Nonnegative matrix factorization with entropy regularization for hyperspectral unmixing

Nonnegative matrix factorization (NMF) has been one of the most widely used techniques for hyperspectral unmixing (HU), which aims at decomposing each mixed pixel into a set of endmembers and their corresponding fractional abundances. However, the standard NMF model is ill-posed with only considering the non-negativity constraint. Therefore, many kinds of regularization (e.g. Tikhonov or sparsity regularization) have been imposed into NMF to well-define the model. Different from the general regularization, we introduce the entropy regularization into the NMF and propose an entropy regularized NMF (ERNMF) model for HU. In ERNMF, we minimize the entropy of that abundances on each pixel, which can achieve the sparsity of abundances. We also introduce a strategy to adaptively adjust the regularization parameter. In addition, we explore the proposed ERNMF with two optimization algorithms and provide the corresponding convergence and complexity analysis. Experimental results on both simulated and real-world data sets demonstrate the effectiveness of our proposed model and algorithms in comparison to the state-of-the-art approaches.