Echo signal processing method based on multi-order FRFT domain feature fusion sparse dictionary

Abstract

The invention discloses an echo signal processing method based on a multi-order FRFT domain feature fusion sparse dictionary, and belongs to the technical field of underwater acoustic signal processing and target detection, and the method comprises the steps: screening out a plurality of differential fractional orders through employing the differential features of a target echo and a reverberation signal in different fractional order transform domains; constructing a sparse sub-dictionary based on each differential fractional order, and training a fusion weight of each sub-dictionary through an adaptive gradient optimization strategy; and finally, target signal extraction and strong reverberation suppression are realized through weighted fusion and sparse reconstruction. According to the method, the accuracy and stability of a sparse reconstruction result can be improved, the signal-to-mixing ratio of signals can be effectively improved, target echoes and strong reverberation are further distinguished, good robustness and engineering application value are achieved, and an effective technical means is provided for underwater weak signal detection and strong interference.

Description

Technical Field

[0001] This invention belongs to the field of underwater acoustic signal processing and target detection technology, specifically relating to an echo signal processing method based on a sparse dictionary fusion of multi-order FRFT domain features under strong reverberation interference. Background Technology

[0002] With the continuous advancement of marine exploration technology, active sonar systems are playing an increasingly important role in underwater target detection, identification, and localization. However, the actual marine environment is complex and variable, with various noise sources such as waves, wind, and underwater organisms, which can affect the analysis of target echoes in sonar signals. Among these, reverberation is one of the main background interferences in active sonar, especially strong reverberation caused by the transmitted signal. Its spectral structure has certain similarities to the transmitted signal, and traditional methods such as time-domain filtering, frequency-domain suppression, and matched filtering cannot effectively remove reverberation. Therefore, under conditions of strong reverberation interference, traditional methods are difficult to effectively extract target echoes, which has become a key bottleneck restricting the performance improvement of sonar systems.

[0003] Sparse representation theory utilizes a small number of atoms in an overcomplete dictionary to simplify the description of a signal, enabling better revelation, differentiation, and extraction of the information features contained within the signal, providing new ideas and methods for underwater target signal extraction. Existing technologies have employed wavelet bases and prior signals to construct dictionaries for signal denoising or reconstruction. These methods utilize wavelet bases or incident signals to construct dictionaries, and interference suppression is achieved by leveraging the principle that the echo signal is correlated with the incident wave, while noise or other interference is uncorrelated. This can filter out interference from environmental noise, random scatterers, etc. However, it is difficult to extract the target signal for strong reverberation, which has the same generation mechanism as the target echo. To achieve strong reverberation suppression, the constructed overcomplete dictionary must be as similar as possible to the characteristics of the target signal, while differing from the characteristics of the strong reverberant signal. This allows for the elimination of the strong reverberant signal during the sparse representation process, leaving only the target signal, thus achieving both target signal extraction and reverberation suppression. For separating the target signal from reverberation interference, the Fractional Fourier Transform (FRFT) can achieve energy accumulation on the chirp basis function, thereby suppressing reverberation. Therefore, many researchers are currently dedicated to using FRFT for related processing of signals in a reverberant background. Existing techniques have utilized the optimal order of the FRFT for reverberation suppression or target detection. However, when the reverberation signal and the target signal have the same generation mechanism, the reverberation will also accumulate energy at the optimal order, making it impossible to effectively separate the two using only the optimal order. This method cannot effectively distinguish between target echoes and strong reverberation. Summary of the Invention

[0004] The purpose of this invention is to provide an echo signal processing method based on a sparse dictionary fusion of multi-order FRFT domain features, so as to solve the problem that traditional methods cannot effectively distinguish between target echoes and strong reverberation.

[0005] To achieve the above objectives, the technical solution of the present invention is as follows:

[0006] This invention relates to an echo signal processing method based on a sparse dictionary fused with features from a multi-order FRFT domain, comprising the following steps:

[0007] S1. Differential fractional order extraction: Perform multi-order fractional Fourier transforms on the target echo signal and reverberation signal, calculate the degree of difference at each order, and select at least one differential fractional order to distinguish between the target echo signal and the reverberation signal.

[0008] S2. Construction of sparse sub-dictionary: Based on each selected fractional difference order, a fractional Fourier transform is performed on the target echo signal, and the sparse sub-dictionary is constructed using the transform result;

[0009] S3. Fusion Weight Training: An adaptive gradient optimization strategy is used to train the fusion weights of multiple sparse sub-dictionaries. The multiple sparse sub-dictionaries with trained fusion weights are then weighted and fused to form a fused sparse dictionary.

[0010] S4. The signal to be processed containing strong reverberation is sparsely decomposed using a fused sparse dictionary to suppress the components corresponding to reverberation, and the pure target echo signal is recovered through a sparse reconstruction algorithm.

[0011] Preferably, the specific steps for extracting the S1 difference fractional order include:

[0012] S1.1. Perform a fractional Fourier transform on the target echo signal and determine the optimal fractional order based on the maximum peak value criterion;

[0013] S1.2. Under a set of preset fractional orders, calculate the error between the fractional order transformation results of the target echo signal and the reverberation signal respectively;

[0014] S1.3. Select a fractional order with an error greater than a preset threshold as the difference fractional order used to distinguish the target echo signal from the reverberation signal.

[0015] Preferably, in step S1.2, the error between the fractional-order transformation results of the target echo signal and the reverberation signal is calculated using the Euclidean distance method or the cosine similarity method.

[0016] Preferably, the weighted model of the sparse reconstruction results of the sparse dictionary fused in S3 is as follows:

[0017] ,

[0018] Among them, S re For reconstructing the signal, i is the index of the sparse sub-dictionary, P represents the number of difference fractions, which also represents the number of sparse sub-dictionaries, and w i φ is the fusion weight corresponding to the sparse sub-dictionary with index i. i D represents the reconstruction result corresponding to the sparse sub-dictionary with index i. i The sub-dictionary constructed for the i-th difference fraction order, α i represents the sparse coefficients under the sparse sub-dictionary numbered i.

[0019] Preferably, the specific steps of S3 in training the fusion weights of multiple sparse sub-dictionaries using an adaptive gradient optimization strategy include:

[0020] S3.1. Construct a loss function, which is the norm of the error between the reconstructed signal from the fused dictionary and the original target echo signal. The loss function is expressed as:

[0021] ,

[0022] Where L is the loss function, S is the target echo signal, φ is the reconstruction result matrix, and w is the weight matrix;

[0023] S3.2. Calculate the gradient of the loss function with respect to the fusion weights of each sub-dictionary. The calculation formula is as follows:

[0024] ,

[0025] Among them, Grad i Let be the gradient of the fusion weights with respect to the sparse sub-dictionary numbered i, where j is the number of the sparse sub-dictionary;

[0026] S3.3. Introducing historical gradient information and loss function curvature estimation to adaptively adjust the learning rate for updating the fusion weights, iteratively updating the fusion weights of each sparse sub-dictionary until the reconstruction error converges or the preset number of iterations is reached; the update method for the fusion weights of the sparse sub-dictionary is as follows:

[0027] ,

[0028] Where L' is the first derivative of the loss function with respect to that weight, FluDegree is the degree of fluctuation of the first derivative of the loss function, and Cur is the current fusion weight. L (2) The second derivative of the fusion weights is expressed as: Var is the variance of the difference values ​​of the loss function, and AdaVar is the adaptive variance, which is obtained by applying a logarithmic function to Var to limit its amplitude, aiming to make it applicable to functions of different orders of magnitude.

[0029] The formula for calculating the volatility of the first derivative of the loss function is as follows:

[0030] ,

[0031] Where Range represents the adaptive neighborhood range. R b R is a gradient-based adaptive factor. r An adaptive factor based on function values. , Grad i 'For the loss function pair w i The first derivative of , Maxgrad is the absolute value of the historical maximum gradient, and MaxLoss is the absolute value of the historical maximum loss function value.

[0032] Preferably, the S3.3 iterative update of the fusion weights of each sparse sub-dictionary adopts an alternating iterative optimization strategy, specifically: fix the sparse coefficients and update the fusion weights of each sparse sub-dictionary; fix the updated fusion weights and recalculate the sparse coefficients; repeat the above process until the convergence condition is met.

[0033] Compared with the prior art, the technical solution provided by this invention has the following advantages:

[0034] 1. The echo signal processing method based on multi-order FRFT domain feature fusion sparse dictionary of the present invention performs time-frequency analysis on target echo signal and reverberation background signal through fractional Fourier transform. It utilizes the focusing characteristics of linear frequency modulated signal at different orders to extract multiple sets of difference fractional orders with discriminative ability. Based on the extracted difference fractional orders, multiple sparse sub-dictionaries are constructed respectively, and weight factors are introduced to realize the fusion expression of multi-domain features, thereby improving the accuracy and stability of sparse reconstruction results, effectively improving the signal-to-mixing ratio of the signal, and distinguishing target echo from strong reverberation.

[0035] 2. The echo signal processing method based on multi-order FRFT domain feature fusion sparse dictionary of the present invention adopts an adaptive gradient optimization strategy to train the fusion weights of multiple sparse sub-dictionaries, so as to achieve the optimal fusion of information of different fractional order in the sparse reconstruction process. Attached Figure Description

[0036] Figure 1 This is a schematic diagram of the sparse representation principle provided in the embodiments of the present invention.

[0037] Figure 2 This is an overall flowchart of the method of the present invention.

[0038] Figure 3 This is a schematic diagram of the experimental deployment in an embodiment of the present invention.

[0039] Figure 4 These are waveforms of the signal to be processed under different initial signal-to-mix ratios.

[0040] Figure 5 It is a normalized waveform diagram of the target signal and the reverberation signal.

[0041] Figure 6 This is a comparison chart of the FRFT transformation results of the target and the reverberation signal at the optimal fractional order.

[0042] Figure 7 This is a diagram showing the sparse reconstruction results of the method of the present invention under different initial signal-to-mix ratios.

[0043] Figure 8 This is a graph showing the improvement in signal-to-mixing ratio (SMR) for a single test signal under different initial SMRs.

[0044] Figure 9 It is the target motion trajectory diagram before processing.

[0045] Figure 10 It is the processed target motion trajectory diagram.

[0046] Figure 11 This is a statistical chart showing the signal-to-mixing ratio improvement effect of all test signals. Detailed Implementation

[0047] To further understand the content of this invention, the invention will be described in detail with reference to the embodiments. The following embodiments are used to illustrate the invention, but are not intended to limit the scope of the invention.

[0048] See attached document Figure 2 As shown, this invention relates to an echo signal processing method based on a sparse dictionary fused with features from a multi-order FRFT domain, which includes the following steps:

[0049] S1. Fractional Difference Extraction: Input the target echo signal and the reverberation signal to be processed, perform multi-order fractional Fourier transforms on the target echo signal and the reverberation signal, calculate the degree of difference at each order, and select at least one fractional difference order to distinguish the target echo signal from the reverberation signal. Specific steps include:

[0050] S1.1. Perform a fractional Fourier transform on the target echo signal and determine the optimal fractional order based on the maximum peak value criterion;

[0051] S1.2. Under a set of preset fractional orders, calculate the error between the fractional-order transformation results of the target echo signal and the reverberation signal (at different fractional orders). The error calculation methods include Euclidean distance method, cosine similarity method, etc.; assuming X1 and X2 are two different signals, the Euclidean distance Dis is calculated as follows:

[0052] ,

[0053] The cosine similarity Sim is calculated as follows:

[0054] ;

[0055] This embodiment uses the Euclidean distance method to calculate the error between the fractional-order transformation results of the target echo signal and the reverberation signal.

[0056] S1.3. Select an error greater than a preset threshold (threshold range is 0.4-0.6). This ratio is represented by the threshold parameter γ and is used as the difference fractional order to distinguish the target echo signal from the reverberation signal. In this embodiment, when the peak value of the extracted fractional order Fourier transform is greater than half of the peak value of the optimal order, it is considered as the difference fractional order.

[0057] S2. Sparse Sub-Dictionary Construction: Based on each selected fractional difference order, a fractional Fourier transform is performed on the target echo signal, and the transform result is used as the atom to construct a sparse sub-dictionary (e.g., ...). Figure 1 (overcomplete dictionary)

[0058] S3. Fusion Weight Training: The initial weights of each sparse sub-dictionary are evenly distributed to obtain the initial sparse reconstruction result. An adaptive gradient optimization strategy is used to train the fusion weights of multiple sparse sub-dictionaries. The multiple sparse sub-dictionaries with trained fusion weights are then weighted and fused to form a fused sparse dictionary.

[0059] The weighted model for the sparse reconstruction results fused with the sparse dictionary is as follows:

[0060] ,

[0061] Among them, S re For reconstructing the signal, i is the index of the sparse sub-dictionary, P represents the number of difference fractions, which also represents the number of sparse sub-dictionaries, and w i φ is the fusion weight corresponding to the sparse sub-dictionary with index i. i D represents the reconstruction result corresponding to the sparse sub-dictionary with index i. i The sub-dictionary constructed for the i-th difference fraction order, α i represents the sparse coefficients under the sparse sub-dictionary numbered i.

[0062] The goal of this weighted model is to train the fusion weights w i This allows the fusion result to approximate the original target echo signal S as closely as possible, thereby achieving more accurate target information reconstruction.

[0063] The specific steps for training the fusion weights of multiple sparse sub-dictionaries include:

[0064] S3.1. Construct a loss function with the objective of minimizing the reconstruction error. The loss function is the norm of the error between the reconstructed signal from the fused dictionary and the original target echo signal. The loss function is expressed as:

[0065] ,

[0066] Where L is the loss function, S is the target echo signal, and φ is the reconstruction result matrix. w is the weight matrix. ;

[0067] S3.2. Calculate the gradient of the loss function with respect to the fusion weights of each sub-dictionary. The calculation formula is as follows:

[0068] ,

[0069] Among them, Grad i Let be the gradient of the fusion weights with respect to the sparse sub-dictionary numbered i, where j is the number of the sparse sub-dictionary;

[0070] S3.3. Historical gradient information and loss function curvature estimation are introduced to adaptively adjust the learning rate of the fusion weight update, iteratively updating the fusion weights of each sparse sub-dictionary until the reconstruction error converges or the preset number of iterations is reached. To further improve the convergence efficiency of weight updates and enhance the stability of the training process, this invention introduces weight... The second derivative is This is done to assist in evaluating the curvature of the objective function, thereby aiding in optimizing the step size selection. Simultaneously, considering that gradients may oscillate dramatically during actual training, this invention dynamically adjusts the learning rate using historical information, introducing an adaptive weight adjustment strategy. The absolute value of the historical maximum gradient represents... The absolute value of the historical maximum loss function is To avoid training getting stuck in local optima or convergence stagnation caused by an excessively small learning rate, this invention also sets an adaptive range. The size of the learning samples is gradually adjusted during the iteration process. When approaching the optimum, the local search range of the learning samples should be appropriately expanded, calculated using the following formula: ,in, , R b R is a gradient-based adaptive factor. r Grad is an adaptive factor based on function values. i 'For the loss function pair w i The first derivative of , Maxgrad is the absolute value of the historical maximum gradient, and MaxLoss is the absolute value of the historical maximum loss function value.

[0071] Based on the above parameters, the update method for the fusion weights of the sparse sub-dictionary is as follows:

[0072] ,

[0073] Where L' is the first derivative of the loss function with respect to that weight, FluDegree is the degree of fluctuation of the first derivative of the loss function, and Cur is the current fusion weight. L (2) The second derivative of the fusion weights is expressed as: Var is the variance of the difference values ​​of the loss function, and AdaVar is the adaptive variance, which is obtained by applying a logarithmic function to Var to limit its amplitude, aiming to make it applicable to functions of different orders of magnitude.

[0074] The formula for calculating the volatility of the first derivative of the loss function is as follows:

[0075] .

[0076] The iterative update of the fusion weights of each sparse sub-dictionary adopts an alternating iterative optimization strategy, specifically: fix the sparse coefficients and update the fusion weights of each sparse sub-dictionary; fix the updated fusion weights and recalculate the sparse coefficients; repeat the above process until the convergence condition is met. The convergence condition is to judge the error change between the fractional-order transform results of the target echo signal and the reverberation signal or to reach the specified number of iterations. When the error decreases, it is determined that the convergence condition is not met; conversely, when the error increases, it is determined that the convergence condition is met.

[0077] After terminating the iteration, output the optimal reconstruction result, minimum error, weight training result, and signal-to-mixing ratio improvement result.

[0078] S4. The signal to be processed containing strong reverberation is sparsely decomposed using a fused sparse dictionary to suppress the components corresponding to reverberation, and the pure target echo signal is recovered through a sparse reconstruction algorithm.

[0079] Experimental Example

[0080] This experimental example presents data from a lake test conducted in December 2023 in the Xin'anjiang River basin, Jiande City, Hangzhou, Zhejiang Province. The experimental setup consisted of a combined transmitter and receiver hydrophone A, placed at a water depth of h. The experimental target was a spherical model B, and the setup was as follows: Figure 3 As shown, the initial distance is L1. During the experiment, the target moves at a velocity v from far to near or from near to far. This experimental example selected 150 test results for processing. This experiment used a combined transmit and receive active sonar system. The system transmits a linear frequency modulated (LFM) signal with the following parameters: frequency modulation bandwidth of 40kHz, center frequency of 60kHz, pulse width of 5ms, and sampling frequency of 1MHz.

[0081] Since the target's motion is from far to near, the obtained test signals are used to construct signals to be processed under different signal-to-mixing ratios (SMRs). The waveforms of the 75th test signal under different SMRs (3dB, 5dB) are shown below. Figure 4 As shown in the figure. The signal with a signal-to-mixing ratio of 3dB is selected as the signal to be processed below.

[0082] According to the method of the present invention, it is necessary to calculate the difference between the target signal sample and the reverberation signal at different fractional orders, so as to determine the final set of difference fractional orders as the fractional orders for constructing the sparse representation dictionary. First, in order to extract the target echo signal in a strong reverberation background, the last measurement signal is used as the target signal, and the reverberation part in this measurement is extracted to extract the difference fractional orders. Figure 5 (a) is the waveform of the target signal after amplitude normalization. Figure 5 (b) shows the reverberation signal waveform after amplitude normalization. The optimal order of the target signal can be obtained using the maximum peak value criterion. The transformation result of the target echo signal at this fractional order is as follows: Figure 6 As shown in (a), the transformation result of the reverberation signal at this order is as follows: Figure 6 As shown in (b), the reverberant signal also has energy accumulation at the optimal order of the target signal, but its accumulation amplitude is significantly lower than that of the target signal at the optimal order. However, it can also be seen that the degree of accumulation of the reverberant signal is still relatively high. Therefore, it is necessary to find a more discriminative fractional order for feature domain processing.

[0083] After obtaining the baseline peak value, a threshold parameter is set according to the method of the present invention. Under these conditions, the fractional order of the difference between the target signal and the reverberation signal is obtained as follows: Next, the method of this invention is used to construct a sparse representation dictionary in each fractional-order domain. Then, the transformed signals in each domain are processed, and the final weight allocation obtained from the training is... The reconstruction result is as follows Figure 7 As shown in (a), its corresponding minimum reconstruction error is The reconstructed signal-to-mixing ratio (SMR) is 18.06 dB, representing an improvement of 15.06 dB. Simultaneously, the method presented in this paper was used to process the 75th test signal with a SMR of 5 dB, and the processing results are as follows. Figure 7 As shown in (b), by comparing the signals before and after reconstruction, it can be clearly seen that the target signal, which was originally submerged by reverberation, has been effectively extracted. The signal-to-mixing ratio (SMR) improvement effect of the 75th test signal under different initial SMRs is shown in (b). Figure 8 As shown, the present invention still has high target signal extraction performance even under strong reverberation background.

[0084] Next, all test signals in this embodiment are processed, specifically all test signals at signal-to-mixing ratios of 3dB and 5dB. Figure 9 The images show the target motion trajectory diagrams for signals with signal-to-mixing ratios of 3dB and 5dB, respectively. First, the initial signal-to-mixing ratio of 3dB is processed as a whole; the result is shown below. Figure 10 As shown in (a), the processing results under the condition of a signal-to-mixture ratio of 5 dB are as follows. Figure 10 As shown in (b). The signal-to-mixing ratio (SMR) improvement effect for different test signals at SMRs of 3dB and 5dB is shown in [the figure]. Figure 11 As shown.

[0085] Through the above process, this example successfully extracted the target signal from a strong reverberant background, significantly improving the signal-to-mixing ratio and verifying the effectiveness of the invention.

[0086] The present invention has been described in detail above with reference to the embodiments, but the content described is only a preferred embodiment of the present invention and should not be considered as limiting the scope of the present invention. All equivalent changes and improvements made in accordance with the scope of the present invention should still fall within the patent coverage of the present invention.

Claims

1. A method for echo signal processing based on multi-order FRFT domain feature fusion sparse dictionary, characterized in that, It comprises the following steps: S1. Difference fractional order extraction: performing multi-order fractional Fourier transform on the target echo signal and the reverberation signal, calculating the difference degree thereof at each order, and screening at least one difference fractional order for distinguishing the target echo signal from the reverberation signal; S2. Sparse sub-dictionary construction: based on each screened difference fractional order, performing fractional Fourier transform on the target echo signal respectively, and constructing a sparse sub-dictionary based on the transform result; S3. Fusion weight training: training the fusion weights of multiple sparse sub-dictionaries by using an adaptive gradient optimization strategy, weighting and fusing the multiple sparse sub-dictionaries with the trained fusion weights to form a fused sparse dictionary; S4. Sparse decomposition of the signal to be processed containing strong reverberation by using the fused sparse dictionary, suppressing the components corresponding to the reverberation, and restoring the pure target echo signal through a sparse reconstruction algorithm. 2.The echo signal processing method based on multi-order FRFT domain feature fusion sparse dictionary according to claim 1, characterized in that: The specific steps of S1. Difference fractional order extraction include: S1.

1. Performing fractional Fourier transform on the target echo signal, and determining the optimal fractional order according to the maximum peak value criterion; S1.

2. Calculating the error between the fractional transform results of the target echo signal and the reverberation signal at a group of preset fractional orders respectively; S1.

3. Selecting the fractional order with an error greater than a preset threshold as the difference fractional order for distinguishing the target echo signal from the reverberation signal. 3.The echo signal processing method based on multi-order FRFT domain feature fusion sparse dictionary according to claim 2, characterized in that: In S1.2, the error between the fractional transform results of the target echo signal and the reverberation signal is calculated by using the Euclidean distance method. 4.The echo signal processing method based on multi-order FRFT domain feature fusion sparse dictionary according to claim 1, characterized in that: In S3, the weighting model of the sparse reconstruction result of the fused sparse dictionary is: ， where S re is the reconstruction signal, i is the index of the sparse sub-dictionary, P represents the number of difference fractional orders, also the number of sparse sub-dictionaries, w i is the fusion weight corresponding to the sparse sub-dictionary with index i, φ i is the reconstruction result corresponding to the sparse sub-dictionary with index i, D i is the sub-dictionary constructed by the i-th difference fractional order, α i is the sparse coefficient under the sparse sub-dictionary with index i.

5. The method according to claim 4, wherein the method is characterized in that: The specific steps of training the fusion weights of multiple sparse sub-dictionaries by using an adaptive gradient optimization strategy in S3 include: S3.

1. Constructing a loss function, which is the norm of the error between the reconstruction signal of the fused dictionary and the original target echo signal, and the loss function is expressed as: ， wherein L is the loss function, S is the target echo signal, φ is the reconstruction result matrix, and w is the weight matrix; S3.

2. Calculating the gradient of the loss function with respect to each sub-dictionary fusion weight, and the calculation formula is: ， where Grad i is the gradient of the fusion weight with respect to the sparse sub-dictionary numbered i, j is the number of the sparse sub-dictionary; S3.

3. Introducing historical gradient information and loss function curvature estimation to adaptively adjust the learning rate of fusion weight update, iteratively updating the fusion weights of each sparse sub-dictionary until the reconstruction error converges or a preset iteration number is reached; the update mode of the fusion weights of the sparse sub-dictionary is: ， wherein L' is the first derivative of the loss function with respect to the weight, FluDegree is the fluctuation degree of the first derivative of the loss function, Cur is the current fusion weight, , L (2) is the second derivative of the fusion weight, and is represented as , Var is the variance of the difference value of the loss function, and AdaVar is the adaptive variance, which is obtained by limiting the amplitude of Var using a logarithmic function, and is intended to be applicable to functions of different orders of magnitude; The calculation formula of the fluctuation degree of the first derivative of the loss function is: ， where Range is the adaptive field range, , R b is a gradient-based adaptive factor, R r is a function value-based adaptive factor, , , Grad i is the first derivative of the loss function with respect to w i , Maxgrad is the absolute value of the historical maximum gradient, and MaxLoss is the absolute value of the historical maximum loss function value.

6. The echo signal processing method based on multi-order FRFT domain feature fusion sparse dictionary according to claim 5, characterized in that: In S3.3, the fusion weights of each sparse sub-dictionary are iteratively updated by using an alternating iterative optimization strategy, specifically: fixing the sparse coefficients, updating the fusion weights of each sparse sub-dictionary; fixing the updated fusion weights, recalculating the sparse coefficients; Repeat the above process until the convergence condition is met.

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