Analytical comparison of subpixel target detectors in structured models for hyperspectral images

Abstract

In the current target detection literature, there are two major approaches to the evaluation of detectors’ performance. One is based on theoretical calculations assuming some simple statistical models, and the other approach uses real or simulated spectral images. The former approach is too simplistic, at this point, to address practical needs. On the other hand, the latter approach does not give us a good understanding of why certain detectors work better than others in the context of specific targets and spectral images. Our goal is to initiate research that will combine these two separate approaches. In this paper, we start with a comparison of two well-known detectors—the matched filter detector (MFD) and the orthogonal subspace projection (OSP) detector. We show a surprising result that MFD always outperforms OSP in a traditional theoretical formulation of the detection problem. We also show that this theoretical formulation is not realistic in practical target detection in real spectral images. However, the obtained results suggest more realistic approaches for providing theoretical background for practical target detection. In this paper, we also point out many detectors introduced in the literature that are equivalent to MFD or OSP detectors.