Graph Regularized Low-Rank and Collaborative Representation for Hyperspectral Anomaly Detection

The aim of hyperspectral anomaly detection is to find targets that are spectrally distinct from their surrounding background pixels. Many algorithms for hyperspectral anomaly detection have been proposed by researchers. Among these, the low-rank and collaborative representation detector (LRCRD) can not only analyze the hyperspectral correlation between all pixels but also constrain the coefficient matrix of the dictionary using low-rank and l(2) norms minimization, which does not require an over-complete dictionary and is more useful for background modeling. However, the LRCRD model ignores the significance of the hyperspectral data's local geometric information to distinguish between background and anomalous pixels. In this paper, the graph-Laplacian regularization is incorporated into the LRCRD formulation and a novel anomaly detection method is proposed based on the graph regularized LRCRD model to analyze nonlinear geometric information. The proposed preserves local geometrical structure in hyperspectral images, thereby improving detection accuracy. The experiments on synthetic and real hyperspectral datasets demonstrate the feasibility of the proposed method.