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, 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 et al. 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. 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

A Signal Processing Perspective on Hyperspectral Unmixing: Insights from Remote Sensing

“…Thus, the projection residuals may serve as an indicator of the number of endmembers. Similar ideas have been considered in [24] and [27].…”

“…VolMin does not have simple closed-form schemes as in VolMax, and requires numerical optimization. In fact, the VolMin problem in (27) is more difficult to handle; a major obstacle is with the simplex constraints in (27), which are nonconvex. This issue can be overcome by transforming the simplex to a polyhedron (see, e.g., [35, pp.…”

“…The equivalent VolMin problem in (30) is arguably easier to handle than the original in (27). Specifically, the constraints in (30), which form a data-enclosing polyhedron, are linear (and convex).…”

“…the section "Convex Geometry." MVC-NMF is essentially a variation of the VolMin formulation [see (27)] in the noisy case, with endmember nonnegativity incorporated. As mentioned before, ) B vol( is nonconvex.…”

Fully Abundance-Constrained Sequential Endmember Finding: Linear Spectral Mixture Analysis

“…6.35b may not be as pure as it was thought to be. As shown in Chang et al (2010Chang et al ( , 2011b, a reasonable value of VD for the HYDICE data in Fig. 9.14 was 18.…”