Image restoration via tight frame regularization and local constraints

In this paper, we propose two variational image denosing/deblurring models which combine tight frame regularization with two types of existing local constraints. Additive white Gaussian noise is assumed in the models. By Lagrangian multiplier method, the local constraints correspond to the fidelity term with spatial adaptive parameters. As the fidelity parameter is bigger in the image regions with textures than in the cartoon region, our models can recover more texture while denoising/deblurring. Fast numerical schemes are designed for the two models based on split Bregman (SB) technique and doubly augmented Lagrangian (DAL) method with acceleration. In the experiments, we show that the proposed models have better performance compared with the existing total variation based image restoration models with global or local constraints and the frame based model with global constraint.