With high spectral resolution hyperspectral imaging is capable of uncovering many subtle signal sources which cannot be known a priori or visually inspected. Such signal sources generally appear as anomalies in the data. Due to high correlation among spectral bands and sparsity of anomalies, a hyperspectral image can be e decomposed into two subspaces: a background subspace specified by a matrix with low rank dimensionality and an anomaly subspace specified by a sparse matrix with high rank dimensionality. This paper develops an approach to finding such low-high rank decomposition to identify anomaly subspace. Its idea is to formulate a convex constrained optimization problem that minimizes the nuclear norm of the background subspace and little ι¹ norm of the anomaly subspace subject to a decomposition of data space into background and anomaly subspaces. By virtue of such a background-anomaly decomposition the commonly used RX detector can be implemented in the sense that anomalies can be separated in the anomaly subspace specified by a sparse matrix. Experimental results demonstrate that the background-anomaly subspace decomposition can actually improve and enhance RXD performance.

Date Published: 18 May 2013
PDF: 7 pages
Proc. SPIE 8743, Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery XIX, 87430N (18 May 2013); doi: 10.1117/12.2015652

Published in SPIE Proceedings Vol. 8743:
Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery XIX
Sylvia S. Shen; Paul E. Lewis, Editor(s)