Enhance Tensor RPCA-Based Mahalanobis Distance Method for Hyperspectral Anomaly Detection

Abstract

This letter proposes a spectral&#x2013;spatial anomaly detection method based on tensor decomposition. First, tensor data are used to represent hyperspectral data to retain the original spectral and spatial information. Second, hyperspectral image (HSI) data are decomposed into low-rank and sparse tensors. The proposed method uses weighted tensor Schatten <inline-formula> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula>-norm minimization (WTSNM) instead of rank minimization. WTSNM assigns different weights to singular values to retain the important information and filter out noise. It efficiently solves the tensor decomposition problem using Fourier transform, generalized soft thresholding, and a tensor singular value decomposition (T-SVD) method. Finally, the obtained low-rank tensor is used to estimate the background statistics, and a Mahalanobis distance-based anomaly detector is developed using the background statistics. The experimental results on three real datasets show that the proposed method outperforms several state-of-the-art algorithms.