Sparsity-Regularized Robust Non-Negative Matrix Factorization for Hyperspectral Unmixing

Hyperspectral unmixing (HU) is one of the crucial steps for many hyperspectral applications, including material classification and recognition. In the last decade, non-negative matrix factorization (NMF) and its extensions have been widely studied and have achieved advanced performances in HU. Unfortunately, most of the existing NMF-based methods make the assumption that the hyperspectral data are only corrupted by Gaussian noise. In real applications, the hyperspectral data are inevitably corrupted by sparse noise, which includes impulse noise, stripes, deadlines, and others types of noise. By separately modeling the sparse noise and Gaussian noise, a robust NMF (RNMF) model is subsequently introduced to unmix the hyperspectral data. The proposed RNMF model is able to simultaneously handle Gaussian noise and sparse noise, and can be efficiently learned with elegant update rules. In addition, sparsity regularizers are added to restrict the abundance maps in the RNMF, with the consideration of the sparse property of the material types within the hyperspectral scene. The experimental results with simulated and real data confirm the superiority of the proposed sparsity-regularized RNMF methods compared to the traditional NMF methods.