Orthogonal Subspace Projection-Based Go-Decomposition Approach to Finding Low-Rank and Sparsity Matrices for Hyperspectral Anomaly Detection
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Date
2020-07-14
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Citation of Original Publication
C. -I. Chang, H. Cao, S. Chen, X. Shang, C. Yu and M. Song, "Orthogonal Subspace Projection-Based Go-Decomposition Approach to Finding Low-Rank and Sparsity Matrices for Hyperspectral Anomaly Detection," in IEEE Transactions on Geoscience and Remote Sensing, vol. 59, no. 3, pp. 2403-2429, March 2021, doi: 10.1109/TGRS.2020.3002724.
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Abstract
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 OSPGoDec, 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.