Compressive beamforming with LASSO

Abstract

For a given sound field observed on an array, compressive beamforming reconstructs the direction-of-arrival (DOA) map using a sparsity constraint on the source distribution. The problem is posed as an underdetermined problem expressing the pressure at each receiver as a superposition of plane waves associated with each DOA, a phase delayed sum of source amplitudes. The L1 sparsity constraint makes the problem solvable with convex optimization and the sparsity constraint gives improved resolution. We here derive the sparse source distribution using maximum a posteriori (MAP) estimates for both single and multiple snapshots. Compressive beamforming does not rely on any matrix inversion and thus works well even for single snapshots where it gives higher resolution than conventional beamforming. For multiple snapshots in a free-space environment, compressive beamforming has a performance similar to MVDR. In a multi-path environment MVDR fails, but compressive beamforming works well. The superior resolution of compressive beamforming is demonstrated with vertical array data from event S5 in the SWellEx96 experiment in a multi-path shallow water environment.