The Successive Projection Algorithm (SPA), an algorithm with a spatial constraint for the automatic search of endmembers in hyperspectral data

Spectral mixing is a problem inherent to remote sensing data and results in few image pixel spectra representing "pure" targets. Linear spectral mixture analysis is designed to address this problem and it assumes that the pixel-to-pixel variability in a scene results from varying proportions of spectral endmembers. In this paper we present a different endmember-search algorithm called the Successive Projection Algorithm (SPA). SPA builds on convex geometry and orthogonal projection common to other endmember search algorithms by including a constraint on the spatial adjacency of endmember candidate pixels. Consequently it can reduce the susceptibility to outlier pixels and generates realistic endmembers. This is demonstrated using two case studies (AVIRIS Cuprite cube and Probe-1 imagery for Baffin Island) where image endmembers can be validated with ground truth data. The SPA algorithm extracts endmembers from hyperspectral data without having to reduce the data dimensionality. It uses the spectral angle (alike IEA) and the spatial adjacency of pixels in the image to constrain the selection of candidate pixels representing an endmember. We designed SPA based on the observation that many targets have spatial continuity (e. g. bedrock lithologies) in imagery and thus a spatial constraint would be beneficial in the endmember search. An additional product of the SPA is data describing the change of the simplex volume ratio between successive iterations during the endmember extraction. It illustrates the influence of a new endmember on the data structure, and provides information on the convergence of the algorithm. It can provide a general guideline to constrain the total number of endmembers in a search.