An Efficient SVD-Based Method for Image Denoising
Abstract— Nonlocal self-similarity of images has attracted considerable interest in the ﬁeld of image processing and led to several state-of-the-art image denoising algorithms, such as BM3D, LPG-PCA, PLOWand SAIST. In this paper, we propose a computationally simple denoising algorithm by using the nonlocal self-similarity and the low-rank approximation. The proposed method consists of three basic steps. Firstly, 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 < Final Year Projects 2016 >and estimated by taking only a few largest singular values and corresponding singular vectors. Lastly, 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 a low-rank approximation of similar patch groups. Unlike other SVD-based methods, the low-rank approximation in SVD domain avoids learning the local basis for representing image patches which usually is computationally expensive.
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