Total generalized variation and wavelet transform for impulsive image restoration

Combining the advantages of total generalized variation and wavelet transform, we propose a new hybrid model based on L1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_{1}$$\end{document} norm for image restoration. Numerically, we obtain the optimal solution by alternating iteration of the efficient augmented Lagrangian method. For the selection of regularization parameters, we use an adaptive criterion based on the value function. Experimental results show that the proposed algorithm can remove impulse noise well and reduce staircase effect while preserving edges. Compared with several classical methods, the proposed model has also higher PSNR and SSIM values.