Compressive beamforming with planar microphone arrays is capable of estimating the two-dimensional direction-of-arrivals (DOAs) and quantifying the strengths of acoustic sources effectively. The multiple-snapshot grid-free method has recently been concerned due to the advantages that it can circumvent the basis mismatch conundrum of the conventional grid-based method and improve the performance of the single-snapshot grid-free method. The existing atomic norm minimization based strategy uses an off-the-peg interior point method (IPM) based solver to solve the positive semidefinite programming equivalent to the atomic norm minimization. We present an alternative algorithm based on alternating direction method of multipliers (ADMM) in this paper. Both simulations and experiments demonstrate that whether a standard uniform rectangular array or a non-uniform array constituted by a small number of microphones is employed, the two-dimensional multiple-snapshot grid-free compressive beamforming using our ADMM based algorithm can estimate the DOAs and quantify the strengths of acoustic sources well, and reaching the same or even better DOA estimation accuracy as the one using the IPM based solver, our ADMM based algorithm is distinctly faster.
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