Spectral–Spatial Reweighted Robust Nonlinear Unmixing for Hyperspectral Images Based on an Extended Multilinear Mixing Model

Abstract

Recently, nonlinear unmixing algorithms have attracted special attention in hyperspectral image (HSI) processing. However, the inherent wavelength-dependent nonlinear intensity and noise effects in real HSIs are often overlooked, and the spatial information of HSIs has not been fully utilized in current studies. In this paper, we propose a spectral-spatial reweighted robust nonlinear unmixing algorithm to solve the above problems. First, a robust unmixing method is built on an extended multilinear mixing model (EMLM), which employs the vectorized nonlinear parameters to describe the nonlinear intensity varying along with spectral bands, and adopts the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2,1</sub> norm-based loss function to suppress the influence of noise. Second, to fully exploit the spectral-spatial information of HSIs, the nonlinear unmixing problem is reformulated with two regularizers. Specifically, a reweighted collaborative sparse regularizer is used to make the pixels in a superpixel-based neighborhood share the same subset of endmembers and have similar abundances because the neighboring pixels are usually composed of several materials in similar proportions, and a reweighted spectral total variation regularizer is utilized to improve the spectral-spatial smoothness of the vectorized nonlinear parameters by considering the local-region similarities of the nonlinear mixing effects. Finally, the constrained optimization problem is solved by the alternating direction method of multipliers (ADMM). Experimental results on simulated, semi-simulated, and real hyperspectral datasets demonstrate that the proposed method outperforms several state-of-the-art nonlinear unmixing methods.