Hyperspectral Image Denoising Using Nonconvex Fraction Function

Hyperspectral image (HSI) denoising is a challenging task, not only because it is unavoidably contaminated by severe mixed noises, but also for its hard-to-recover spatial-spectral structure. Since it has been found that HSI has low-rank property, low-rank models have received extensive attention in dealing with the HSI denoising task. However, these models either use nuclear norm, which can only obtain sub-optimal solutions, or require some predefined information that is difficult to determine. To address these issues, in this paper we propose a new HSI denoising model based on non-convex fraction function, which has excellent performance in removing mixed noises. Specifically, the proposed model can capture the rank information of HSI automatically, which allows it to separate clean HSI from noises more accurately. Then, an iterative optimization algorithm is developed by exploiting the framework of the augmented Lagrange multiplier (ALM). Meanwhile, the subproblems at each iteration can be solved by the proximal operator with a closed-form solution. Besides, the convergence of the proposed algorithm is also provided theoretically. Extensive experiments implemented with simulated and real datasets demonstrate that our proposed model performs better than state-of-the-art models in HSI denoising. MATLAB code is available at https://github.com/wangzhi-swu/HSI-Denosing.