Augmented Lagrangian Methods for p-Harmonic Flows with the Generalized Penalization Terms and Application to Image Processing

In this paper,we propose a generalized penalization technique and a convex constraint minimization approach for the p-harmonic flow problem following the ideas in[Kang&March,IEEE T.Image Process.,16(2007),2251–2261].We use fast algorithms to solve the subproblems,such as the dual projection methods,primal-dual methods and augmented Lagrangian methods.With a special penalization term,some special algorithms are presented.Numerical experiments are given to demonstrate the performance of the proposed methods.We successfully show that our algorithms are effective and efficient due to two reasons:the solver for subproblem is fast in essence and there is no need to solve the subproblem accurately(even 2 inner iterations of the subproblem are enough).It is also observed that better PSNR values are produced using the new algorithms.

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 variation-al image restoration methods.It broadens the applications of boosting techniques to a wide range of image restoration problems,including not only denoising but also deblur-ring 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 analy-sis 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 im-age restoration problems such as denoising,inpainting and deblurring.The numerical results demonstrate promising improvement over standard variational restoration mod-els such as total variation based models and higher order variational model as total generalized variation.

New Splitting Algorithms for Multiplicative Noise Removal Based on Aubert-Aujol Model

In this paper,we propose new algorithms for multiplicative noise removal based on the Aubert-Aujol(AA)model.By introducing a constraint from the forward model with an auxiliary variable for the noise,the NEMA(short for Noise Estimate based Multiplicative noise removal by alternating direction method of multipliers(ADMM))is firstly given.To further reduce the computational cost,an additional proximal term is considered for the subproblem with regard to the original variable,the NEMA_(f)(short for a variant of NEMA with fully splitting form)is further proposed.We conduct numerous experiments to show the convergence and performance of the proposed algorithms.Namely,the restoration results by the proposed algorithms are better in terms of SNRs for image deblurring than other compared methods including two popular algorithms for AA model and three algorithms of its convex variants.