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 (termed as WTR1) for nonlocal image denoising. Although the low-rank approximation problem has been well studied for matrices, it remains elusive of the theoretical extension to tensors due to the NP-hard 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 3D 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.