Smooth and Sparse Regularization for NMF Hyperspectral Unmixing

Abstract

In this paper, we propose a matrix factorization method for hyperspectral unmixing using the linear mixing model. In this method, we add the $\arctan$ functions of the endmembers to the $\ell _2$ -norm of the error in order to exploit the sparse property of the fractional abundances. Most of the energy of spectral signatures of materials is concentrated around the first few subbands resulting in smooth spectral signatures. To exploit this smoothness, we also add a weighted norm of the spectral signatures of the materials and to limit their nonsmooth errors. We propose a multiplicative iterative algorithm to solve this minimization problem as a nonnegative matrix factorization (NMF) problem. We apply our proposed Arctan-NMF method on the synthetic data from real spectral library and compare the performance of Arctan-NMF method with several state-of-the-art unmixing methods. Moreover, we evaluate the efficiency of Arctan-NMF on two different types of real hyperspectral data. Our simulations show that the Arctan-NMF is more effective than the state-of-the-art methods in terms of spectral angle distance and abundance angle distance.