Nonlocal Tensor-Ring Decomposition for Hyperspectral Image Denoising

Hyperspectral image (HSI) denoising is a fundamental problem in remote sensing and image processing. Recently, nonlocal low-rank tensor approximation-based denoising methods have attracted much attention due to their advantage of being capable of fully exploiting the nonlocal self-similarity and global spectral correlation. Existing nonlocal low-rank tensor approximation methods were mainly based on two common decomposition [Tucker or CANDECOMP/PARAFAC (CP)] methods and achieved the state-of-the-art results, but they are subject to certain issues and do not produce the best approximation for a tensor. For example, the number of parameters for Tucker decomposition increases exponentially according to its dimensions, and CP decomposition cannot better preserve the intrinsic correlation of the HSI. In this article, a novel nonlocal tensor-ring (TR) approximation is proposed for HSI denoising by using TR decomposition to explore the nonlocal self-similarity and global spectral correlation simultaneously. TR decomposition approximates a high-order tensor as a sequence of cyclically contracted third-order tensors, which has strong ability to explore these two intrinsic priors and to improve the HSI denoising results. Moreover, an efficient proximal alternating minimization algorithm is developed to optimize the proposed TR decomposition model efficiently. Extensive experiments on three simulated data sets under several noise levels and two real data sets verify that the proposed TR model provides better HSI denoising results than several state-of-the-art methods in terms of quantitative and visual performance evaluations.