Linear unmixing of hyperspectral images using a scaled gradient method

This paper addresses the problem of linear unmixing for hyperspectral imagery. This problem can be formulated as a linear regression problem whose regression coefficients (abundances) satisfy sum-to-one and positivity constraints. Two scaled gradient iterative methods are proposed for estimating the abundances of the linear mixing model. The first method is obtained by including a normalization step in the scaled gradient method. The second method inspired by the fully constrained least squares algorithm includes the sum-to-one constraint in the observation model with an appropriate weighting parameter. Simulations on synthetic data illustrate the performance of these algorithms.