A compressed sensing approach to hyperspectral classification

Abstract

Although hyperspectral technology has continued to improve over the years, its use is often still limited due to size, weight and power (SWaP) constraints. One of the more taxing requirements, is the need to sample a large number of very fine spectral bands. The prohibitively large size of hyperpsectral data creates challenges in both archival and processing. Compressive sensing is an enabling technology for reducing the overall processing and SWaP requirements. This paper explores the viability of performing classification on sparsely sampled hyperspectral data without the need of performing sparse reconstruction. In particular, a spatial-spectral classifier based on a Support Vector Machine (SVM) and edgepreserving filters (EPFs) is applied directly in the compressed domain. The well-known Restricted Isometry Property (RIP) and a random spectral sampling strategy are used to evaluate analytically, the error between the compressed classifier and the full band classifier. The mathematical analysis presented shows that the classification error can be expressed in terms of the Restricted Isometry Constant (RIC) and that it is indeed possible to achieve full classification performance in the compressed domain, given that sufficient sampling conditions are met. A set of experiments are performed to empirically demonstrate compressed classification. Images from both the Airborne Visible / Infrared Imaging Spectrometer (AVIRIS) and Reflective Optics System Imaging Spectrometer (ROSIS) are examined to draw inferences on the impact of scene complexity. The results presented clearly demonstrate the possibility of compressed classification and lead to several open research questions to be addressed in future work.