Component Decomposition Analysis for Hyperspectral Anomaly Detection

Low-rank and sparse representation (LRaSR)-based approaches have been widely used for anomaly detection (AD). Their central ideas are to minimize the rank of the low-rank space constrained to predetermined values, while using various regularization parameters to control the sparse representation. Three key issues arise from LRaSR. The first is how to determine the constrained rank. The second is an appropriate selection of regularization parameters. The third one is the detector used for AD. This article presents a new but rather simple competing model, called component decomposition analysis (CDA) which represents a data space X as a linear orthogonal decomposition of three components, X = PC
$^{{m}} +$
IC
$^{{j}} +$
N with
${m}$
principal components, PC
$^{{m}}$
, generated by principal component analysis (PCA) and
${j}$
independent components, IC
$^{{j}}$
, generated by independent component analysis (ICA) plus a noise component N. CDA offers several advantages over LRaSR. First, CDA uses well-known component analysis techniques to decompose the dataset without solving constrained optimization problems. Second, the values of
${m}$
and
${j}$
can be automatically determined by virtual dimensionality (VD) and a minimax-singular value decomposition (MX-SVD). To better extract anomalies from the IC
$^{{j}}$
component space, the concept of sparsity cardinality (SC) is further incorporated into CDA to derive a CDASC anomaly detector (CDASC-AD). The experimental results demonstrate that CDASC-AD is very competitive against the LRaSR-based models and performs well in hyperspectral AD.