SuperRPCA: A Collaborative Superpixel Representation Prior-Aided RPCA for Hyperspectral Anomaly Detection

Recently, numerous hyperspectral anomaly detection (HAD) methods have been proposed for broad and crucial applications. Among these, robust principal component analysis (RPCA) gains considerable attention in HAD, as it separates the matrix into global low-rank and sparse components, corresponding to the property of background and anomaly. However, RPCA solves the problem by treating hyperspectral imagery (HSI) as a matrix, but this approach alone cannot well describe the local spatial texture information. In addition, a pixel-wise detection method, collaborative representation detector (CRD), has been proposed, which exploits the vital piece of local information by assuming that background pixels can be composed of their neighbor pixels, while abnormal ones cannot. Although several CRD-based methods achieve promising HAD performances, they generally suffer from high computational costs due to the pixel-wise optimization scheme. To overcome the aforementioned two limitations, we propose a novel algorithm, SuperRPCA. First, we improve CRD to superpixel-wise calculation and reconstruct the background with a simplex-based algebraic solution. Subsequently, the rebuilt background is tailored to serve as a convex regularizer and integrated into RPCA. Besides, the regularizer inherently possesses a low-rank property, adeptly substituting the nuclear norm in traditional RPCA and hence significantly reducing computational costs. SuperRPCA demonstrates easily identifiable visual qualities and state-of-the-art quantitative performance with all the closed-form algorithmic expressions explicitly derived.