Image denoising via Graph regularized K-SVD

Sparse representation theory has been well developed in recent years. In this paper, we consider an image denoising problem which can be efficiently solved under the framework of the sparse representation theory. The traditional image denoising methods based on the sparse representation seldom take into account the special structure of the data. As an attempt to overcome such problem, the Graph regularized K-means singular value decomposition (Graph K-SVD) algorithm is proposed with the manifold learning. The local geometrical structure of the image is considered in the sparse optimization model with the graph Laplacian. This manifold-based optimization problem is well solved in the framework of the traditional K-SVD algorithm. Since the novel strategy adds a graph regularizer to the sparse representation model in order to emphasize the correlations among image blocks, the Graph K-SVD can achieve better denoising performance than the traditional K-SVD.