Hyperspectral mixed noise removal using nonconvex low-rank and total generalized variation

To better preserve the structural features while removing the mixed noise in hyperspectral image (HSI), this paper presents a novel HSI denoising method based on nonconvex low-rank (NLR) and total generalized variation (TGV) minimization. The proposed NLRTGV solver closely incorporates the advantages of TGV regularization, nonconvex nuclear norm, and ${\ell }_1$-norm. More specifically, the TGV regularizer, which maintains the spatial structure features, is adopted to eliminate Gaussian noise and prevent the staircase artifacts. The usage of nonconvex penalty is to explore the spectral low-rank properties, which contributes to suppress the sparse noise and preserve the major data components. Besides, we further employ the ${\ell }_1$-norm regularization to detect the sparse noise that includes impulse noise, deadlines and stripes. Computationally, by combining the iteratively reweighted ${\ell }_1$ algorithm, singular value shrinkage method and primal-dual framework, we construct in detail a modified alternating direction method of multipliers to solve the resulting optimization problem. Finally, as evidently demonstrated in both simulated and real-world HSI datasets experiments, our proposed approach shows the outstanding denoising performance in terms of mixed noise removal and detail features preservation, over the existing state-of-the-art competitors.