An Efficient SVD-Based Method for Image Denoising

Nonlocal self-similarity of images has attracted considerable interest in the field of image processing and has led to several state-of-the-art image denoising algorithms, such as block matching and 3-D, principal component analysis with local pixel grouping, patch-based locally optimal wiener, and spatially adaptive iterative singular-value thresholding. In this paper, we propose a computationally simple denoising algorithm using the nonlocal self-similarity and the low-rank approximation (LRA). The proposed method consists of three basic steps. First, our method classifies similar image patches by the block-matching technique to form the similar patch groups, which results in the similar patch groups to be low rank. Next, each group of similar patches is factorized by singular value decomposition (SVD) and estimated by taking only a few largest singular values and corresponding singular vectors. Finally, an initial denoised image is generated by aggregating all processed patches. For low-rank matrices, SVD can provide the optimal energy compaction in the least square sense. The proposed method exploits the optimal energy compaction property of SVD to lead an LRA of similar patch groups. Unlike other SVD-based methods, the LRA in SVD domain avoids learning the local basis for representing image patches, which usually is computationally expensive. The experimental results demonstrate that the proposed method can effectively reduce noise and be competitive with the current state-of-the-art denoising algorithms in terms of both quantitative metrics and subjective visual quality.