Robust Sparse Unmixing for Hyperspectral Imagery

A linear sparse unmixing method based on spectral library has been widely used to tackle the hyperspectral unmixing problem, under the assumption that the spectrum of each pixel in the hyperspectral scene can be expressed as a linear combination of pure endmembers in the spectral library. However, because of the ion (atom) substitution in the geological process, there often exists spectral variability between the measured endmembers in the real environment and corresponding ones in the spectral library, which poses a significant challenge to linear sparse unmixing. Physically, the substitution leads to the variation of absorption peaks of endmembers, making the spectral variation of sparse property. To address the above problem, we introduce redundant spectrum to represent the spectral variation caused by ion (atom) substitution and develop a sparse redundant unmixing model by adding the redundant regularization into the classical sparse regression formulation. Based on the alternating direction method of multipliers, we develop a unified algorithm called sparse redundant unmixing to obtain the solution. Both simulation experiment and real data experiment demonstrate that the proposed method can effectively use the redundant spectrum to address the spectral variation problem caused by the ion (atom) substitution.