavelet transform deep convolutional network is used for sparse decomposition and reconstruction. ​ 6.An electronic device comprising a memory and a processor, the memory storing a computer program, wherein, ​ 7. A computer readable storage medium for storing computer instructions, characterized in that, ​

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