Greedy Sparsification WM Algorithm for Endmember Induction in Hyperspectral Images

Abstract

The Linear Mixing Model (LMM) of hyperspectral images asumes that pixel spectra are affine combinations of basic spectral signatures, called endmembers, which are the vertices of a convex polytope covering the image data. Endmember induction algorithms (EIA) extract the endmembers from the image data, obtaining a precise spectral characterization of the image. The WM algorithm assumes that a set of Affine Independent vectors can be extracted from the rows and columns of dual Lattice Autoassociative Memories (LAAM) built on the image spectra. Indeed, the set of endmembers induced by this algorithm defines a convex polytope covering the hyperspectral image data. However, the number of induced endmembers obtained by this procedure is too high for practical purposes, besides they are highly correlated. In this paper, we apply a greedy sparsification algorithm aiming to select the minimal set of endmembers that explains the data in the image. We report results on a well known benchmark image.