Sound field reconstruction using block sparse Bayesian learning equivalent source method

Abstract

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.