Graph Laplacian for image deblurring

Image deblurring is a relevant problem in many fields of science and engineering. To solve this problem, different approaches have been proposed, and, among the various methods, variational ones are extremely popular. These substitute original with minimization where functional composed two terms, data fidelity term regularization term. In paper we propose, classical non-negative constrained $\ell^2$-$\ell^1$ framework, use graph Laplacian as operator. Firstly, describe how to construct from observed noisy blurred image. Once has built, efficiently proposed by splitting convolution operator Alternating Direction Multiplier Method (ADMM). Some selected numerical examples show good performances algorithm.