Sparse reconstruction of sound field using pattern-coupled Bayesian compressive sensing

Conventional near-field acoustic holography based on compressive sensing either does not fully exploit the underlying block-sparse structures of the signal or suffers from a mismatch between the actual and predefined block structure due to the lack of prior information about block partitions, resulting in poor accuracy in sound field reconstruction. In this paper, a pattern-coupled Bayesian compressive sensing method is proposed for sparse reconstruction of sound fields. The proposed method establishes a hierarchical Gaussian-Gamma probability model with a pattern-coupled prior based on the equivalent source method, transforming the sound field reconstruction problem into recovering the sparse coefficient vector of the equivalent source strengths within the compressive sensing framework. A set of hyperparameters is introduced to control the sparsity of each element in the sparse coefficient vector of the equivalent source strengths, where the sparsity of each element is determined by both its own hyperparameters and those of its immediate neighbors. This approach enables the promotion of block sparse solutions and achieves better performance in solving for the sparse coefficient vector of the equivalent source strengths without prior information of block partitions. The effectiveness and superiority of the proposed method in reconstructing sound fields are verified by simulations and experiments.