Weighted Tensor Rank-1 Decomposition for Nonlocal Image Denoising

Natural images often contain patches with high similarity. In this paper, to effectively utilize the local and nonlocal self-similarity for low-rank models, we propose a novel weighted tensor rank-1 decomposition method (terms as WTR1) for nonlocal image denoising. Although the low-rank approximation problem has been well studied for matrices, it remains elusive of the theoretically extension to tensors due to the NPhard tensor decomposition. To tackle this problem, the proposed WTR1 method designs a new efficient CANDECOMP/PARAFAC (CP) decomposition algorithm and constructs a straightforward low-rank tensor approximation strategy. This is achieved by elegantly manipulating the CP-rank, called intrinsic low-rank tensor approximation. Specifically, the WTR1 method first groups similar patches into a 3-D stack and converts the stack into a finite sum of rank-1 products. Then, we deploy the intrinsic low-rank tensor approximation to produce the final denoised image. The proposed WTR1 method can jointly exploit the local and nonlocal self-similarity, thus improving the nonlocal image denoising quality. Experimental results have shown that the proposed WTR1 outperforms several state-of-the-art denoising methods.