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Abstract
Orthogonal subspace projection (OSP) is a versatile hyperspectral imaging technique which has shown great potential in dimensionality reduction, target detection, spectral unmixing, etc. However, due to its inherent requirement of prior target knowledge, OSP has not been explored in anomaly detection. This article takes advantage of an unsupervised OSP-based algorithm, automatic target generation process (ATGP), and a recently developed OSP-go decomposition (OSP-GoDec) along with data sphering (DS) to make OSP applicable to anomaly detection. Its idea is to implement ATGP on the background (BKG) and target subspaces constructed from the low-rank matrix L and sparse matrix S generated by OSP-GoDec to derive an OSP-based anomaly detector (OSP-AD). In particular, OSP-AD also includes DS to remove BKG interference from the target subspace so as to enhance anomaly detection. Surprisingly, operating data samples on different constructions of the BKG subspace and the target subspace yields various versions of OSP-AD. Experiments show that given an appropriate construction of the BKG subspace and the target subspace, OSP-AD can be shown to outperform existing anomaly detectors including Reed-Xiaoli anomaly detector and collaborative representation-based anomaly detector (CRD).
Highlights
D UE to its use of hundreds of contiguous spectral bands, a hyperspectral imaging sensor is capable of uncoveringManuscript received February 6, 2021; revised March 3, 2021; accepted March 20, 2021
By realizing that anomalies may be corrupted with noise in the sparse component produced by robust principal component analysis (RPCA), [21] proposed an low rank and sparse matrix decomposition (LRaSMD)-based Mahalanobis distance method for hyperspectral anomaly detection (LSMAD) where a data space can be decomposed into three components—low rank, sparse, and noise matrices modeled by LRaSMD
In order to evaluate the performance of orthogonal subspace projection (OSP)-AD in (35) and OSPDS-AD in (36), a sparse representation-based model, referred to as l2-norm minimization and distance weighted regularization matrix and sum-to-one constraint (CRD-DW-STO), developed in [10] was used for comparison since it was shown to outperform sparse representation-based detector (SRD), RPCAbased anomaly detector, and local RX-AD
Summary
D UE to its use of hundreds of contiguous spectral bands, a hyperspectral imaging sensor is capable of uncovering. In order for OSP to work as an anomaly detector, the key issue is how to remove the requirement of prior knowledge of d and U in (2) from OSP-TD. To resolve this issue, two approaches were investigated in the past. One key measure to assess the effectiveness of AD is the BKG suppressibility of an anomaly detector It has been shown in [50] that the traditional 2-D receiver operating characteristic (ROC) curve was not capable of doing so. CHANG et al.: ORTHOGONAL SUBSPACE PROJECTION TARGET DETECTOR reviews OSP-GoDec. Section VI derives OSP-AD which constructs the BKG and target subspaces from the OSP-Godec generated low rank and sparse matrices.
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