Coupled sparse denoising and unmixing with low-rank constraint for hyperspectral image

Hyperspectral image (HSI) denoising is significant for correct interpretation. In this paper, a sparse representation framework that unifies denoising and spectral unmixing in a closed-loop manner is proposed. While conventional approaches treat denoising and unmixing separately, the proposed scheme utilizes spectral information from unmixing as feedback to correct spectral distortion. Both denoising and spectral unmixing act as constraints to the others and are solved iteratively. Noise is suppressed via sparse coding, and fractional abundance in spectral unmixing is estimated using the sparsity prior of endmembers from a spectral library. The abundance of endmembers is used as a spectral regularizer for denoising based on the hypothesis that spectral signatures obtained from a denoising process result are close to those of unmixing. Unmixing restrains spectral distortion and results in better denoising, which reciprocally leads to further improvements in unmixing. The strength of our proposed method is illustrated by simulated and real HSIs with performance competitive to the state-of-the-art denoising and unmixing methods.