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

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) developed by Kuybeda for estimating the rank of a rare vector space in a high-dimensional noisy data space which was 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 a stopping rule for the ATGP provided by MOSP turns out to be equivalent to a procedure for estimating the rank of a rare vector space by the MOCA and the number of targets determined by the MOSP to generate is the desired value of the parameter p. Furthermore, a Neyman-Pearson detector version of MOCA, referred to as ATGP/NPD can be also derived where the MOCA can be considered as a Bayes detector. Surprisingly, the ATGP/NPD has a very similar design rationale to that of a technique, called Harsanyi-Farrand-Chang method that was developed to estimate the virtual dimensionality (VD) where the ATGP/NPD provides a link between MOCA and VD.