# Image Denoising Via Sparse Dictionaries Constructed by Subspace Learning

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## Abstract

In this paper, we propose a combinational algorithm for the removal of zero-mean white and homogeneous Gaussian additive noise from a given image. Image denoising is formulated as an optimization problem. This is iteratively solved by a weighted basis pursuit (BP) in the closed affine subspace. The patches extracted from a given noisy image can be sparsely and approximately represented by adaptively choosing a few nearest neighbors. The approximate reconstruction of these denoised patches is performed by the sparse representation on two dictionaries, which are built by a discrete cosine transform and the noisy patches, respectively. Experiments show that the proposed algorithm outperforms both BP denoising and Sparse K-SVD. This is because the underlying structure of natural images is better captured and preserved. The results are comparable to those of the block-matching 3D filtering algorithm.

## Keywords

Image denoising Optimization problem Weighted BPDN K-SVD Sparse K-SVD Closed affine subspace learning## Notes

### Acknowledgments

This work was supported by National Basic Research Program of China (973 Program) under Grant No. 2011CB302201, National Nature Science Foundation of China under Grants Nos. 61322203 and 61332002, and Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant No. 20120181130007.

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