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Image Denoising Using Low-Rank Dictionary and Sparse Representation

In this paper, we propose an image denoising model by using low-rank dictionary and sparse representation (LRSR). The K-SVD algorithm learns a universal dictionary for all patches in an image and the NLM exploits similarities of nonlocal patches, both achieve effective denoising performance. Motivated by these methods, we propose to use a low-rank dictionary for each cluster of similar patches and the dictionary is used to simultaneously produce sparse representations of all patches in the cluster. Our algorithm has two advantages. The first one is, we use a dictionary particular to each cluster of similar patches so that the dictionary can exploit the peculiar structure underlying the cluster and better adapts to the cluster. The second, we represent the similar patches in a cluster simultaneously by the dictionary so that we can impose a structured sparsity to make full use of similarities of these patches and get better restoration quality. Experimental results show that our method performs better than or on par with the state-of-the-art denoising methods such as BM3D and TDNL.