Newtonized orthogonal matching pursuit-based compressive spherical beamforming in spherical harmonic domain

Abstract

Compressive spherical beamforming (CSB) with spherical microphone arrays is a promising approach for acoustic source identification due to its high spatial resolution and applicability to incoherent and coherent sources. However, the original CSB based on fixed discrete grids suffers from basis mismatch problem. The grid-free CSB requires a priori signal-to-noise ratio (SNR), bears heavy computational load at high frequencies and is subject to a limited number of the sources that can be simultaneously identified at low frequencies. This paper extends Newtonized orthogonal matching pursuit (NOMP) algorithm to solve underdetermined equations of CSB with spherical microphone arrays, and proposes NOMP-based CSB (NOMP-CSB). The proposed approach establishes a maximum likelihood estimation (MLE) model, with direction of arrivals (DOAs) and source strengths as unknown parameters to be solved, in spherical harmonic domain. NOMP-CSB first selects the best candidate from discrete grids and then performs Newton optimization in the local continuous region near the selected grid to iteratively solve the MLE model, thereby achieving DOA estimation and source strength quantification. Besides, NOMP-CSB uses the variations of sound pressure residual to adaptively control iterations, avoiding the estimation of SNR and the number of sources. Numerical simulations and experiments demonstrate that NOMP-CSB can effectively overcome basis mismatch problem and enjoys high source identification accuracy, computational efficiency, spatial resolution, and accuracy of estimating the number of sources. Furthermore, this paper develops NOMP-CSB with multiple-frequency synchronous processing, that is, multiple-frequency synchronous NOMP-CSB (MF-NOMP-CSB), which jointly uses the measured sound pressures at multiple frequencies to synchronously estimate DOAs and the strengths of all frequencies. MF-NOMP-CSB outperforms NOMP-CSB under single-snapshot measurement, and can improve the performance of identifying unstable wideband sources.