L1/2 Sparsity Constrained Nonnegative Matrix Factorization for Hyperspectral

Hyperspectral unmixing is a crucial preprocessing step for material classification and recognition. In the last decade, nonnegative matrix factorization (NMF) and its ex-tensions have been intensively studied to unmix hyperspec-tral imagery and recover the material end-members. As an important constraint, sparsity has been modeled mak-ing use of L1 or L2 regularizers. However, the full additiv-ity constraint of material abundances is often overlooked, hence, limiting the practical efficacy of these methods. In this paper, we extend the NMF algorithm by incorporat-ing the L1/2 sparsity constraint. The L1/2-NMF provides more sparse and accurate results than the other regular-izers by considering the end-member additivity constraint explicitly in the optimisation process. Experiments on the synthetic and real hyperspectral data validate the proposed algorithm. 1