Graph Laplacian and dictionary learning, Lagrangian method for image denoising

Removing the noise while keeping the image features like edges, textures is a challenging problem in image denoising. Because it is an under-determined problem, defining appropriate image priors to regularize the problem plays an important role. Recently a popular one among proposed image priors is the graph Laplacian regularizer, which can exploit the local geometry structure of the image. Introducing a graph Laplacian matrix term and a dictionary learning term, in this paper we propose a new model to restore the original image. The objective consists of a data fidelity term, a graph Laplacian regularizer term and a sparse representation term. To solve this non-convex model, we propose an alternating minimization method via Lagrangian optimization. In addition, we choose the eigenvectors of the normalized graph Laplacian matrix as the initial dictionary for the sparse coding. Experimental results demonstrate that the proposed model outperforms BF and NLM, in terms of both objective measurements and perceptual quality.