A sparse constraint strength adaptive line spectral enhancement method and system
By adaptively adjusting the sparsity constraint strength, the instability problem of traditional line spectrum enhancement methods under complex colored noise conditions is solved, and stable and efficient line spectrum enhancement is achieved in edge computing environments.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- SOUTHEAST UNIV
- Filing Date
- 2026-03-06
- Publication Date
- 2026-06-09
AI Technical Summary
Traditional line spectrum enhancement methods are unstable in convergence under complex colored noise conditions and have strong dependence on sparse constraint parameters, making it difficult to achieve stable and efficient line spectrum enhancement in edge computing environments.
An adaptive adjustment mechanism for sparse constraint strength is introduced. The probability distribution of the frequency domain coefficient vector is modeled by the kernel density estimation method, and the sparse constraint strength is adaptively updated to construct a line spectrum enhancement model with frequency domain adaptive sparse constraint.
The algorithm's robustness and adaptability under colored noise conditions were improved, its dependence on human experience settings was reduced, and a stable line spectrum enhancement effect was achieved.
Smart Images
Figure CN122173758A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of passive sonar detection technology, specifically relating to a line spectrum enhancement method and system with sparse constraint strength adaptive. Background Technology
[0002] Underwater target detection is a crucial research area in underwater acoustic signal processing. Underwater target detection is generally categorized into active and passive modes. Passive detection does not require active signal transmission; instead, it relies on passive sonar to receive the radiated noise of the target platform to determine its presence. The radiated noise of an underwater acoustic target consists of a broadband continuous spectrum and a narrowband discrete line spectrum. The line spectrum components are typically caused by the target platform's mechanical vibrations, propulsion system, etc., and carry characteristic information closely related to the target. It boasts advantages such as long propagation distance and high signal-to-noise ratio, and is therefore widely used in passive detection missions.
[0003] However, with the continuous improvement of target platform noise reduction capabilities in recent years, line spectrum components are often submerged in strong background noise at long distances or under weak target conditions, significantly increasing the difficulty of extraction. Meanwhile, marine environmental background noise typically exhibits distinct colored characteristics, rather than ideal white noise. Therefore, line spectrum enhancement algorithms not only need to possess a certain enhancement capability but also need robustness in simultaneously enhancing multiple target line spectrum components under complex statistical characteristic variations. Traditional line spectrum enhancement methods are often quite sensitive to model assumptions and parameter settings under complex colored noise conditions, easily leading to convergence instability, fluctuations in enhancement performance, or even failure, making it difficult to guarantee stable enhancement of weak line spectra.
[0004] With the development and widespread application of distributed intelligent marine monitoring systems, passive sonar systems are increasingly being deployed on unmanned platforms such as ocean buoys, underwater moorings, and underwater unmanned vehicles. Due to limitations in underwater information transmission capabilities, it is extremely difficult to transmit signal data acquired by sensors on these underwater unmanned platforms back to shore-based processing centers. Therefore, sensor data preprocessing, feature enhancement, and extraction must be performed on front-end edge computing nodes to reduce data transmission burden and improve system response speed. Furthermore, the energy supply of underwater unmanned platforms is limited, and the storage and computing capabilities of their onboard edge computing nodes are significantly different from those of shore-based systems. This places high demands on the real-time performance of algorithms, requiring signal enhancement and feature extraction to be completed under limited computing resources. Therefore, in practical engineering deployments, line spectrum enhancement algorithms typically need to balance enhancement performance with real-time processing capabilities to adapt to application scenarios such as edge computing.
[0005] Adaptive Line Enhancer (ALE) is an effective line spectrum enhancement technique that leverages the strong correlation of line spectra in the time domain and the weak correlation of broadband noise to improve the output signal-to-noise ratio (SNR). ALE does not rely on prior target information and can dynamically adjust the filter coefficient vector according to the input data, and has been validated in various scenarios. However, under conditions of low SNR and colored background noise, traditional ALE and its improved methods often suffer from strong parameter selection dependence and unstable convergence. To improve performance, researchers have recently implemented ALE in the frequency domain and applied sparse constraints to the frequency domain coefficient vector to further enhance the line spectrum. However, existing frequency domain sparse constraint methods typically use fixed or empirically set sparse constraint strengths, which can easily lead to instability in the coefficient vector update process when the signal statistical characteristics change. In real-time processing environments oriented towards edge computing, higher demands are placed on algorithm stability and adaptability. Summary of the Invention
[0006] Purpose of the invention: The purpose of this invention is to propose a line spectrum enhancement method and system with adaptive sparse constraint strength. It addresses the problem of algorithm convergence instability caused by improper fixing or updating of frequency domain sparse constraint parameters under colored background noise conditions. By introducing an adaptive adjustment mechanism for sparse constraint strength, the stability and robustness of the line spectrum enhancement process are improved.
[0007] Technical solution: To achieve the above-mentioned objective, the present invention provides a sparse constraint strength adaptive line spectrum enhancement method, characterized by comprising the following steps:
[0008] Step 1: Initialize the parameters used for line spectrum enhancement and the frequency domain coefficient vector of the adaptive filter;
[0009] Step 2: Delay and Fourier transform the input time-domain signal to obtain the frequency-domain input signal;
[0010] Step 3: Based on the frequency domain coefficient vector, perform weighted processing on the frequency domain input signal to obtain the line spectrum enhanced output signal, and calculate the corresponding error signal;
[0011] Step 4: Construct a cost function based on the error signal and introduce a sparse constraint term weighted by the sparse constraint strength.
[0012] Step 5: Minimize the Kullback-Leibler (KL) divergence between the probability distribution of the frequency domain coefficient vector and the sparse prior distribution, and adaptively iteratively update the sparse constraint strength. Here, the kernel density estimation method is used to model the probability distribution of the frequency domain coefficient vector, and a mapping relationship inversely proportional to the bandwidth parameter in the estimation is introduced. The sparse prior distribution is taken as the Dirac function, the KL divergence optimization objective is simplified, and the gradient of the objective function with respect to the sparse constraint strength is obtained by combining the mapping relationship.
[0013] Step 6: Update the frequency domain coefficient vector based on the error signal and the iteratively updated sparse constraint strength;
[0014] Step 7: Repeat steps 2 through 6 to process all time-domain input signals.
[0015] Preferably, in step 4, the cost function The expression is:
[0016]
[0017] in, For kernel width, This represents an exponential function with the natural constant as its base. To enhance the output signal of the line spectrum With the corresponding time-domain input signal Error signals between Here, L is the sparse regularization parameter, used to balance the weights of the sparse constraint term and the original cost term, and L is the order of the adaptive filter. Represents the frequency domain coefficient vector at time n The i-th component, Let be the sparse constraint strength at time n, which is adaptively updated during the iteration process and is used to adjust the constraint strength of the sparse constraint term on the frequency domain coefficient vector.
[0018] Preferably, in step 5, the goal is to minimize the KL divergence between the probability distribution and the sparse prior distribution of the frequency domain coefficient vector. To establish the sparse constraint strength with respect to time n, we set the target value. The optimization criterion, the objective function is expressed as:
[0019]
[0020] in, Let n be a random variable used to describe the statistical properties of its frequency domain coefficients, and let n be the set of observed samples in the frequency domain coefficient vector. , The sparse prior distribution is used to characterize the sparsity of frequency domain coefficients. A probability density estimate is constructed based on the observation samples at time n, used to characterize the current sparse constraint strength. Statistical distribution characteristics of the lower frequency domain coefficients.
[0021] Preferably, in step 5, the probability density function of the frequency domain coefficient vector is modeled using a Gaussian kernel-based kernel density estimation method, and its expression is:
[0022]
[0023] in, For the bandwidth parameter in kernel density estimation, and Satisfy mapping relationship .
[0024] Preferably, in step 5, under the condition that the sparse prior distribution function is a Dirac function, the objective function is simplified to a form that depends only on the value of the probability density estimation function at zero, and its relation to... The gradient expression is as follows:
[0025]
[0026] Preferably, in step 5, the mapping relationship is considered. , regarding The conversion is related to the sparse constraint strength. The gradient is calculated, and the stochastic gradient descent method is used to... By performing adaptive updates, the iterative update formula is obtained as follows:
[0027] ;
[0028] in, This refers to the learning rate.
[0029] The present invention provides a sparse constraint strength adaptive line spectrum enhancement system for implementing the aforementioned sparse constraint strength adaptive line spectrum enhancement method, comprising:
[0030] The initialization module is used to initialize the parameters for line spectrum enhancement and the frequency domain coefficient vector of the adaptive filter;
[0031] The frequency domain transformation module is used to perform time-delay and Fourier transform on the input time-domain signal to obtain the frequency-domain input signal;
[0032] The output calculation module is used to perform weighted processing on the frequency domain input signal based on the frequency domain coefficient vector to obtain the line spectrum enhanced output signal and calculate the corresponding error signal.
[0033] The cost function construction module is used to construct a cost function based on the error signal and introduce sparse constraint terms weighted by the sparse constraint strength.
[0034] The sparse constraint strength update module is used to minimize the KL divergence between the probability distribution of the frequency domain coefficient vector and the sparse prior distribution, and adaptively iteratively update the sparse constraint strength. The kernel density estimation method is used to model the probability distribution of the frequency domain coefficient vector, and a mapping relationship inversely proportional to the bandwidth parameter in the estimation is introduced. The sparse prior distribution is taken as the Dirac function, the KL divergence optimization objective is simplified, and the gradient of the objective function with respect to the sparse constraint strength is obtained by combining the mapping relationship.
[0035] The coefficient update module is used to update the frequency domain coefficient vector based on the error signal and the sparse constraint strength after iterative update.
[0036] The iterative control module is used to control the frequency domain transformation module, output calculation module, cost function construction module, sparse constraint strength update module and coefficient update module to execute cyclically and process all time-domain input signals.
[0037] The present invention also provides a computer system, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the computer program, when executed by the processor, implements the steps of the described sparse constraint strength adaptive line spectrum enhancement method.
[0038] The present invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the described method for adaptive line spectrum enhancement based on sparse constraint strength.
[0039] The present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the described sparse constraint strength adaptive line spectrum enhancement method.
[0040] Beneficial Effects: This invention introduces the concept of frequency-domain sparse modeling, incorporating the sparse distribution characteristics of the target line spectrum in the frequency domain into the coefficient vector update process of the adaptive line spectrum enhancer, thus constructing a frequency-domain adaptive sparse constraint line spectrum enhancement model. Through modeling and analyzing the statistical distribution of frequency-domain coefficients, the adaptive adjustment of the sparse constraint strength is achieved, effectively reducing the dependence of sparse constraint parameters on manual experience settings and enhancing the robustness of the algorithm in colored noise. Compared with existing technologies, this invention has the following outstanding advantages:
[0041] 1. Adaptive adjustment of sparsity constraint strength enhances algorithm adaptability. This invention introduces an adaptive adjustment mechanism for sparsity constraint strength, avoiding the problem of traditional methods where sparsity constraint parameters depend on empirical settings. This allows the sparsity constraint strength to be dynamically adjusted according to the statistical distribution characteristics of the frequency domain coefficients, improving the adaptability and robustness of the algorithm under different acoustic environments and noise conditions while ensuring the line spectrum enhancement effect.
[0042] 2. The algorithm has a simple structure and good engineering feasibility. The overall structure of this invention is clear, the physical meaning of the parameters is well-defined, it does not rely on complex prior assumptions or high-dimensional parameter searches, it is easy to implement and deploy in engineering, and it can run stably in real-time underwater acoustic signal processing application environments and obtain continuous and reliable line spectrum enhancement effects. Attached Figure Description
[0043] Figure 1 This is a flowchart illustrating the implementation of the method according to an embodiment of the present invention.
[0044] Figure 2 This is a frequency-domain adaptive line spectrum enhancement structure in an embodiment of the present invention.
[0045] Figure 3 The above are the time-frequency spectra of the input signals in two experimental examples in this invention, with three spectral lines at 114, 127, and 142 Hz.
[0046] Figure 4 The time spectrum diagram of the output signal in Experiment Example 1 shows three spectral lines at 114, 127, and 142 Hz.
[0047] Figure 5 The time spectrum of the output signal in Experiment Example 2 has three spectral lines at 114, 127, and 142 Hz. Detailed Implementation
[0048] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. The specific implementation methods of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
[0049] like Figure 1 As shown, this embodiment of the invention discloses a sparse constraint strength adaptive line spectrum enhancement method, combined with... Figure 2The frequency-domain adaptive line spectrum enhancement structure shown in this method first initializes the relevant parameters; then, it processes the input time-domain signal and maps it to the frequency domain; based on this, it uses a line spectrum enhancement filter to weight the frequency-domain input signal, obtains the line spectrum enhanced output signal, and calculates the corresponding error signal; it constructs a cost function containing a sparse regularization term based on the error signal, and adaptively adjusts the sparsity constraint strength according to the statistical distribution characteristics of the frequency-domain coefficient vector; under the constraint of the sparse constraint strength update result, iteratively updates the frequency-domain coefficient vector of the line spectrum enhancement filter; the above process is repeated until the time-domain signal iteration is completed, and a stable line spectrum enhancement result is output. The following describes the detailed steps of the sparse constraint strength adaptive line spectrum enhancement method described in this embodiment, using a simulated ship radiated noise time-domain signal as the processing object.
[0050] Step 1: Initialize the parameters used for line spectrum enhancement and the frequency domain coefficient vector of the adaptive filter. The parameters include order, delay, step size, kernel width, and initial sparsity constraint strength. Specifically, this includes the following steps:
[0051] Step 1.1: Set the order L and delay Δ of the adaptive filter;
[0052] Step 1.2, set the parameters used for line spectrum enhancement. , , ,in This is the update step size for the frequency domain coefficient vector; The kernel width is determined according to Silverman's rule. The sparse regularization parameter has a value range set to... 10 -4 ~10 -3 times;
[0053] Step 1.3: Set the initial value of the sparse constraint strength. ;
[0054] Step 1.4: Initialize a frequency domain coefficient vector of length L. , where n is the index at the current time. Let L(L) be the (L-1)th element of the frequency domain coefficient vector, [·] T This represents the transpose of a vector.
[0055] Step 2: Delay and Fourier transform the input time-domain signal to obtain the frequency-domain input signal. Details are as follows:
[0056] At time n, select L sampling points from the time-domain input signal up to and including that time, and construct the time-domain input sequence in descending order of time index. ,in N is the total number of signal sampling points.
[0057] Introducing a delay Δ, a time-domain delayed input sequence is constructed. :
[0058]
[0059] Wherein, the value of time n must satisfy... .
[0060] To fully utilize the frequency domain sparsity of the line spectrum, the time-delayed input sequence is mapped to the frequency domain using the Discrete Fourier Transform (DFT) to obtain the frequency domain input signal. :
[0061]
[0062] in, It is a normalized DFT unitary matrix and satisfies :
[0063]
[0064] Step 3: Based on the frequency domain coefficient vector, perform weighted processing on the frequency domain input signal to obtain the line spectrum enhanced output signal, and calculate the corresponding error signal, as follows:
[0065] Based on the adaptive filter coefficient vector at time n, the frequency domain input signal is weighted to obtain the line spectrum enhanced output signal at time n. :
[0066]
[0067] in, This represents the conjugate transpose of a vector.
[0068] Line spectrum enhancement output signal Error signal between the corresponding time domain signal for:
[0069]
[0070] Step 4: Construct a cost function based on the error signal obtained in Step 3, and introduce a sparse constraint term weighted by the sparse constraint strength. The specific cost function constructed is as follows. The expression is:
[0071]
[0072] in, Represents an exponential function with the natural constant as its base; This is a sparse regularization parameter used to balance the weights of the sparse constraint term and the original cost term. Represents the frequency domain coefficient vector at time n The i-th component, Let be the sparse constraint strength at time n, which is adaptively updated during the iteration process and is used to adjust the constraint strength of the sparse constraint term on the frequency domain coefficient vector.
[0073] Step 5: Minimize the KL divergence between the probability distribution of the frequency domain coefficient vector and the sparse prior distribution, and adaptively iteratively update the sparse constraint strength, which includes the following steps:
[0074] Step 5.1, minimize the KL divergence between the probability distribution of the frequency domain coefficient vector and the sparse prior distribution. To establish the sparse constraint strength with respect to time n, we set the target value. The optimization criterion, whose objective function can be expressed as:
[0075]
[0076] in, Let n be a random variable used to describe the statistical properties of its frequency domain coefficients, and let n be the set of observed samples in the frequency domain coefficient vector. , The sparse prior distribution is used to characterize the sparsity of frequency domain coefficients. A probability density estimate is constructed based on the observation samples at time n, used to characterize the current sparse constraint strength. Statistical distribution characteristics of the lower frequency domain coefficients.
[0077] Step 5.2: The probability density function of the frequency domain coefficient vector is modeled using a Gaussian kernel-based kernel density estimation method. Its expression is:
[0078]
[0079] in, The bandwidth parameter in kernel density estimation controls the range of influence of the kernel function on the amplitude differences of frequency domain coefficients, thereby affecting the distribution shape of the estimated probability density.
[0080] Due to bandwidth parameters With sparsity constraint strength To maintain consistency in constraining the concentration characteristics of frequency domain coefficients, and to achieve an equivalent characterization and unified adjustment of the sparsity constraint strength within the kernel density estimation framework, the following mapping relationship is introduced:
[0081]
[0082] Step 5.3, under the condition that the sparse prior distribution function is the Dirac function δ(w), the objective function in step 5.1 can be simplified to a form that depends only on the value of the probability density estimation function at the zero point. Combining the mapping relationship between the sparse constraint strength and the kernel width parameter, the simplified objective function is then... Taking the partial derivative, we obtain its gradient as:
[0083]
[0084] Step 5.4, combining the mapping relationship The gradient result obtained in step 5.3 is converted into a function of the sparse constraint strength. The gradient is calculated, and the stochastic gradient descent method is used to... By performing adaptive updates, the iterative update formula is obtained as follows:
[0085]
[0086] in, This refers to the learning rate.
[0087] Step 6: Update the frequency domain coefficient vector based on the error signal and the sparse constraint strength after iteration, as follows:
[0088] The gradient expression of the cost function at time n is:
[0089]
[0090] The gradient expression of the cost function at time n is about the frequency domain coefficient vector. Unlike real numbers, the gradient of the conjugate form of the function gives the steepest descent direction of the optimization surface. Therefore, the update of the frequency domain coefficient vector can be expressed as:
[0091]
[0092] in, This is an element-wise symbolic function.
[0093] Step 7: Iterate through steps 2 to 6 to process all time-domain input signals, as follows:
[0094] Let n = n+1. If the input data has not been fully iterated, i.e., n < N, then return to step 2 to continue updating the frequency domain coefficient vector; otherwise, the iteration ends.
[0095] The following section combines two simulation examples, and... Figures 3 to 5 The method of the present invention will be illustrated by example and the effects of the present invention will be verified.
[0096] In Experiment Example 1, the processed data is a simulated time-domain signal of ship radiated noise, containing three spectral lines at 114, 127, and 142 Hz, with colored background noise simulating a marine environment added. The sampling rate is 512 Hz, the duration is 250 seconds, and the number of data points N = 128000. Based on step 1 above, the relevant parameters are initialized as follows: the order L of the adaptive filter can generally be taken as 1000~6000, here L = 4096; the delay Δ can generally be taken as 50~200, here Δ = 100; the update step size of the frequency domain coefficient vector is set. = 10 -5 Core width = 0.5, sparse regularization parameter = 10 -9 ; Set the initial value of the sparse constraint strength in the parameters used for line spectrum enhancement. =500; Initialize the frequency domain coefficient vector of length L. .
[0097] The method of the present invention shall be performed in accordance with steps 2 to 7 above.
[0098] Experimental Example 1 shows that, using the method of this invention, under complex colored background noise conditions, it is possible to stably enhance the low-frequency line spectrum of underwater target radiated noise, such as... Figure 4 As shown, the three target line spectra at 114, 127, and 142 Hz in the output spectrum are clearly visible and remain stable throughout the observation time, thus providing a reliable signal basis for subsequent line spectrum detection and extraction.
[0099] The overall processing flow of Experiment 2 is the same as that of Experiment 1, both including steps 1 to 7. The difference lies in the initial setting parameters for the sparsity constraint strength. In Experiment 2, when setting the parameters for line spectrum enhancement in step 1, the initial value of the sparsity constraint strength is set to... =50, and the other parameter settings and processing methods of each step are consistent with those of Experiment Example 1.
[0100] With the above settings, Experiment 2 further demonstrates that, under different initial sparse constraint strengths, the line spectrum enhancement method based on adaptive sparse constraint strength can still achieve adaptive adjustment of the sparse constraint strength through an iterative process, effectively reducing the dependence of sparse constraint parameters on human experience settings and enhancing the robustness of the algorithm in colored noise.
[0101] Based on the same inventive concept, this invention discloses a sparse constraint strength adaptive line spectrum enhancement system, used to implement the sparse constraint strength adaptive line spectrum enhancement method described in any of the foregoing embodiments, comprising: an initialization module for initializing parameters for line spectrum enhancement and the frequency domain coefficient vector of the adaptive filter; a frequency domain transformation module for performing delay and Fourier transform on the input time domain signal to obtain a frequency domain input signal; an output calculation module for weighting the frequency domain input signal based on the frequency domain coefficient vector to obtain a line spectrum enhanced output signal and calculating the corresponding error signal; a cost function construction module for constructing a cost function based on the error signal and introducing a sparse constraint term weighted by the sparse constraint strength; and a sparse constraint strength update module for minimizing the frequency constraint strength. The KL divergence between the probability distribution of the frequency domain coefficient vector and the sparse prior distribution is used to adaptively and iteratively update the sparse constraint strength. A kernel density estimation method is employed to model the probability distribution of the frequency domain coefficient vector, introducing a mapping relationship between the bandwidth parameter in the estimation and the sparse constraint strength. The sparse prior distribution is taken as a Dirac function, simplifying the KL divergence optimization objective. The gradient of the objective function with respect to the sparse constraint strength is obtained by combining the mapping relationship. A coefficient update module updates the frequency domain coefficient vector based on the error signal and the iteratively updated sparse constraint strength. An iterative control module controls the cyclic execution of the frequency domain transformation module, output calculation module, cost function construction module, sparse constraint strength update module, and coefficient update module, processing all time-domain input signals.
[0102] An embodiment of the present invention discloses a computer system, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the computer program is executed by the processor, it implements the steps of a sparse constraint strength adaptive line spectrum enhancement method as described in any of the foregoing embodiments.
[0103] The present invention discloses a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps of a sparse constraint strength adaptive line spectrum enhancement method as described in any of the foregoing embodiments.
[0104] The present invention discloses a computer program product, including a computer program, which, when executed by a processor, implements the steps of a sparse constraint strength adaptive line spectrum enhancement method as described in any of the foregoing embodiments.
[0105] The program code used to implement the method of the present invention can be written in any combination of one or more programming languages. This program code can be provided to a processor or controller of a general-purpose computer, a special-purpose computer, or other programmable data processing device, such that when executed by the processor or controller, the program code causes the steps of the method of the present invention to be performed.
[0106] It should be noted that the various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the systems or apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple, and relevant parts can be referred to the method section.
[0107] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of this application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these modifications and improvements all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.
Claims
1. A line spectrum enhancement method with adaptive sparse constraint strength, characterized in that, Includes the following steps: Step 1: Initialize the parameters used for line spectrum enhancement and the frequency domain coefficient vector of the adaptive filter; Step 2: Delay and Fourier transform the input time-domain signal to obtain the frequency-domain input signal; Step 3: Based on the frequency domain coefficient vector, perform weighted processing on the frequency domain input signal to obtain the line spectrum enhanced output signal, and calculate the corresponding error signal; Step 4: Construct a cost function based on the error signal and introduce a sparse constraint term weighted by the sparse constraint strength. Step 5: Minimize the KL divergence between the probability distribution of the frequency domain coefficient vector and the sparse prior distribution, and adaptively iteratively update the sparse constraint strength. The kernel density estimation method is used to model the probability distribution of the frequency domain coefficient vector. A mapping relationship between the bandwidth parameter in the estimation and the sparse constraint strength is introduced. The sparse prior distribution is taken as the Dirac function. The KL divergence optimization objective is simplified. The gradient of the objective function with respect to the sparse constraint strength is obtained by combining the mapping relationship. Step 6: Update the frequency domain coefficient vector based on the error signal and the iteratively updated sparse constraint strength; Step 7: Repeat steps 2 through 6 to process all time-domain input signals.
2. The line spectrum enhancement method with adaptive sparse constraint strength according to claim 1, characterized in that, In step 4, the cost function The expression is: ； in, For kernel width, This represents an exponential function with the natural constant as its base. To enhance the output signal of the line spectrum With the corresponding time-domain input signal Error signals between Here, L is the sparse regularization parameter, used to balance the weights of the sparse constraint term and the original cost term, and L is the order of the adaptive filter. Represents the frequency domain coefficient vector at time n The i-th component, Let be the sparse constraint strength at time n, which is adaptively updated during the iteration process and is used to adjust the constraint strength of the sparse constraint term on the frequency domain coefficient vector.
3. The line spectrum enhancement method with adaptive sparse constraint strength according to claim 1, characterized in that, In step 5, the goal is to minimize the KL divergence between the probability distribution and the sparse prior distribution of the frequency domain coefficient vector. To establish the sparse constraint strength with respect to time n, we set the target value. The optimization criterion, the objective function is expressed as: ； in, Let n be a random variable used to describe the statistical properties of its frequency domain coefficients, and let n be the set of observed samples in the frequency domain coefficient vector. , The sparse prior distribution is used to characterize the sparsity properties of frequency domain coefficients. A probability density estimate is constructed based on the observation samples at time n, used to characterize the current sparse constraint strength. Statistical distribution characteristics of the lower frequency domain coefficients.
4. The line spectrum enhancement method with adaptive sparse constraint strength according to claim 1, characterized in that, In step 5, the probability density function of the frequency domain coefficient vector is modeled using a Gaussian kernel-based kernel density estimation method, and its expression is: ； in, For the bandwidth parameter in kernel density estimation, Let L represent the random variable used to describe the statistical characteristics of the frequency domain coefficients, and let L be the order of the adaptive filter. This represents an exponential function with the natural constant as its base. Represents the frequency domain coefficient vector at time n The sparse constraint strength of the i-th component at time n and Satisfy mapping relationship .
5. The line spectrum enhancement method with adaptive sparse constraint strength according to claim 4, characterized in that, In step 5, given that the sparse prior distribution function is the Dirac function, the objective function simplifies to a form that depends only on the value of the probability density estimation function at the zero point. The gradient expression is as follows: 。 6. The line spectrum enhancement method with adaptive sparse constraint strength according to claim 5, characterized in that, In step 5, the mapping relationship is combined. , regarding The conversion is related to the sparse constraint strength. The gradient is calculated, and the stochastic gradient descent method is used to... By performing adaptive updates, the iterative update formula is obtained as follows: ； in, This refers to the learning rate.
7. A sparse constraint strength adaptive line spectrum enhancement system, used to implement the sparse constraint strength adaptive line spectrum enhancement method according to any one of claims 1-6, characterized in that, include: The initialization module is used to initialize the parameters for line spectrum enhancement and the frequency domain coefficient vector of the adaptive filter; The frequency domain transformation module is used to perform time-delay and Fourier transform on the input time-domain signal to obtain the frequency-domain input signal; The output calculation module is used to perform weighted processing on the frequency domain input signal based on the frequency domain coefficient vector to obtain the line spectrum enhanced output signal and calculate the corresponding error signal. The cost function construction module is used to construct a cost function based on the error signal and introduce sparse constraint terms weighted by the sparse constraint strength. The sparse constraint strength update module is used to minimize the KL divergence between the probability distribution of the frequency domain coefficient vector and the sparse prior distribution, and adaptively iteratively update the sparse constraint strength. The kernel density estimation method is used to model the probability distribution of the frequency domain coefficient vector. A mapping relationship between the bandwidth parameter in the estimation and the sparse constraint strength is introduced. The sparse prior distribution is taken as the Dirac function. The KL divergence optimization objective is simplified. The gradient of the objective function with respect to the sparse constraint strength is obtained by combining the mapping relationship. The coefficient update module is used to update the frequency domain coefficient vector based on the error signal and the sparse constraint strength after iterative update. The iterative control module is used to control the frequency domain transformation module, output calculation module, cost function construction module, sparse constraint strength update module and coefficient update module to execute cyclically and process all time-domain input signals.
8. A computer system comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the computer program is executed by the processor, it implements the steps of the line spectrum enhancement method according to any one of claims 1-6, which is an adaptive sparse constraint strength method.
9. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the steps of the line spectrum enhancement method according to any one of claims 1-6, which is an adaptive sparse constraint strength method.
10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the steps of the line spectrum enhancement method according to any one of claims 1-6, which is an adaptive sparse constraint strength method.