Dictionary-aided hyperspectral unmixing based on constrained l2,q–l2,p optimization

Abstract

Dictionary-aided unmixing has been introduced as a semi-supervised unmixing method, under the assumption that the observed mixed pixel of a hyperspectral image can be expressed in the form of different linear combinations of a few spectral signatures from an available spectral library. Sparse-regression-based unmixing methods have been recently proposed to solve this problem. Mostly, lp-norm minimization is a closer surrogate to the l0-norm minimization and can be solved more efficiently than l1-norm minimization. In this paper, we model the hyperspectral unmixing as a constrained l2,q–l2,p optimization problem. To effectively solve the induced optimization problems for any q (1≤q≤2) and p (0<p≤1), an iteratively reweighted least squares algorithm is developed and the convergence of the proposed method is also demonstrated. Experimental evaluation carried out on synthetic and real hyperspectral data shows that the proposed method yields better spectral unmixing accuracy in both quantitative and qualitative evaluations than state-of-the-art unmixing algorithms.