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

Abstract

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Orthogonal Subspace Projection Target Detector for Hyperspectral Anomaly Detection

“…DS can effectively reduce BKG interference, while retaining anomalies after the LRaSMD decomposition and prior to OSP-AD. Despite that there are works reported in [24,49] using OSP to suppress BKG, their used anomaly detectors were still RXD-type anomaly detectors. It seems that using OSP-TD as anomaly detector has not been investigated for AD.…”

“…Most recently, [49] re-derived GoDec as an OSP-GoDec which made use of OSP to re-implement GoDec. In particular, it was the first work ever reported to resolve the issues of determining the parameter, r, rank of Low-rank matrix and k, cardinality of sparsity, both of which have been determined empirically and manually in the past.…”

“…In particular, it was the first work ever reported to resolve the issues of determining the parameter, r, rank of Low-rank matrix and k, cardinality of sparsity, both of which have been determined empirically and manually in the past. Most importantly, [49] used the LRaSMD generated by GoDec and OSP-Godec to further derive a number of RXD variants which implemented the low rank matrix and sparse matrix in various forms and showed to outperform many existing RXD-type anomaly detectors including the collaborative representation-based anomaly detector (CRD) proposed in [10].…”

“…Specifically, the widely used go decomposition (GoDec) in [48] can be used to produce an LRaSMD model. Most recently, GoDec was further extended to an OSP version of GoDec, referred to as OSP-GoDec in [49] where the commonly used RX-AD and R-AD were extended to be implemented by operating the data sample vector r and the K/R not in the original data space X but rather in their own respective spaces, low rank matrix L and sparse matrix S.…”

“…This DS process is included to mimic what K -1 /R -1 accomplishes in the RX/R-AD by suppressing the 2 nd order statistics in BKG. This DS is absent in [49] because K -1 /R -1 used by RX/R-AD basically performs data whitening similar to DS.…”