A Novel Tensor-Based Hyperspectral Image Restoration Method With Low-Rank Modeling in Gradient Domains

The hyperspectral image (HSI) is easily contaminated by various kinds of mixed noise (such as Gaussian noise, impulse noise, stripes, and deadlines) during the process of data acquisition and conversion, which significantly affect the quality and applications of HSI. As an important and effective scheme for the quality improvement of HSI, the HSI restoration problem aims to recover a clean HSI from the noisy HSI with mixed noise. Thus, based on the tensor modeling of HSI, we propose a novel tensor-based HSI restoration model with low-rank modeling in gradient domains in a unified tensor representation framework in this article. First, for the spectral low-rank modeling of HSI in spectral gradient domain, we particularly exploit the low-rank property of spectral gradient, and propose the spectral gradient-based weighted nuclear norm low-rank prior term. Second, for the spatial-mode low-rank modeling of HSI in spatial gradient domain, we particularly exploit the low-rank property of spatial gradient tensors via the discrete Fourier transform, and propose the spatial gradient-based tensor nuclear norm low-rank prior term. Then, we use the alternative direction method of multipliers to solve the proposed model. Finally, the restoration results on both the simulated and real HSI datasets demonstrate that the proposed method is superior to many state-of-the-art methods in the aspects of visual and quantitative comparisons.