Solving adundance estimation in hyperspectral unmixing as a least distance problem

This work presents an algorithm for abundance estimation in hyperspectral imagery. The fully constrained abundance estimation problem where the positivity and the sum to less than or equal to one (or sum equal to one) constraints are enforced is solved by reformulating the problem as a least distance (LSD) least squares (LS) problem. The advantage of reformulating the problem as a least distance problem is that the resulting LSD problem can be solved using a duality theory using a nonnegative LS problem (NNLS). The NNLS problem can then be solved using Hanson and Lawson algorithm or one of several multiplicative iterative algorithms presented in the literature. The paper presents the derivation of the algorithm.