Cross-spectral matrix denoising for beamforming based on Schatten-p norm

Abstract

Acoustic imaging is often severely affected by incoherent noise. However, whether it is Diagonal Removal (DR) or Diagonal Denoising (DD), these methods only remove the noise concentrated on the diagonal of the Cross-Spectral Matrix (CSM). In this work, a Robust Principal Component Analysis (RPCA) based on the non-convex Schatten-p (0<p<1) norm is proposed for CSM denoising. Non-convex accelerated proximal gradient (APG) and accelerated proximal gradient line-search-like (APGL) are combined to form a non-convex APGL algorithm to solve CSM denoising based on the Schatten-p norm. This problem is also solved under the framework of the alternate direction method of multipliers (ADMM) algorithms. According to simulation data, the Schatten-p norm has a more accurate reconstruction ability than the nuclear norm at low SNR. The specific performance is that the reconstruction error is smaller, and the rank estimation of the CSM is more accurate. The Schatten-p norm can effectively remove the influence of incoherent noise. Moreover, the Schatten-p norm is more beneficial in reducing the sensitivity of the regularization parameter than the nuclear norm. Experimental results show that the proposed method is an accurate CSM denoising algorithm, which can effectively remove incoherent noise pollution under low SNR conditions.