L_1/2 Sparsity constrained nonnegative matrix factorization for hyperspectral unmixing

Hyperspectral unmixing is a crucial preprocessing step for material classification and recognition. In the last decade, nonnegative matrix factorization (NMF) and its extensions have been intensively studied to unmix hyperspectral imagery and recover the material end-members. As an important constraint, sparsity has been modeled making use of L₁ or L ₂ regularizers. However, the full additivity constraint of material abundances is often overlooked, hence, limiting the practical efficacy of these methods. In this paper, we extend the NMF algorithm by incorporating the L _1/2 sparsity constraint. The L_1/2-NMF provides more sparse and accurate results than the other regularizers by considering the end-member additivity constraint explicitly in the optimisation process. Experiments on the synthetic and real hyperspectral data validate the proposed algorithm.