The acoustic inverse problem in the framework of alternating direction method of multipliers

Spatial basis interpretation for implementing the acoustic imaging of non-synchronous measurements

Achieving the sparse acoustical holography via the sparse bayesian learning

An improvement of the generalized discrete Fourier series based patch near-field acoustical holography

Nearfield acoustic holography based on the compressed sensing theory can realize the accurate reconstruction of sound fields with fewer measurement points on the premise that an appropriate sparse basis is obtained. However, for different types of sound sources, the appropriate sparse bases are diverse and should be constructed elaborately. In this paper, a block sparse Bayesian learning (SBL) equivalent source method is proposed for realizing the reconstruction of the sound fields radiated by different types of sources, including the spatially sparse sources, the spatially extended sources, and the mixed ones of the above two, without the elaborate construction of the sparse basis. The proposed method constructs a block sparse equivalent source model and promotes a block sparse solution by imposing a structured prior on the equivalent source model and estimating the posterior of the model by using the SBL, which can achieve the accurate reconstruction of the radiated sound fields of different types of sources simply by adjusting the block size. Numerical simulation and experimental results demonstrate the validity and superiority of the proposed method, and the effects of two key parameters, the block size, and sparsity pruning threshold value are investigated through simulations.

Sound field reconstruction using block sparse Bayesian learning equivalent source method.

To overcome the contradiction between the resolution and the measurement cost, various algorithms for reconstructing the sound field with sparse measurement have been developed. However, limited attention is paid to the computation efficiency. In this study, a fast sparse reconstruction method is proposed based on the Bayesian compressive sensing. First, the reconstruction problem is modeled by a sparse decomposition of the sound field via singular value decomposition. Then, the Bayesian compressive sensing is adapted to reconstruct the sound field with sparse measurement of sound pressure. Numerical results demonstrate that the proposed method is applicable to either the spatially sparse distributed sound sources or the spatially extended sound sources. And comparisons with other two sparse reconstruction methods show that the proposed one has the advantages in terms of reconstruction accuracy and computational efficiency. In addition, as it is developed in the framework of multitask compressive sensing, the method can use multiple snapshots to perform reconstruction, which greatly enhances the robustness to noise. The validity and the advantage of the proposed method are further proved by experimental results.

Fast sparse reconstruction of sound field via Bayesian compressive sensing

To solve the problem of sound field reconstruction with fewer measurement points, a sound field reconstruction method based on Bayesian compressive sensing is proposed. In this method, a sound field reconstruction model based on a combination of the equivalent source method and sparse Bayesian compressive sensing is established. The MacKay iteration of the relevant vector machine is used to infer the hyperparameters and estimate the maximum a posteriori probability of both the sound source strength and noise variance. The optimal solution for sparse coefficients with an equivalent sound source is determined to achieve the sparse reconstruction of the sound field. The numerical simulation results demonstrate that the proposed method has higher accuracy over the entire frequency range compared to the equivalent source method, indicating a better reconstruction performance and wider frequency applicability with undersampling. Moreover, in environments with low signal-to-noise ratios, the proposed method exhibits significantly lower reconstruction errors than the equivalent source method, indicating a superior anti-noise performance and greater robustness in sound field reconstruction. The experimental results further verify the superiority and reliability of the proposed method for sound field reconstruction with limited measurement points.

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Yue Xiao

Papers

Fast sparse reconstruction of sound field via Bayesian compressive sensing

Sparse Reconstruction of Sound Field Using Bayesian Compressive Sensing and Equivalent Source Method