Recently, sparse unmixing (SU) of hyperspectral data has received particular attention for analyzing remote sensing images. However, most SU methods are based on the commonly admitted linear mixing model (LMM), which ignores the possible nonlinear effects (i.e., nonlinearity). In this paper, we propose a new method named robust collaborative sparse regression (RCSR) based on the robust LMM (rLMM) for hyperspectral unmixing. The rLMM takes the nonlinearity into consideration, and the nonlinearity is merely treated as outlier, which has the underlying sparse property. The RCSR simultaneously takes the collaborative sparse property of the abundance and sparsely distributed additive property of the outlier into consideration, which can be formed as a robust joint sparse regression problem. The inexact augmented Lagrangian method (IALM) is used to optimize the proposed RCSR. The qualitative and quantitative experiments on synthetic datasets and real hyperspectral images demonstrate that the proposed RCSR is efficient for solving the hyperspectral SU problem compared with the other four state-of-the-art algorithms.
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