Maximum orthogonal subspace projection approach to estimating the number of spectral signal sources in hyperspectral imagery

Abstract

Estimating the number of spectral signal sources, denoted by p, in hyperspectral imagery is very challenging due to the fact that many unknown material substances can be uncovered by very high spectral resolution hyperspectral sensors. This paper investigates a recent approach, called maximum orthogonal complement algorithm (MOCA), for this purpose. The MOCA was originally developed by Kuybeda et al. for estimating the rank of a rare vector space in a highdimensional noisy data space. Interestingly, the idea of the MOCA is essentially derived from the automatic target generation process (ATGP) developed by Ren and Chang. By appropriately interpreting the MOCA in context of the ATGP a potentially useful technique, called maximum orthogonal subspace projection (MOSP) can be further developed where determining a stopping rule for the ATGP turns out to be equivalent to estimating the rank of a rare vector space by the MOCA and the number of targets determined by the stopping rule for the ATGP to generate is the desired value of the parameter p. Furthermore, a Neyman-Pearson detector version of MOCA, NPD-MOCA can be also derived by the MOSP as opposed to the MOCA considered as a Bayes detector. Surprisingly, the MOCA-NPD has very similar design rationale to that of a technique referred to as Harsanyi-Farrand-Chang method that was developed to estimate the virtual dimensionality (VD) which is defined as the p.