Image Denoising Via Sparse Dictionaries Constructed by Subspace Learning

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.