  Non-local low-rank tensor approximation has been developed as a
state-of-the-art method for hyperspectral image (HSI) restoration, which
includes the tasks of denoising, compressed HSI reconstruction and inpainting.
Unfortunately, while its restoration performance benefits from more spectral
bands, its runtime also substantially increases. In this paper, we claim that
the HSI lies in a global spectral low-rank subspace, and the spectral subspaces
of each full band patch group should lie in this global low-rank subspace. This
motivates us to propose a unified paradigm combining the spatial and spectral
properties for HSI restoration. The proposed paradigm enjoys performance
superiority from the non-local spatial denoising and light computation
complexity from the low-rank orthogonal basis exploration. An efficient
alternating minimization algorithm with rank adaptation is developed. It is
done by first solving a fidelity term-related problem for the update of a
latent input image, and then learning a low-dimensional orthogonal basis and
the related reduced image from the latent input image. Subsequently, non-local
low-rank denoising is developed to refine the reduced image and orthogonal
basis iteratively. Finally, the experiments on HSI denoising, compressed
reconstruction, and inpainting tasks, with both simulated and real datasets,
demonstrate its superiority with respect to state-of-the-art HSI restoration
methods.
