Compressive Spherical Beamforming for Acoustic Source Identification

This study examines a compressive spherical beamforming (CSB) method, using a rigid spherical microphone array to localize and quantify the acoustic contribution of sources. The method relies on the array signal model in the spherical harmonics domain that can be represented as a spatially sparse problem. This makes it possible to use compressive sensing to solve an underdetermined problem via promoting sparsity. The estimation of the angular position of sources with respect to the microphone array, as well as the three-dimensional localization over a volume are investigated. Several sparse recovery algorithms [orthogonal matching pursuit (OMP), generalized OMP, ϱ1-norm minimization, and reweighted ϱ1-norm minimization] are examined for this purpose. The numerical and experimental results indicate that sparse recovery methods outperform conventional spherical harmonics beamforming. Reweighted ϱ1-norm has good adaptability to noise, improving the robustness of CSB. The method can successfully localize the angular position of sources, and quantify their relative pressure contribution. The method is promising to localize sources in a three-dimensional domain of interest. However, the three-dimensional localization is more sensitive to noise, source distance, and properties of the sensing matrix than the two-dimensional localization.