Sound field reconstruction using sparse Bayesian learning equivalent source method with hyperparametric-coupled prior

Abstract

Block sparse Bayesian learning (SBL) equivalent source method (ESM) suffers from the block structure mismatch problem that leads to poor sound field reconstruction accuracy for block sparse sources. To address this issue, this paper proposes to employ a hyperparametric-coupled prior in the SBL-ESM. In the method, a hierarchical SBL model is established based on the ESM, and then the coupling constraint is imposed to the hyper-prior of equivalent source strengths by a projection transformation. The proposed method can produce a coupling effect, such that the sparsity of equivalent source strengths is controlled not only by each corresponding hyper-parameter, but also by their immediate neighbors. Therefore, it enables to promote block sparse solutions and reconstruct the sound fields of block sparse sources well without the prior information of block partition. Numerical simulations of linear-block sources are used to verify the effectiveness and superiority of the proposed method, and the effects of sound power ratio, signal-to-noise ratio and reconstruction distance on the reconstructed results are investigated. Subsequently, the performance of the proposed method is further verified through an experiment of a composite loudspeaker and an experiment of the mixed sources consisting of a small loudspeaker and an impacted steel plate.