Hyperspectral Anomaly Detection via S 1/2 and Total Variation Low Rank Matrix Decomposition

Abstract

Anomaly detection (AD) on hyperspectral images has been widely researched in recent decades due to its high practicability and wide range of application scenarios. Such AD methods derived from low-rank matrix decomposition (LRMD) have appeared rapidly and been applied effectively. However, most of them focused on the use of spectral information and neglected the abundant spatial characteristics. In this letter, a spectral-spatial total variation (TV) (SSTV) regularized low-rank matrix decomposition method with a Schatten 1/2 quasi-norm (<inline-formula> <tex-math notation="LaTeX">$S_{1/2}$ </tex-math></inline-formula>) and denoising is proposed. First, to exploit the hyperspectral imagery (HSI) characteristics from the spectral perspective, we propose the low-rank matrix decomposition method with <inline-formula> <tex-math notation="LaTeX">$S_{1/2}$ </tex-math></inline-formula> norm and image denoising modules. Second, we incorporate the SSTV regularization by employing a 2-D TV (TV) spatially and 1-D TV along the spectral dimension to realize the maximized utilization of spatial characteristics of HSI. Finally, the alternating direction multiplier method (ADMM) is brought in the calculating process to attain the consequent detection results. The superiority of the proposed method has been demonstrated by the excellent performance on three real datasets.