Hyperspectral images (HSIs) are usually corrupted by various noises during the image acquisition process, e.g., Gaussian noise, impulse noise, stripes, deadlines and many others. Such complex noise severely degrades the data quality, reduces the interpretation accuracy of HSIs, and restricts the subsequent HSI applications. In this paper, a spatial non-local and local rank-constrained low-rank regularized Plugand-Play (NLRPnP) model is presented for mixed noise removal in HSIs. Specifically, we first divide HSIs into local overlapping patches. Local rank-constrained low-rank matrix recovery is adopted to effectively separate the low-rank clean HSI patches from the sparse noise and a part of Gaussian noise, and to significantly preserve local structure and detail information in HSIs. Then the spatial non-local based denoiser is introduced to promote the non-local self-similarity and obviously depress the Gaussian noise. Without increasing the difficulty of solving optimization problems, we combine the local and non-local based methods into the Plug-and-Play framework, and develop an efficient algorithm for solving the proposed NLRPnP model by using the alternating direction method of multipliers method. Finally, several experiments are conducted in both simulated and real data conditions to illustrate the better performance of the proposed NLRPnP model than the existing state-of-the-art denoising models. INDEX TERMS Hyperspectral images, denoising, plug-and-play framework, local low-rank matrix recovery, non-local regularization.

During the acquisition process, hyperspectral images (HSIs) are inevitably contaminated by mixed noise, which seriously affects the image quality. To improve the image quality, HSI denoising is a critical preprocessing step. In HSI denoising tasks, the method based on low-rank prior has achieved satisfying results. Among numerous denoising methods, the tensor nuclear norm (TNN), based on the tensor singular value decomposition (t-SVD), is employed to describe the low-rank prior approximately. Its calculation can be sped up by the fast Fourier transform (FFT). However, TNN is computed by the Fourier transform, which lacks the function of locating frequency. Besides, it only describes the low-rankness of the spectral correlations and ignores the spatial dimensions’ information. In this paper, to overcome the above deficiencies, we use the basis redundancy of the framelet and the low-rank characteristics of HSI in three modes. We propose the framelet-based tensor fibered rank as a new representation of the tensor rank, and the framelet-based three-modal tensor nuclear norm (F-3MTNN) as its convex relaxation. Meanwhile, the F-3MTNN is the new regularization of the denoising model. It can explore the low-rank characteristics of HSI along three modes that are more flexible and comprehensive. Moreover, we design an efficient algorithm via the alternating direction method of multipliers (ADMM). Finally, the numerical results of several experiments have shown the superior denoising performance of the proposed F-3MTNN model.

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