Blind decomposition of low‐dimensional multi‐spectral image by sparse component analysis

Abstract

AbstractA multilayer hierarchical alternating least square nonnegative matrix factorization approach has been applied to blind decomposition of low‐dimensional multi‐spectral image. The method performs blind decomposition exploiting spectral diversity and spatial sparsity between materials present in the image and, unlike many blind source separation methods, is invariant with respect to statistical (in)dependence among spatial distributions of the materials. As opposed to many existing blind source separation algorithms, the method is capable of estimating the unknown number of materials present in the image. This number can be less than, equal to, or greater than the number of spectral bands. The method is validated on underdetermined blind source separation problems associated with blind decomposition of experimental red‐green‐blue images composed of four materials. Achieved performance has been superior when compared against methods based on minimization of the ℓ1‐norm: linear programming and interior‐point methods. In addition to tumor demarcation, as demonstrated in the paper, other areas that can also benefit from the proposed method include cell, chemical, and tissue imaging. Copyright © 2009 John Wiley & Sons, Ltd.