Orthogonal Subspace Projection-Based Go-Decomposition Approach to Finding Low-Rank and Sparsity Matrices for Hyperspectral Anomaly Detection

Low-rank and sparsity-matrix decomposition (LRaSMD) has received considerable interests lately. One of effective methods for LRaSMD is called go decomposition (GoDec), which finds low-rank and sparse matrices iteratively subject to the predetermined low-rank matrix order $m$ and sparsity cardinality $k$ . This article presents an orthogonal subspace-projection (OSP) version of GoDec to be called OSP-GoDec, which implements GoDec in an iterative process by a sequence of OSPs to find desired low-rank and sparse matrices. In order to resolve the issues of empirically determining $p = m+ j$ and $k$ , the well-known virtual dimensionality (VD) is used to estimate $p$ in conjunction with the Kuybeda et al. developed minimax-singular value decomposition (MX-SVD) in the maximum orthogonal complement algorithm (MOCA) to estimate $k$ . Consequently, LRaSMD can be realized by implementing OSP-GoDec using $p$ and $k$ determined by VD and MX-SVD, respectively. Its application to anomaly detection demonstrates that the proposed OSP-GoDec coupled with VD and MX-SVD performs very effectively and better than the commonly used LRaSMD-based anomaly detectors.