A patch-based low-rank tensor approximation model for multiframe image denoising

Compared with matrix, tensor is a more natural representation for multiframe image, such as hyperspectral image and MRI image. Low-rankness of tensor is essential to describe the intrinsic geometrical structure of these data. Patch-based low-rank models have shown their ability to exploit spatial redundancy of computer vision data especially for natural image denoising. However, most of the existed patch-based matrix models are based on two dimensional low-rankness, which cannot fully reveal the correlation of every direction in high-order multiframe images; the existed patch-based tensor models either need additional assumptions or need SVD in every loop of iteration which is computationally expensive. In this paper, we propose a novel patch-based model to recover a low-rank tensor by simultaneously performing low-rank matrix factorizations to the all-mode matricizations of the underlying low-rank tensor. An augmented Lagrangian alternating minimization algorithm is implemented to solve the model along with two adaptive rank-adjusting strategies when the exact rank is unknown. We apply the proposed algorithm to multiframe image denoising by exploiting the nonlocal self-similarity. Experimental results show that our algorithm can better preserve the sharpness of important image structures and outperforms several state-of-the-art denoising methods.