A panoramic continuous compressive beamformer with cuboid microphone arrays

Compressive beamforming is a powerful approach for the direction-of-arrival (DOA) estimation and strength quantification of acoustic sources. The conventional grid-based discrete compressive beamformer suffers from the basis mismatch conundrum. Its result degrades under the situation that sources fall off the grid. The existing continuous compressive beamformer with linear or planar microphone arrays can circumvent the conundrum, but work well only for sources in a local region. Here we develop a panoramic continuous compressive beamformer with cuboid microphone arrays based on an atomic norm minimization (ANM) and a matrix pencil and paring method. To solve the positive semidefinite programming equivalent to the ANM efficiently, we formulate a solving algorithm based on the alternating direction method of multipliers. We also present an iterative reweighted ANM to enhance sparsity and resolution. The beamformer is capable of estimating the DOAs and quantifying the strengths of acoustic sources panoramically and accurately, whether a standard uniform or a sparse cuboid microphone array is utilized.