Two-dimensional block sparse Bayesian learning algorithm for sound field reconstruction

Abstract

The invention relates to the field of acoustic signal processing, and discloses a two-dimensional block sparse Bayesian learning algorithm for sound field reconstruction, which comprises the following steps of: S1, constructing a sound field receiving signal model of a microphone array, and representing a sound field signal as a linear combination of sparse signals; s2, under the Bayesian framework, applying coupling prior to the coefficient of the signal by using the structural correlation of the two-dimensional block sparse sound source, and introducing hyper-prior distribution for the hyper-parameter of the prior distribution; and S3, estimating parameters of the sparse signals through an expectation maximization algorithm. The sparsity of the block sparse sound source is jointly controlled through coupling constraint, the algorithm can adaptively learn the two-dimensional structure of the block sparse sound source, and block sparse solution is promoted. And in combination with an expectation maximization algorithm, sparse representation and parameter estimation can be effectively carried out on the two-dimensional block sparse signal. The coupling prior mode enables the algorithm to more accurately capture the structural features of the sparse sound source of the two-dimensional block in the sound field when processing the sound field signal, thereby realizing accurate sound field reconstruction.

Description

Technical Field

[0001] The present invention relates to the field of acoustic signal processing, and in particular to a two-dimensional block sparse Bayesian learning algorithm for sound field reconstruction. Background Art

[0002] Sound field reconstruction technology has garnered widespread attention in recent years, particularly in areas such as acoustic imaging, noise control, and sound source localization. Traditional sound field reconstruction methods primarily rely on microphone arrays to capture sound field signals and then reconstruct them using signal processing algorithms. However, these traditional methods have limitations when dealing with complex sound field environments. For example, traditional methods are typically designed to handle the sound field distribution of a single sound source and are less effective when dealing with sound fields with complex source distributions.

[0003] Research has shown that sparse Bayesian learning algorithms have autoregressive and uncertain estimation characteristics, can adaptively update parameters, and have been widely used in the field of signal processing. By introducing sparse prior distributions, sparse Bayesian learning algorithms can effectively represent signals sparsely, thereby improving the accuracy and efficiency of signal processing. However, sparse Bayesian learning algorithms in the existing technology still face some challenges in sound field reconstruction. For example, existing sparse Bayesian learning algorithms have little research on block sparse sound sources, and most of them focus on one-dimensional block sparse sound sources. However, in practice, sound sources often exhibit complex spatial distribution characteristics and have two-dimensional block sparsity characteristics, that is, the sound source structure exhibits block sparse characteristics in both the horizontal and vertical directions. This multi-dimensional block sparsity characteristic requires the algorithm to consider not only the sparsity of the sound source in a single dimension, but also the multi-dimensional adjacent relationship of the sound source in space, so as to more comprehensively reflect the structured characteristics of the sound source.

[0004] Therefore, developing a sound field reconstruction algorithm that can adapt to different sound field environments and has higher accuracy and robustness is an important issue facing current sound field reconstruction technology. Summary of the Invention

[0005] In view of the deficiencies of the prior art, the present invention provides a two-dimensional block sparse Bayesian learning algorithm for sound field reconstruction, which solves the problems raised in the above background technology.

[0006] To achieve the above objectives, the present invention is implemented through the following technical solutions: a two-dimensional block sparse Bayesian learning algorithm for sound field reconstruction, comprising the following steps:

[0007] S1. Construct a sound field receiving signal model of the microphone array and represent the sound field signal as a linear combination of sparse signals;

[0008] S2. Under the Bayesian framework, the structural correlation of the two-dimensional block sparse sound source is used to impose a coupling prior on the coefficients of the signal, and a hyper-prior distribution is introduced for the hyper-parameters of the prior distribution;

[0009] S3. estimating the parameters of the sparse signal by using an expectation maximization algorithm;

[0010] S4. Reconstruct the sound field signal based on the parameter estimation result, and achieve reconstruction of the sound field.

[0011] Preferably, the sound field signal model takes into account the sparse characteristics of the signal in space and the propagation characteristics of the sound field, and the sound field signal model is:

[0012] y=Ax+n

[0013] Where y is the measurement signal of the microphone array, A is the steering vector matrix of the scanning grid plane, x is the sparse signal, and n is the noise signal.

[0014] Preferably, the matrix A is calculated using the Green's function of the sound field and the geometric position information of the microphone array, wherein the Green's function is used to describe the propagation characteristics of the sound field in space.

[0015] Preferably, the sparse prior distribution in step S2 is a Gaussian prior distribution, so as to facilitate the selection of a conjugate distribution and simplify the calculation process.

[0016] Preferably, the coupling prior in step S2 means that the parameters of each grid point on the target plane are controlled not only by its own hyperparameters, but also by the hyperparameters of the grid points at adjacent positions, thereby adaptively learning the two-dimensional structure of the block sparse sound source and promoting block sparse solution.

[0017] Preferably, the hyper-prior distribution is a Gamma distribution, which is used to model the hyper-parameters of the sparse prior distribution to achieve adaptive learning and sparsity constraints on sparse signal coefficients.

[0018] Preferably, the parameter estimation step in step S3 includes the following sub-steps:

[0019] S301, input observation data, steering vector matrix and coupling parameters;

[0020] S302, initializing the parameters and convergence conditions of the sparse signal, including the number of iterations and tolerance value;

[0021] S303, iteratively updating the posterior distribution of the parameters through an expectation-maximization algorithm;

[0022] S304, determining whether the iterative update satisfies a convergence condition; if so, stopping the iteration and outputting the estimated values of the coefficients of the sparse signal and its hyperparameters; otherwise, continuing the iterative update;

[0023] S305: After the iterative update is completed, the signal to be reconstructed is output.

[0024] Preferably, the algorithm further comprises a post-processing step for the sound field reconstruction result, and the post-processing step comprises a smoothing process and a noise suppression process for the reconstructed sound field.

[0025] Preferably, the algorithm is applicable to a sound field environment with two-dimensional block sparse sound sources, and can adaptively learn the structural information of the sound sources and update parameters in different scenarios.

[0026] The present invention provides a two-dimensional block sparse Bayesian learning algorithm for sound field reconstruction. It has the following effects:

[0027] 1. This paper constructs a universal sound field reception signal model by considering the sparse nature of signals in space and the propagation characteristics of the sound field. This model makes the algorithm more widely applicable in practical applications and can meet the needs of sound field reconstruction in different scenarios.

[0028] 2. By introducing a Gaussian sparse prior distribution and a Gamma hyper-prior distribution, combined with Bayesian inference, this invention effectively performs sparse representation and parameter estimation on sound field signals. This sparse representation method enables the algorithm to more accurately capture key features of the sound field when processing sound field signals, thereby achieving high-precision sound field reconstruction. Compared with traditional methods, this algorithm significantly improves the accuracy of sound field reconstruction, especially when dealing with complex sound field environments.

[0029] 3. This paper uses a parameter coupling approach to construct a Bayesian hierarchical model, leveraging the two-dimensional structural correlation of block-sparse sound sources to assign a block-sparse prior to the variables. The parameters of each grid point in the model are controlled not only by its own hyperparameters but also by the hyperparameters of adjacent locations. This coupled constraint jointly controls the sparsity of the block-sparse sound source, promoting a block-sparse solution. In this way, the algorithm can adaptively learn the two-dimensional structure of block-sparse sound sources, facilitating a block-sparse solution.

[0030] 4. The present invention uses an expectation-maximization algorithm to iteratively update hyperparameters, enabling the algorithm to adaptively adjust sparsity constraints based on the sparsity of the sound field signal during the hyperparameter update process. This update mechanism enables the algorithm to maintain good sparsity when processing sound field signals of varying sparsity, thereby improving the efficiency and quality of sound field reconstruction. Furthermore, data-driven parameter updates reduce the algorithm's reliance on prior assumptions, making the algorithm more stable. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 is the actual sound field distribution diagram;

[0032] Figure 2 Comparison of sound field reconstruction results of four algorithms;

[0033] Figure 3Actual sound field distribution of rectangular sound source;

[0034] Figure 4 Comparison diagram of reconstruction effects in the embodiment of the present invention

[0035] Figure 5 It is the overall flow chart of the present invention;

[0036] Figure 6 A flow chart of constructing a sound field receiving signal model of the present invention;

[0037] Figure 7 Detailed flow chart of the parameter estimation step of the present invention. DETAILED DESCRIPTION

[0038] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the drawings in the present specification. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0039] Please see the attached Figure 1 - Attachment Figure 7 , an embodiment of the present invention provides a two-dimensional block sparse Bayesian learning algorithm for sound field reconstruction, comprising the following steps:

[0040] S1. Construct a sound field receiving signal model of the microphone array and represent the sound field signal as a linear combination of sparse signals;

[0041] The sound field signal model is:

[0042] y=Ax+n

[0043] Where y is the measurement signal of the microphone array, A is the steering vector matrix of the scanning grid plane, x is the sparse signal, and n is the noise signal.

[0044] Specifically, the geometric position information of the microphone array is the key to constructing the matrix A. Due to the different positions of the microphone array elements in space, there is a difference in the wave path when the same sound source reaches different microphone array elements, resulting in a time delay difference in the signal received by the microphone. The signal received by the microphone has different time delays relative to the reference point. Therefore, by calculating the time delay difference, the phase difference can be obtained, and then the azimuth and pitch angle of the sound source can be determined, and the sound source position and sound pressure intensity can be obtained to reconstruct the sound field. The propagation characteristics of the sound field are described by the Green's function. According to the Green's function, a transfer function that is universal for far field and near field can be derived:

[0045]

[0046] Among them, rmn represents the distance from the nth grid point to the mth microphone, r n represents the distance from the nth grid point to the coordinate origin, c represents the speed of sound in air, ω=2πf is the angular frequency, and i is the imaginary unit.

[0047] Each element of the matrix A can be calculated using the transfer function and the geometric position information of the microphone array.

[0048] S2. Under the Bayesian framework, the structural correlation of the two-dimensional block sparse sound source is used to impose a coupling prior on the coefficients of the signal, and a hyper-prior distribution is introduced for the hyper-parameters of the prior distribution;

[0049] The sparse prior distribution is a Gaussian prior distribution, which makes it easy to select a conjugate distribution to simplify the calculation process.

[0050] The hyper-prior distribution is a Gamma distribution, which is used to model the hyper-parameters of the sparse prior distribution to achieve adaptive sparsity constraints on the sparse signal coefficients.

[0051] In the Bayesian framework, in order to achieve the estimation of sparse signals, a sparse prior distribution is introduced for the coefficients of the sparse signal. The signal is modeled using a generalized complex Gaussian distribution with zero mean and a coupling constraint is imposed. That is, a single variable in x is controlled not only by its own hyperparameters but also by the hyperparameters of the adjacent positions:

[0052]

[0053] Among them, ω is the parameter that controls sparsity, ω i-1 ,ω i+1 Represents the parameters of the adjacent grid points in the horizontal direction, ω i-(R+1) ,ω i+(R+1) represents the parameter of the vertically adjacent grid points above and below. β is the coupling weight, which controls the potential correlation between a grid point and its neighbors. The value of β ranges from 0 ≤ β ≤ 1. ∑0 is the covariance of the prior x.

[0054] To facilitate parameter updating, assume that the parameter ω follows the Gamma distribution with respect to a and b:

[0055]

[0056] In this Bayesian hierarchical model, the signal x obeys the Gaussian prior on ω. On top of the prior ω, the Gamma prior on a and b is considered to form a hierarchical dependency structure, further improving the sparsity of the solution. By constructing this Bayesian hierarchical model, an independent student-t prior is given to the signal x to encourage sparsity.

[0057] By constructing a sound field receiving signal model of a microphone array, introducing sparse prior distribution and super prior distribution and applying coupled prior under a Bayesian framework, the algorithm of the present invention can effectively realize sparse representation and parameter estimation of sound field signals. When processing sound field signals of different structures, it can adaptively learn the two-dimensional structure of block sparse sound sources, thereby improving the accuracy and robustness of sound field reconstruction.

[0058] S3. Estimate the parameters of the sparse signal by using an expectation maximization algorithm.

[0059] The parameter estimation step consists of the following substeps:

[0060] S301, input observation data, steering vector matrix and coupling parameters;

[0061] Specifically, before starting sparse signal reconstruction, the following key data needs to be input:

[0062] 1. Observation data y: The actual received microphone array signal, usually represented in vector or matrix form, whose dimension depends on the number of array elements and the number of sampling points;

[0063] 2. Steering vector matrix A: A matrix related to the array geometry, used to establish a linear mapping relationship between the observed data and the sparse signal;

[0064] 3. Coupling parameter β: A parameter that controls the potential correlation between a grid point and its adjacent grid points.

[0065] These input data provide physical model constraints for subsequent sparse signal estimation.

[0066] S302, initializing the parameters and convergence conditions of the sparse signal, including the number of iterations and tolerance value;

[0067] Specifically, before starting the estimation, it is necessary to set an initial value for the coefficients and hyperparameters of the sparse signal. These initial values are guesses based on experience and are intended to provide a starting point for subsequent iterative updates.

[0068] S303, iteratively updating the posterior distribution of the parameters through an expectation-maximization algorithm;

[0069] Specifically, the expectation-maximization algorithm is an optimization algorithm that performs maximum likelihood estimation through iteration. It seeks a set of parameters that maximizes the likelihood of a given observation (i.e., the likelihood function). It is primarily used to estimate the parameters of probabilistic models with latent variables. The expectation-maximization algorithm consists of an expectation step (E-step) and a maximization step (M-step). The E-step estimates the parameters using the observed data and the existing model, then uses these estimated parameters to calculate the expected value of the likelihood function. The M-step searches for the parameters that maximize the likelihood function. In this model, x is treated as a latent variable, and the expected value of the log-marginal posterior with respect to the parameters is calculated. The expected value is maximized by updating the parameters.

[0070] S304, determining whether the iterative update satisfies a convergence condition; if so, stopping the iteration and outputting the estimated values of the coefficients of the sparse signal and its hyperparameters; otherwise, continuing the iterative update;

[0071] Specifically, the convergence condition is that the change in the estimated value is less than a certain threshold or the maximum number of iterations is reached. If the convergence condition is met, it means that the estimated value has stabilized and the iteration can be stopped; otherwise, the next iteration update is continued.

[0072] S305: After the iterative update is completed, the signal to be reconstructed is output.

[0073] Specifically, the algorithm terminates the iteration process when the iterative update meets preset convergence conditions (such as reaching the maximum number of iterations or the residual is less than a tolerance value). At this point, the estimated value of the sparse signal tends to stabilize, and the reconstructed signal is finally output. This signal reflects the spatial distribution of the original sparse signal and incorporates the constraints of the observed data, array model, and coupling parameters to ensure the accuracy and reliability of the reconstruction result.

[0074] Through the above steps, we can achieve parameter estimation for sparse signals. This process is iterative, and each update brings the estimated value closer to the true value. This method can effectively handle sparse signal estimation problems and is suitable for applications such as sound field reconstruction.

[0075] S4. Based on the parameter estimation results, reconstruct the sound field signal and achieve reconstruction of the sound field.

[0076] The spatial distribution of the sound field is calculated using the estimated value of the sparse signal, thereby recovering the intensity and location information of the sound source. This process comprehensively considers the influence of array observation data and coupling parameters. The final reconstructed sound field output matches the actual measurement results, providing high-resolution sound source localization and sound field visualization.

[0077] The algorithm also includes a post-processing step for the sound field reconstruction result, and the post-processing step includes smoothing processing and noise suppression processing of the reconstructed sound field.

[0078] Specifically, the noise suppression process aims to reduce noise interference in the reconstructed sound field, improve the signal-to-noise ratio of the signal, and make the reconstructed sound field clearer.

[0079] It includes the following methods:

[0080] Spectral subtraction: Noise is suppressed by estimating the power spectrum of the noise and subtracting it from the power spectrum of the signal.

[0081] Wiener filtering: Utilizes the statistical characteristics of signals and noise to suppress noise through filter design.

[0082] Deep learning method: Noise suppression is achieved by training a neural network to learn the mapping relationship between noisy signals and clean signals.

[0083] This algorithm is also applicable to sound fields with sparse, two-dimensional block sources, and can adaptively learn the structural information of sound sources and update parameters in different scenarios. Given the differences in sound field signal characteristics across different sound fields, this algorithm establishes a universal acoustic propagation model and considers the two-dimensional correlation of signals within a Bayesian framework. This enables high-precision sound field reconstruction in sound fields with sparse, two-dimensional block sources, demonstrating its broad applicability.

[0084] To verify the effectiveness and superiority of our proposed two-dimensional block sparse Bayesian learning algorithm for sound field reconstruction, we conducted a series of experiments. We simulated sparse sound sources with different block structures and compared the performance of our proposed algorithm with existing algorithms (SBL, BSBL, and BOMP).

[0085] The experimental setup is as follows:

[0086] Microphone array configuration: A multi-arm spiral array containing 64 microphones was used, and the aperture of the array was set to 150 mm.

[0087] Sound source setup: Experiments were conducted using two-dimensional block sparse sound sources with triangular and rectangular distributions. The source positions were described by azimuth and elevation angles, with the starting positions of the two block sparse sound sources located at [40°, 68°] and [70°, 44°], respectively.

[0088] Environmental settings: The scanning plane range is 30° to 80°, the scanning interval is set to 2°, and the environmental signal-to-noise ratio is set to 20dB.

[0089] The experimental results are shown in Table 1 below:

[0090] Please refer to the instruction manual Figure 1 and instructions attached Figure 2 , Figure 1 is the actual sound field distribution of the triangular sound source, Figure 2Table 1 compares the actual sound source location with the localization results of the four algorithms. The solid red box in the figure indicates the actual sound source location.

[0091] Table 1 Comparison of positioning results

[0092]

[0093] Please refer to the instruction manual Figure 3 and instructions attached Figure 4 ,in Figure 3 is the actual sound field distribution of the rectangular sound source, Figure 4 Table 2 compares the actual sound source location with the positioning results of the four algorithms.

[0094] Table 2 Comparison of positioning results

[0095]

[0096]

[0097] Conclusion: The proposed algorithm demonstrates higher accuracy and robustness in reconstructing the sound field of two-dimensional block sparse sound sources with different structures. It can accurately capture the location and structural distribution of the sound source and effectively reconstruct the sound field. The other three algorithms, on the other hand, suffer from varying degrees of localization error and insufficient structural resolution.

[0098] This shows that the algorithm of the present invention can more effectively utilize coupling constraints, adaptively learn the two-dimensional structure of block sparse sound sources, and improve reconstruction accuracy.

[0099] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to these embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the appended claims and their equivalents.

Claims

1. A two-dimensional block sparse Bayesian learning algorithm for sound field reconstruction, characterized by The two-dimensional structural correlation of block-sparse sound sources is utilized, and the adjacent position parameters of a single variable are introduced to impose coupling constraints on the variable, encouraging a two-dimensional block-sparse solution. That is, a single variable in the signal is controlled not only by its own parameters but also by its adjacent parameters, thereby adaptively learning the two-dimensional structure of the block-sparse sound source. The method includes the following steps: S1. Construct a sound field receiving signal model of the microphone array and represent the sound field signal as a linear combination of sparse signals; S2. Under the Bayesian framework, the structural correlation of two-dimensional block sparse sound sources is used to impose a coupling prior on the signal, and a hyper-prior distribution is introduced for the hyper-parameters of the prior distribution; S3. estimating the parameters of the sparse signal by using an expectation maximization algorithm; S4. Reconstruct the sound field signal based on the parameter estimation result, and achieve reconstruction of the sound field.

2. The two-dimensional block sparse Bayesian learning algorithm for sound field reconstruction according to claim 1, characterized in that: The sound field signal model also takes into account the sparse characteristics of the signal in space and the propagation characteristics of the sound field. The sound field reception signal model is: y=Ax+n Where y is the measurement signal of the microphone array, A is the steering vector matrix of the scanning grid plane, x is the sparse signal, and n is the noise signal.

3. The two-dimensional block sparse Bayesian learning algorithm for sound field reconstruction according to claim 2, characterized in that: The matrix A is calculated using the Green's function of the sound field and the geometric position information of the microphone array. The Green's function is used to describe the propagation characteristics of the sound field in space.

4. The two-dimensional block sparse Bayesian learning algorithm for sound field reconstruction according to claim 1 is characterized in that The signal student-t prior is given through a multi-layer Bayesian framework to encourage sparsity. The sparse prior distribution in the S2 step is a Gaussian prior distribution to facilitate the selection of a conjugate distribution and simplify the calculation process.

5. The two-dimensional block sparse Bayesian learning algorithm for sound field reconstruction according to claim 1, characterized in that: By imposing a coupling prior on the signal through the structural correlation of two-dimensional block sparse sound sources, the parameters of each grid point on the target plane are controlled not only by its own hyperparameters, but also by the hyperparameters of the grid points at its adjacent positions, thereby promoting block sparse solution.

6. The two-dimensional block sparse Bayesian learning algorithm for sound field reconstruction according to claim 1, characterized in that: The hyper-prior distribution is a Gamma distribution, which is used to model the hyper-parameters of the sparse prior distribution to achieve adaptive learning and sparsity constraints on sparse signal coefficients.

7. The two-dimensional block sparse Bayesian learning algorithm for sound field reconstruction according to claim 1 is characterized in that The posterior estimation of parameters and latent variables is achieved through prior information and observation data. The parameter estimation step in step S3 includes the following sub-steps: S301, input observation data, steering vector matrix and coupling parameters; S302, initializing the parameters and convergence conditions of the sparse signal, including the number of iterations and tolerance value; S303, iteratively updating the posterior distribution of the parameters through an expectation-maximization algorithm; S304, determining whether the iterative update satisfies a convergence condition; if so, stopping the iteration and outputting the estimated values of the coefficients of the sparse signal and its hyperparameters; otherwise, continuing the iterative update; S305: After the iterative update is completed, the signal to be reconstructed is output.

8. The two-dimensional block sparse Bayesian learning algorithm for sound field reconstruction according to claim 1, characterized in that: The algorithm further comprises a post-processing step for the sound field reconstruction result, wherein the post-processing step comprises a smoothing process and a noise suppression process for the reconstructed sound field.

9. The two-dimensional block sparse Bayesian learning algorithm for sound field reconstruction according to claim 1, characterized in that: The algorithm is applicable to a sound field environment with two-dimensional block sparse sound sources, and can adaptively learn the structural information of the sound sources and update parameters in different scenarios.

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