Hybrid constraint whistle de-reverberation method based on divergence convolution non-negative matrix factorization

Abstract

The invention discloses a mixed constraint whistle de-reverberation method based on divergence convolution non-negative matrix factorization, which belongs to the technical field of sound processing, and comprises the following steps: constructing a reverberation model of dolphin whistle signals and underwater sound channel impulse response (CIR) based on short-time Fourier transform (STFT), constructing a de-reverberation model of the dolphin whistle signals, and constructing a de-reverberation model of the dolphin whistle signals; and obtaining a total cost function of a basic dictionary, a matrix matrix and a time-frequency matrix of the CIR related to a whistle time-frequency spectrum, calculating time-frequency standard evaluation of a pure whistle signal through the optimized total cost function of the basic dictionary, the matrix matrix and the time-frequency matrix of the CIR, and reconstructing a time domain of the whistle signal through short-time Fourier inversion (ISTFT). According to the method, the definition and the analysis accuracy of the dolphin whistle signal are improved, the quality of the whistle signal is effectively improved, and the detection performance of the PAM system on the whistle signal is remarkably improved.

Description

Technical Field

[0001] The invention discloses a mixed constraint whistle dereverberation method based on divergence convolution non-negative matrix decomposition, belonging to the technical field of sound processing. Background Art

[0002] Underwater passive acoustic monitoring (PAM) is an important tool for studying the behavior and distribution of marine mammals, especially dolphins. Dolphins use a complex communication system to communicate through amplitude-modulated AM and frequency-modulated FM whistle signals, which vary significantly between populations and are associated with specific behavioral patterns. However, human activities in shallow water areas, such as chemical pollution, industrial development, land reclamation, and coastal construction, have negatively affected the habitat of dolphins, resulting in changes in the number and spectral characteristics of dolphin whistle signals. Therefore, passive acoustic monitoring of dolphin whistle signals in shallow water environments faces the challenge of multipath reverberation. To overcome these challenges, existing technology solutions have been exploring more advanced signal processing methods. Non-negative matrix factorization (NMF) and convolutional NMF are powerful tools for learning dictionary matrices and processing audio signals. However, these methods have limitations in processing underwater reverberant signals, especially in blind environments, because they need to learn a large number of variables from sparse data. Summary of the invention

[0003] The object of the present invention is to provide a hybrid constrained whistle dereverberation method based on divergence convolution non-negative matrix decomposition to solve the problem of multipath reverberation faced by the whistle in the prior art.

[0004] A hybrid constrained whistle dereverberation method based on divergence convolution non-negative matrix decomposition includes: S1. Construct a reverberation model of dolphin whistle signal and underwater acoustic channel impulse response CIR based on short-time Fourier transform STFT; S2, based on Divergence constructs a demeverberation model for dolphin whistle signals and obtains a basic dictionary of the whistle's time-frequency spectrum , matrix And the time-frequency matrix of CIR The total cost function is represents the dimension of matrix decomposition, is the discrete time index of CIR, is the frequency band index; S3. Building auxiliary functions ,get The update rule is updated and the optimal dictionary is obtained through iterative updates. , is the auxiliary dictionary used in the current iteration step, which is equivalent to the one in the next iteration step. ; S4. And joint constraints, build auxiliary functions and ,get and The iteration rule, It is under the frame index , after iterative update, the optimal matrix is ​​obtained And the optimal CIR matrix , is the auxiliary matrix used in the current iteration step, which is equivalent to the matrix in the next iteration step. , is the auxiliary time-frequency matrix used in the current iteration step, which is equivalent to the one in the next iteration step. ; S5. Pass , and Calculate the time-frequency standard evaluation of the pure whistle signal , the time domain of the whistle signal is reconstructed by inverse short-time Fourier transform (ISTFT).

[0005] Only the approximate models of the analysis filter and the synthesis filter are considered, and the reverberation model of the dolphin whistle signal and the underwater acoustic channel impulse response CIR is obtained by combining underwater passive acoustic monitoring with STFT: ; ; In the formula, The time-frequency matrix representing the reverberation model of the dolphin whistle signal and the underwater acoustic channel impulse response CIR, represents the time-frequency matrix of the pure whistle signal, Indicates the length of the CIR discrete form, is the frame index, Indicates the length of the Fourier transform analysis window.

[0006] The total cost function is: ; ; ; ; ; ; In the formula, is the total cost function, yes The cost function is yes The penalty item, yes The penalty item, yes Divergence, is the time-frequency of the reverberated whistle signal based on the elastic approximation preservation criterion under CIR interference, is the parameter time-frequency, is the total number of discrete time indices, is the upper limit of the dimension of matrix decomposition, is the approximation error in non-negative matrix factorization, is the penalty parameter, and yes The weight parameter, is the time-difference series matrix.

[0007] Will The divergence is decomposed into a convex part, a concave part, and a constant part: ; In the formula, It is the convex part. It is the concave part. is the constant part.

[0008] when When , the convex part, concave part and constant part are: ; ; ; In the formula, yes The parameter time-frequency under yes The parameter time-frequency under when When , the convex part, concave part and constant part are: ; ; ; when When , the convex part, concave part and constant part are: ; ; ; when When , the convex part, concave part and constant part are: ; ; ; In the formula, yes Next .

[0009] Iterate and update to get the optimal dictionary Convert to Minimize ,definition for Auxiliary function, replaced by iterative update of auxiliary function Optimization: ; ; ; ; ; In the formula, is the intermediate parameter, is the auxiliary parameter time-frequency, yes In divergence The value of The convexity and differentiability of , minimizing the gradient to 0 , we can conclude The recursive formula of ; The recursive formula is: ; In the formula, yes After recursive calculation, we get , yes After recursive calculation, we get The value is The parameter time-frequency, is a very small positive number, yes The value is The recursive index of .

[0010] Helper functions related to activation matrices for: ; ; ; ; In the formula, is the intermediate parameter, yes The auxiliary matrix matrix is ​​in S3 The recursive formula is: ; In the formula, yes After recursive calculation, we get .

[0011] The optimal matrix will be found Transformed to minimize under the sparsity constraint of the pure whistle time-frequency representation , build auxiliary functions : ; ; ; ; In the formula, is an intermediate parameter, in S4 The recursive formula is: ; In the formula, yes The value is The auxiliary parameters of time-frequency, yes The value is The auxiliary parameters of time-frequency, yes The value is The recursive index of .

[0012] The optimal CIR matrix will be found The transformation is to minimize the sparsity and attenuation characteristics of the underwater sound channel in the time domain. , build auxiliary functions : ; ; ; ; ; In the formula, is the intermediate parameter, The recursive formula is: ; ; ; In the formula, is a recursive intermediate variable, yes The frame index obtained after recursive calculation is , is a diagonal matrix, is the unit diagonal matrix, yes After recursive calculation, we get The value is The auxiliary parameters of time-frequency, yes After recursive calculation, we get The value is The auxiliary parameters of time-frequency, is the recursive difference, .

[0013] for: ; ; In the formula, is the time-varying gain function; Reconstruct the whistle signal using the inverse short-time Fourier transform: ; In the formula, It is a pure whistle signal after removing reverberation. The length of the inverse short-time Fourier transform is The synthetic window, is the discrete time offset, is the counting parameter, is an imaginary unit, is a natural constant.

[0014] Compared with the prior art, the present invention has the following beneficial effects: it improves the clarity and analysis accuracy of dolphin whistle signals, effectively improves the quality of whistle signals, and significantly improves the detection performance of PAM systems for whistle signals; it can adaptively handle variable underwater acoustic propagation conditions to ensure stable operation in various underwater acoustic environments. Whether in a short-distance water environment or a long-distance complex underwater acoustic propagation condition, the algorithm can effectively remove reverberation interference and restore clear signal characteristics, thereby providing more accurate and reliable technical support for underwater communications, ocean monitoring and marine biology research. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 This is the pure wav1 segment time spectrum; Figure 2 is Spectrum diagram of the reverberated whistle signal under interference; Figure 3 is Spectrum diagram of the reverberated whistle signal under interference; Figure 4 is Spectrum diagram of the whistle signal reconstructed after dereverberation under interference; Figure 5 is Time-frequency spectrum of the whistle signal reconstructed after dereverberation under interference. DETAILED DESCRIPTION

[0016] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the present invention is described clearly and completely below. Obviously, the described embodiments are part of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0017] A hybrid constrained whistle dereverberation method based on divergence convolution non-negative matrix decomposition includes: S1. Construct a reverberation model of dolphin whistle signal and underwater acoustic channel impulse response CIR based on short-time Fourier transform STFT; S2, based on Divergence constructs a demeverberation model for dolphin whistle signals and obtains a basic dictionary of the whistle's time-frequency spectrum , matrix And the time-frequency matrix of CIR The total cost function is represents the dimension of matrix decomposition, is the discrete time index of CIR, is the frequency band index; S3. Building auxiliary functions ,get The update rule is updated and the optimal dictionary is obtained through iterative updates. , is the auxiliary dictionary used in the current iteration step, which is equivalent to the one in the next iteration step. ; S4. And joint constraints, build auxiliary functions and ,get and The iteration rule, It is under the frame index , after iterative update, the optimal matrix is ​​obtained And the optimal CIR matrix , is the auxiliary matrix used in the current iteration step, which is equivalent to the matrix in the next iteration step. , is the auxiliary time-frequency matrix used in the current iteration step, which is equivalent to the one in the next iteration step. ; S5. Pass , and Calculate the time-frequency standard evaluation of the pure whistle signal , the time domain of the whistle signal is reconstructed by inverse short-time Fourier transform (ISTFT).

[0018] Only the approximate models of the analysis filter and the synthesis filter are considered, and the reverberation model of the dolphin whistle signal and the underwater acoustic channel impulse response CIR is obtained by combining underwater passive acoustic monitoring with STFT: ; ; In the formula, The time-frequency matrix representing the reverberation model of the dolphin whistle signal and the underwater acoustic channel impulse response CIR, represents the time-frequency matrix of the pure whistle signal, Indicates the length of the CIR discrete form, is the frame index, Indicates the length of the Fourier transform analysis window.

[0019] The total cost function is: ; ; ; ; ; ; In the formula, is the total cost function, yes The cost function is yes The penalty item, yes The penalty item, yes Divergence, is the time-frequency of the reverberated whistle signal based on the elastic approximation preservation criterion under CIR interference, is the parameter time-frequency, is the total number of discrete time indices, is the upper limit of the dimension of matrix decomposition, is the approximation error in non-negative matrix factorization, is the penalty parameter, and yes The weight parameter, is the time-difference series matrix.

[0020] Will The divergence is decomposed into a convex part, a concave part, and a constant part: ; In the formula, It is the convex part. It is the concave part. is the constant part.

[0021] when When , the convex part, concave part and constant part are: ; ; ; In the formula, yes The parameter time-frequency under yes The parameter time-frequency under when When , the convex part, concave part and constant part are: ; ; ; when When , the convex part, concave part and constant part are: ; ; ; when When , the convex part, concave part and constant part are: ; ; ; In the formula, yes Next .

[0022] Iterate and update to get the optimal dictionary Convert to Minimize ,definition for Auxiliary function, replaced by iterative update of auxiliary function Optimization: ; ; ; ; ; In the formula, is the intermediate parameter, is the auxiliary parameter time-frequency, yes In divergence The value of The convexity and differentiability of , minimizing the gradient to 0 , we can conclude The recursive formula of ; The recursive formula is: ; In the formula, yes After recursive calculation, we get , yes After recursive calculation, we get The value is The parameter time-frequency, is a very small positive number, yes The value is The recursive index of .

[0023] Helper functions related to activation matrices for: ; ; ; ; In the formula, is the intermediate parameter, yes The auxiliary matrix matrix is ​​in S3 The recursive formula is: ; In the formula, yes After recursive calculation, we get .

[0024] The optimal matrix will be found Transformed to minimize under the sparsity constraint of the pure whistle time-frequency representation , build auxiliary functions : ; ; ; ; In the formula, is an intermediate parameter, in S4 The recursive formula is: ; In the formula, yes The value is The auxiliary parameters of time-frequency, yes The value is The auxiliary parameters of time-frequency, yes The value is The recursive index of .

[0025] The optimal CIR matrix will be found The transformation is to minimize the sparsity and attenuation characteristics of the underwater sound channel in the time domain. , build auxiliary functions : ; ; ; ; ; In the formula, is the intermediate parameter, The recursive formula is: ; ; ; In the formula, is a recursive intermediate variable, yes The frame index obtained after recursive calculation is , is a diagonal matrix, is the unit diagonal matrix, yes After recursive calculation, we get The value is The auxiliary parameters of time-frequency, yes After recursive calculation, we get The value is The auxiliary parameters of time-frequency, is the recursive difference, .

[0026] for: ; ; In the formula, is the time-varying gain function; Reconstruct the whistle signal using the inverse short-time Fourier transform: ; In the formula, It is a pure whistle signal after removing reverberation. The length of the inverse short-time Fourier transform is The synthetic window, is the discrete time offset, is the counting parameter, is an imaginary unit, is a natural constant.

[0027] The present invention first needs to process the collected dolphin whistle signals, that is, to construct a reverberation model of the dolphin whistle signal and the underwater acoustic channel impulse response based on short-time Fourier transform. By converting the time domain signal to the time-frequency domain, the AM and FM characteristics of the signal are analyzed, providing a theoretical basis and mathematical description for the subsequent dereverberation algorithm.

[0028] Introducing a generalized -divergence is used as a non-negative fidelity term to construct the basic dictionary of the time-frequency spectrum of dolphin whistles. At the same time, the characteristics of dolphin whistle signals and the characteristics of underwater acoustic channel impulse responses are combined to formulate hybrid constraints. -Convolutional Non-Negative Matrix Factorization ( -CNMF-HC) dolphin whistle dereverberation model. The problem is transformed into minimization Problem, and build helper functions , so that the iterative update of the auxiliary function can replace By minimizing the gradient of the auxiliary function to 0, we get Finally, after a certain number of iterative updates, the optimal dictionary is obtained. .

[0029] In the best dictionary and joint constraints, we will find and the time-frequency representation of the channel impulse response (CIR) The problem is transformed into minimizing under the sparsity constraint of the pure whistle time-frequency representation and are minimized under the constraints of sparsity and attenuation characteristics of the underwater acoustic channel in time domain Problem, set up auxiliary functions according to the method of building auxiliary functions and Similarly, by minimizing the gradients of the above two auxiliary functions to 0, we get and Finally, after the same number of iterations, the most suitable and .

[0030] According to non-negative matrix factorization (NMF) and in order to further match the time-varying characteristics of the underwater sound channel, three optimal variables are obtained through two-stage iterative updates. , and Standard evaluation of time-frequency representations of pure whistle signals Finally, the time domain of the whistle signal is reconstructed by inverse short-time Fourier transform.

[0031] The implementation time interval of this invention is from July 2017 to March 2018, a nine-month data collection process, collecting about 3000 minutes of whistle signals emitted by two captive Indo-Pacific bottlenose dolphins. In this way, a pure dolphin whistle data set was constructed, containing 200 calls, each lasting about 3.5 seconds, containing 1 to 5 whistle signals.

[0032] Considering the physical characteristics of underwater acoustic propagation and the random characteristics of underwater sound channels, a channel simulator based on a statistical channel model is used in the implementation process of the present invention to better describe the channel impulse response within the dolphin whistle frequency band. The parameters of the statistical channel model are set to the default values, and the focus is on studying the channel impulse response by constructing the statistical multipath impulse response (CIRd1−d2_dist) under different scenarios, where d1 and d2 are the depths of the hydrophone and the dolphin, and dist is the relative distance. The hydrophone was placed at a depth of 50 meters, while the depth of the dolphin simulated the shallow water area of ​​the natural habitat. During the implementation process, two scenarios were simulated to test the algorithm: in the first scenario, the dolphin depth was fixed at 10 meters and the relative distance varied from 300 meters to 1500 meters; in the second scenario, the relative distance was fixed at 300 meters and the dolphin depth varied from 10 meters to 90 meters. Finally, by convolving the pure whistle signal with different underwater channel responses, the dolphin whistle data set under different reverberation conditions was obtained, and the expression is: ; in For pure dolphin whistle signal, is the channel impulse response, A reverberated whistle signal captured for underwater PAM, Indicates signal fusion.

[0033] In order to effectively capture the obvious amplitude modulation and frequency modulation characteristics of the dolphin whistle signal, the reverberation whistle signal is converted into the time-frequency domain using short-time Fourier transform. In actual underwater PAM, the corresponding discrete form needs to be used with a sampling frequency of The pure whistle signal obtained by sampling the discrete short-time Fourier transform It can be expressed as: ; In the formula, The length of the short-time Fourier transform is The synthesis window.

[0034] Then, use the inverse short-time Fourier transform from Get the time domain representation The completeness condition is expressed as: .

[0035] The recursion index in the present invention is, When , the recursion index is , When , the recursion index is 1, When , the recursion index is .

[0036] In order to further evaluate the effectiveness of the proposed method in enhancing the whistle signal under multipath reverberation interference, four objective evaluation indicators are introduced. These indicators are designed to evaluate the improvement of whistle signal quality by comparing the differences between the reverberation and reconstructed signals and the pure whistle signal in different dimensions. The specific indicators are described as follows.

[0037] It measures the change in the signal-to-reverberation ratio before and after signal enhancement and is defined as: ; In the formula, is the total number of signals.

[0038] The absolute error change in temporal similarity before and after enhancement is evaluated, defined as: ; It measures the difference in the average signal-to-reverberation ratio across all whistle frames and is defined as: ; is the number of sampling points in each whistle signal frame.

[0039] The difference in normalized weighted spectral slope distance in each frequency band was evaluated and was expressed as: ; In the formula, is the total number of frequency bands, is the weight factor, expressed as: ; In the formula, and They are Clean and enhanced keyband spectra of frame whistle signals, is the maximum log spectrum in all frequency bands, and It is The peak value of the frequency band. and is a constant, and the correlation between the subjective hearing test results and the objective measurement results can be maximized by adjusting. In the present invention, the upper limit of the analyzed frequency range is set to 24 kHz.

[0040] In the verification process of the present invention, it is necessary to determine the optimal parameter settings under the interference of various channels. Set to , to ensure the sparseness of the whistle signal. Since reverberation is frequency-dependent, Set to , the iteration parameter of the first step is , the termination condition is set as: ; In the second step, set the iteration parameter to , the termination condition is set as: ; In the formula, is the frequency band index Next , yes After iterations ; Since the method proposed by the present invention middle and Selection of underwater CIR time-frequency representation Therefore, in order to accurately capture the whistle characteristics, Set to 192. Again, to capture early reverberation and avoid overlap, Set to 128.

[0041] The main goal of the whistle feature representation stage in the present invention is to establish a And determine the parameters Adjusted optimal divergence . is optimized for characterizing the whistle profile in the spectrogram. , by iterative minimization Get the optimal dictionary. In the whistle reconstruction phase, its goal is to be based on minimize By imposing the constraint and Constructing the optimal activation matrix and time-frequency representation , thereby reconstructing the dedeverberated whistle signal. Due to the different objectives of the two stages, the optimal and May be different.

[0042] In order to determine the two-stage parameters The optimal value of , also adopts a two-stage optimization strategy. In the first stage, we focus on optimizing the parameters specific to the whistle feature representation stage First, Processing is done by minimizing the divergence Building an optimal dictionary , in obtaining After that, by minimizing get For the above optimization process, the present invention adopts a grid search method with a boundary setting of [0,2] and a step size of 0.05. The improvement of the segmented signal-to-noise ratio (SNR) verifies that the optimal dictionary is effective in representing the whistle signal. effectiveness in terms of.

[0043] In the second phase, we focus on determining the parameters of the whistle reconstruction phase and The optimal value of Got .when When , assuming that it obeys Gaussian distribution, the divergence term Simplified to the corresponding maximum a posteriori estimate MAP. The choice of penalty term consists of a combination of mixed constraints, which can be regarded as different types of prior distributions in MAP, where Corresponding to the Laplace prior, corresponds to a Gaussian prior. Therefore, choose To enhance the robustness and stability of the whistle reconstruction process. , the grid search method is also used, the boundary is set to [0,1], and the step size is 0.1. The improvement of the segment SNR of accuracy.

[0044] Furthermore, the effect of whistle dereverberation is verified based on a typical whistle segment. First, a typical pure whistle segment wav1 is selected, and its time-frequency (tf) spectrogram is as follows: Figure 1 As shown in Figure 1, three different whistle signals are included: concave, upsweep, and multiple signals. The time-frequency (TF) spectrogram is generated by short-time Fourier transform with a window length of 256 samples, an overlap of 128 samples, and 1024 FFT points. In order to evaluate the effectiveness of the proposed method in enhancing the dolphin whistle signal, the TF spectrogram is used. Introduce reverberation interference to wav1.

[0045] Secondly, according to the proposed two-stage parameter optimization method, the optimal parameter combination is determined ,at this time To verify the accuracy of the optimization algorithm, a method was used to simultaneously The optimization method is expressed as: ; Analyze different ranges of , and Improvement in the segmented SNR of the dereverberated wav1 segment under the parameter combination The largest observed , whose value is 6.98dB, verifies It is the optimal parameter choice to characterize the whistle characteristics.

[0046] When the algorithm proposed by the present invention is used to reconstruct the whistle signal under reverberation conditions, different The value will affect the ability of the dictionary to represent signal features during the reconstruction process, and different The value determines the constraints on the sparsity and attenuation characteristics of the UAC in the underwater acoustic channel.

[0047] When the relative distances between the hydrophone and the dolphin are 300 meters and 3000 meters respectively (the corresponding underwater channel impulse response CIR is expressed as and ), these CIRs are convolved with wav1 segments to generate whistle signals with different reverberation interferences, and their time-frequency (tf) spectrograms are shown in Figure 2 , Figure 3 Then, a two-stage parameter optimization method is used to optimize the parameters under different reverberation conditions. .

[0048] for , the optimal parameters obtained are (0.5, 1.35, 2), corresponding to is 6.67dB. , the optimal parameters are (0.1, 0.05, 2), corresponding to It is 7.45dB. Figure 4 and Figure 5 The dereverberation results in these two scenarios and under the optimal parameters are shown respectively. The figure shows that the algorithm proposed in the present invention can effectively remove reverberation in different scenarios.

[0049] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, a person skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some or all of the technical features may be replaced by equivalents, and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A hybrid constrained whistle dereverberation method based on divergence convolution non-negative matrix decomposition, characterized in that: include: S1. Construct a reverberation model of dolphin whistle signal and underwater acoustic channel impulse response CIR based on short-time Fourier transform STFT; S2, based on Divergence constructs a demeverberation model for dolphin whistle signals and obtains a basic dictionary of the whistle's time-frequency spectrum , matrix And the time-frequency matrix of CIR The total cost function is represents the dimension of matrix decomposition, is the discrete time index of CIR, is the frequency band index; S3. Building auxiliary functions ,get The update rule is updated and the optimal dictionary is obtained through iterative updates. , is the auxiliary dictionary used in the current iteration step, which is equivalent to the one in the next iteration step. ; S4. And joint constraints, build auxiliary functions and ,get and The iteration rule, It is under the frame index , after iterative update, the optimal matrix is ​​obtained And the optimal CIR matrix , is the auxiliary matrix used in the current iteration step, which is equivalent to the matrix in the next iteration step. , is the auxiliary time-frequency matrix used in the current iteration step, which is equivalent to the one in the next iteration step. ; S5. Pass , and Calculate the time-frequency standard evaluation of the pure whistle signal , the time domain of the whistle signal is reconstructed by inverse short-time Fourier transform (ISTFT).

2. The hybrid constrained whistle dereverberation method based on divergence convolution non-negative matrix decomposition according to claim 1 is characterized in that: Only the approximate models of the analysis filter and the synthesis filter are considered, and the reverberation model of the dolphin whistle signal and the underwater acoustic channel impulse response CIR is obtained by combining underwater passive acoustic monitoring with STFT: ； ； In the formula, The time-frequency matrix representing the reverberation model of the dolphin whistle signal and the underwater acoustic channel impulse response CIR, represents the time-frequency matrix of the pure whistle signal, Indicates the length of the CIR discrete form, is the frame index, Indicates the length of the Fourier transform analysis window.

3. The hybrid constrained whistle dereverberation method based on divergence convolution non-negative matrix decomposition according to claim 2 is characterized in that: The total cost function is: ； ； ； ； ； ； In the formula, is the total cost function, yes The cost function is yes The penalty item, yes The penalty item, yes Divergence, is the time-frequency of the reverberated whistle signal based on the elastic approximation preservation criterion under CIR interference, is the parameter time-frequency, is the total number of discrete time indices, is the upper limit of the dimension of matrix decomposition, is the approximation error in non-negative matrix factorization, is the penalty parameter, and yes The weight parameter, is the time-difference series matrix.

4. The hybrid constrained whistle dereverberation method based on divergence convolution non-negative matrix decomposition according to claim 3 is characterized in that: Will The divergence is decomposed into a convex part, a concave part, and a constant part: ； In the formula, It is the convex part. It is the concave part. is the constant part.

5. The hybrid constrained whistle dereverberation method based on divergence convolution non-negative matrix decomposition according to claim 4 is characterized in that: when When , the convex part, concave part and constant part are: ； ； ； In the formula, yes The parameter time-frequency under yes The parameter time-frequency under when When , the convex part, concave part and constant part are: ； ； ； when When , the convex part, concave part and constant part are: ； ； ； when When , the convex part, concave part and constant part are: ； ； ； In the formula, yes Next .

6. The hybrid constrained whistle dereverberation method based on divergence convolution non-negative matrix decomposition according to claim 5, characterized in that: Iterate and update to get the optimal dictionary Convert to Minimize ,definition for Auxiliary function, replaced by iterative update of auxiliary function Optimization: ； ； ； ； ； In the formula, is the intermediate parameter, is the auxiliary parameter time-frequency, yes In divergence The value of The convexity and differentiability of , minimizing the gradient to 0 , we can conclude The recursive formula of ; The recursive formula is: ； In the formula, yes After recursive calculation, we get , yes After recursive calculation, we get The value is The parameter time-frequency, is a very small positive number, yes The value is The recursive index of .

7. The hybrid constrained whistle dereverberation method based on divergence convolution non-negative matrix decomposition according to claim 6 is characterized in that: Helper functions related to activation matrices for: ； ； ； ； In the formula, is the intermediate parameter, yes The auxiliary matrix matrix is ​​in S3 The recursive formula is: ； In the formula, yes After recursive calculation, we get .

8. The hybrid constrained whistle dereverberation method based on divergence convolution non-negative matrix decomposition according to claim 7, characterized in that: The optimal matrix will be found Transformed to minimize under the sparsity constraint of the pure whistle time-frequency representation , build auxiliary functions : ； ； ； ； In the formula, is an intermediate parameter, in S4 The recursive formula is: ； In the formula, yes The value is The auxiliary parameters of time-frequency, yes The value is The auxiliary parameters of time-frequency, yes The value is The recursive index of .

9. The hybrid constrained whistle dereverberation method based on divergence convolution non-negative matrix decomposition according to claim 8, characterized in that: The optimal CIR matrix will be found The transformation is to minimize the sparsity and attenuation characteristics of the underwater sound channel in the time domain. , build auxiliary functions : ； ； ； ； ； In the formula, is the intermediate parameter, The recursive formula is: ； ； ； In the formula, is a recursive intermediate variable, yes The frame index obtained after recursive calculation is , is a diagonal matrix, is the unit diagonal matrix, yes After recursive calculation, we get The value is The auxiliary parameters of time-frequency, yes After recursive calculation, we get The value is The auxiliary parameters of time-frequency, is the recursive difference, .

10. The hybrid constrained whistle dereverberation method based on divergence convolution non-negative matrix decomposition according to claim 9, characterized in that: for: ； ； In the formula, is the time-varying gain function; Reconstruct the whistle signal using the inverse short-time Fourier transform: ； In the formula, It is a pure whistle signal after removing reverberation. The length of the inverse short-time Fourier transform is The synthetic window, is the discrete time offset, is the counting parameter, is an imaginary unit, is a natural constant.

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