Robust Sparse Hyperspectral Unmixing With $\ell_{2,1}$ Norm

Abstract

Sparse unmixing (SU) of hyperspectral data have recently received particular attention for analyzing remote sensing images, which aims at finding the optimal subset of signatures to best model the mixed pixel in the scene. However, most SU methods are based on the commonly admitted linear mixing model, which ignores the possible nonlinear effects (i.e., nonlinearity), and the nonlinearity is merely treated as outlier. Besides, the traditional SU algorithms often adopt the $\ell _{2}$ norm loss function, which makes them sensitive to noises and outliers. In this paper, we propose a robust SU (RSU) method with $\ell _{2,1}$ norm loss function, which is robust for noises and outliers. Then, the RSU can be solved by the alternative direction method of multipliers. Finally, the experiments on both synthetic data sets and real hyperspectral images demonstrate that the proposed RSU is efficient for solving the hyperspectral SU problem compared with the state-of-the-art algorithms.