Hyperspectral Anomaly Detection via Structured Sparsity Plus Enhanced Low-Rankness

Abstract

Hyperspectral anomaly detection (HAD), distinguishing anomalous pixels or subpixels from the background, has received increasing attention in recent years. Low-Rank Representation (LRR)-based methods have also been promoted rapidly for HAD, but they may encounter three challenges: (1) they adopted the nuclear norm as the convex approximation, yet a sub-optimal solution of the rank function; (2) they overlook the structured spatial correlation of anomalous pixels; (3) they fail to comprehensively explore the local structure details of the original background. To address these challenges, in this paper, we proposed the Structured Sparsity Plus Enhanced Low-Rank (S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ELR) method for HAD. Specifically, our S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ELR method adopts the weighted tensor Schatten- <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> norm, acting as an enhanced approximation of the rank function than the tensor nuclear norm, and the structured sparse norm to characterize the low-rank properties of the background and the sparsity of the abnormal pixels, respectively. To preserve the local structural details, the position-based Laplace regularizer is accompanied. An iterative algorithm is derived from the popular alternating direction methods of multipliers. Compared to the existing state-of-the-art HAD methods, the experimental results have demonstrated the superiority of our proposed S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ELR method.