We use a nonlinear dimensionality reduction technique to improve anomaly detection in a hyperspectral imaging application. A nonlinear transformation, diffusion map, is used to map pixels from the high-dimensional spectral space to a (possibly) lower-dimensional manifold. The transformation is designed to retain a measure of distance between the selected pixels. This lower-dimensional manifold represents the background of the scene with high probability and selecting a subset of points reduces the computational overhead associated with diffusion map. The remaining pixels are mapped to the manifold by means of a Nystr¨om extension. A distance measure is computed for each new pixel and those that do not reside near the background manifold, as determined by a threshold, are identified as anomalous. We compare our results with the RX and subspace RX methods of anomaly detection.

Date Published: 12 May 2010
PDF: 5 pages
Proc. SPIE 7695, Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery XVI, 769507 (12 May 2010); doi: 10.1117/12.851811

Published in SPIE Proceedings Vol. 7695:
Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery XVI
Sylvia S. Shen; Paul E. Lewis, Editor(s)