A Boosting Procedure for Variational-Based Image Restoration

Variational methods are an important class of methods for general image restoration. Boosting technique has been shown capable of improving many image denoising algorithms. This paper discusses a boosting technique for general variational image restoration methods. It broadens the applications of boosting techniques to a wide range of image restoration problems, including not only denoising but also deblurring and inpainting. In particular, we combine the recent SOS technique with dynamic parameter to variational methods. The dynamic regularization parameter is motivated by Meyer’s analysis on the ROF model. In each iteration of the boosting scheme, the variational model is solved by augmented Lagrangian method. The convergence analysis of the boosting process is shown in a special case of total variation image denoising with a “disk” input data. We have implemented our boosting technique for several image restoration problems such as denoising, inpainting and deblurring. The numerical results demonstrate promising improvement over standard variational restoration models such as total variation based models and higher order variational model as total generalized variation. AMS subject classifications: 68U10, 90C25, 49M37