  Non-local low-rank tensor approximation has been developed as a
state-of-the-art method for hyperspectral image (HSI) denoising. Unfortunately,
with more spectral bands for HSI, while the running time of these methods
significantly increases, their denoising performance benefits little. In this
paper, we claim that the HSI underlines a global spectral low-rank subspace,
and the spectral subspaces of each full band patch groups should underlie this
global low-rank subspace. This motivates us to propose a unified
spatial-spectral paradigm for HSI denoising. As the new model is hard to
optimize, we further propose an efficient algorithm for optimization, which is
motivated by alternating minimization. This is done by first learning a
low-dimensional projection and the related reduced image from the noisy HSI.
Then, the non-local low-rank denoising and iterative regularization are
developed to refine the reduced image and projection, respectively. Finally,
experiments on synthetic and both real datasets demonstrate the superiority
against the other state-of-the-arts HSI denoising methods.
