A blind identification and source separation method based on subspace intersections for hyperspectral astrophysical data

Abstract

This paper presents a geometric method for solving the Blind Source Separation problem. The method is based on a weak sparsity assumption: for each source, there should exist at least one pair of zones that share only this source. The process consists first in finding the pairs of zones sharing a unique source with an original geometric approach. Each pair of zones, having a mono-dimensional intersection, yields an estimate of a column of the mixing matrix up to a scale factor. All intersections are identified by Singular Value Decomposition. The intersections corresponding to the same column of the mixing matrix are then grouped by a clustering algorithm so as to derive a single estimate of each column. The sources are finally reconstructed from the observed vectors and mixing parameters with a least square algorithm. Various tests on synthetic and real hyperspectral astrophysical data illustrate the efficiency of this approach.