Hyperspectral image denoising via weighted double sparsity total variation and low-rank representation

Hyperspectral images (HSIs) are always contaminated by various mixed noise, which degrades the quality of acquired images and seriously affects the subsequent extensive applications. Total variation (TV) is popular for its capability of preserving details and promoting smoothness in HSI denoising. However, TV may cause over-smoothness and details loss. To tackle the above problems, we propose a double sparsity TV and low-rank representation denoising model (LRDSTV) for the mixed noise removal. Specifically, the double sparsity TV means fiber sparsity with sparse fibers in the gradient domain, promoting piecewise smooth structures and properly using the spatial information of the HSI. Moreover, we utilize the weighted nuclear norm to explore the low-rank property of mode-3 unfolding of the HSI, taking advantage of the spectral correlation and helping maintain more details to avoid over-smoothing. Then, the alternating direction method of multipliers (ADMM) is applied for the optimization of the LRDSTV model. Finally, a series of denoising experiments on simulated and real data sets demonstrate the effectiveness and superiority of the proposed algorithm compared with some state-of-the-art algorithms.