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

• Published in: IEEE transactions on geoscience and remote sensing Vol. 59; no. 3; pp. 2403 - 2429
• Main Authors: Chang, Chein-I, Cao, Hongju, Chen, Shuhan, Shang, Xiaodi, Yu, Chunyan, Song, Meiping
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.03.2021; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Anomalies; Anomaly detection; Decomposition; Detection; Detectors; Go decomposition (GoDec); Hyperspectral imaging; Iterative algorithms; Iterative methods; low-rank and sparsity-matrix decomposition (LRaSMD); Matrix decomposition; Minimax technique; minimax-singular value decomposition (MX-SVD); orthogonal subspace projection GoDec (OSP-GoDec); Reed and Xiaoli anomaly detector (RX-AD); Singular value decomposition; Sparse matrices; Sparsity; virtual dimensionality (VD)
• ISSN: 0196-2892; 1558-0644
• DOI: 10.1109/TGRS.2020.3002724

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 <inline-formula> <tex-math notation="LaTeX">m </tex-math></inline-formula> and sparsity cardinality <inline-formula> <tex-math notation="LaTeX">k </tex-math></inline-formula>. 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 <inline-formula> <tex-math notation="LaTeX">p = m+ j </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">k </tex-math></inline-formula>, the well-known virtual dimensionality (VD) is used to estimate <inline-formula> <tex-math notation="LaTeX">p </tex-math></inline-formula> in conjunction with the Kuybeda et al. developed minimax-singular value decomposition (MX-SVD) in the maximum orthogonal complement algorithm (MOCA) to estimate <inline-formula> <tex-math notation="LaTeX">k </tex-math></inline-formula>. Consequently, LRaSMD can be realized by implementing OSP-GoDec using <inline-formula> <tex-math notation="LaTeX">p </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">k </tex-math></inline-formula> 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.