Iterative algorithm for solving acoustic source characterization problems under block sparsity constraints.

In this paper, an iterative Compressive Sensing (CS) algorithm is proposed for acoustical source characterization problems with block sparsity constraints. Source localization and signal separation are accomplished in a unified CS framework. The inverse problem is formulated with the Equivalent Source Method as a linear underdetermined system of equations. As conventional approaches based on convex optimization can be computationally expensive and fail to deal with continuously distributed sources, the proposed approach that is adapted from the Newton's method and is augmented with a special pruning procedure is capable of solving the inverse problem far more efficiently with comparable accuracy. The pruning procedure employs a binary mask that admits sparsity constraints of two-dimensional block sources. The binary mask is heuristic in that it tends to promote nonzero positive source magnitudes. In each iteration, the source amplitude vector is on one hand updated by the Newton's method and on the other hand pruned with the binary mask. With the pruning procedure, the source magnitudes become increasingly sparse and clustered such that the block characteristics are enhanced. In the post-processing phase, particle velocity is calculated on the basis of the equivalent source amplitudes. Numerical and experimental investigations are conducted to validate the proposed technique. The results have demonstrated the efficacy of the proposed Compressive Newton's method in imaging block sources and extracting signal waveforms with little computational cost, as compared to a convex optimization package.