Graph Laplacian Regularized Sparse Representation for Image Denoising

In this paper, we propose a sparse representation model using the eigenvectors of the graph Laplacian, called Graph Laplacian based sparse representation (GL-SR), for image denoising. In this model, the high-order eigenvectors of graph Laplacian are introduced into the traditional sparse model as a regularization, and then the solution of the corresponding model is efficiently presented. Moreover, a denoising framework based on the GL-SR is further given. In details, the noisy patches are firstly clustered into several categories to enhance the structure relationship among them. Then, the eigenvectors of the graph Laplacian are obtained with the high-order ones carefully selected. A sparse model is sequently presented with these high-order eigenvectors as a regularization term. Finally, the proposed model is well solved by employing the solution of double sparse model. Experiments show the proposed method can achieve a better performance than some sparse-based methods, especially in the noise of large deviations.