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Hyperspectral image (HSI) restoration is to recover the clean image from degraded version, such as the noisy, blurred, or damaged. Recent low-rank tensor-based recovery methods have been widely explored in HSIs restoration. Most of previous methods, however, neglect an inconspicuous but important phenomenon that the physical meaning and dimension along the spatial, spectral, and nonlocal mode are markedly different. In this work, we discover the low-rank property discrepancy along spatial, spectral, and nonlocal self-similarity mode in the HSIs, and argue that the intrinsic low-rank correlations along each mode contribute different to the final restoration results. Consequently, we figure out that the combination of the spectral and nonlocal-induced low-rank is most beneficial for HSIs modeling, and propose an optimal low-rank tensor (OLRT) model for HSIs restoration. Furthermore, we not only explore the low-rank property in the image component, but also in the sparse error component (stripe noise in HSIs). Thus, we extend OLRT to the OLRT-robust principal component analysis (RPCA) with low-rank tensor priors for both the HSIs and sparse error. Besides, previous methods are usually designed for one specific HSI task, which is less robust to various tasks. We prove that the proposed optimal low-rank prior is very flexible for various HSI restoration problems including denoising, deblurring, inpainting, and destriping. The proposed methods have been extensively evaluated on several benchmarks and tasks, and greatly outperform state-of-the-art (STOA). We show the simple yet effective OLRT strategy is also beneficial to STOA. [ABSTRACT FROM AUTHOR]

The spectral and the spatial information in hyperspectral images (HSIs) are the two sides of the same coin. How to jointly model them is the key issue for HSIs’ noise removal, including random noise, structural stripe noise, and dead pixels/lines. In this paper, we introduce the deep convolutional neural network (CNN) to achieve this goal. The learned filters can well extract the spatial information within their local receptive filed. Meanwhile, the spectral correlation can be depicted by the multiple channels of the learned 2-D filters, namely, the number of filters in each layer. The consequent advantages of our CNN-based HSI denoising method (HSI-DeNet) over previous methods are threefold. First, the proposed HSI-DeNet can be regarded as a tensor-based method by directly learning the filters in each layer without damaging the spectral-spatial structures. Second, the HSI-DeNet can simultaneously accommodate various kinds of noise in HSIs. Moreover, our method is flexible for both single image and multiple images by slightly modifying the channels of the filters in the first and last layers. Last but not least, our method is extremely fast in the testing phase, which makes it more practical for real application. The proposed HSI-DeNet is extensively evaluated on several HSIs, and outperforms the state-of-the-art HSI-DeNets in terms of both speed and performance. [ABSTRACT FROM AUTHOR]