Hybrid Sparse Linear and Lattice Method for Hyperspectral Image Unmixing

Abstract

Linear spectral unmixing aims to estimate the fractional abundances of spectral signatures in each pixel. The Linear Mixing Model (LMM) of hyperspectral images assumes that pixel spectra are affine combinations of fundamental spectral signatures called endmembers. Endmember induction algorithms (EIA) extract the endmembers from the hyperspectral data. 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 endmembers extracted can be huge. This calls for additional endmember selection steps, and to approaching the unmixing problem with linear sparse regression techniques. In this paper, we combine WM algorithm with clustering techniques and Conjugate Gradient Pursuit (CGP) for endmember induction. Our experiments are conducted using hyperspectral imaging obtained by the Airborne Visible/Infrared Imaging Spectometer of the NASA Jet Propulsion Laboratory. The limited length of the paper limits the experimental depth to the confirmation of the validity of the proposed method.