Based On A Discrete Energy Functional Variational Image Denoising

Digital image processing is a new discipline which combines mathematical science with computer technology.Image denoising is one of the researching focus in this field. Recently the application of Partial Differential Equations(PDEs) in image denoising is commonly concerned by researchers in the areas of mathematics,graphics and images. The PDEs used are usually constructed by two approaches.One method is to construct PDEs directly,which always describe physical phenomena.The other method is to construct PDEs from the Euler-Lagrange equation of an energy functional by variational approach.The latter is widely used in recent years.This thesis first surveys some classical models.The strengths and weaknesses of each model is analyzed and commented.Our main work is to establish denoising model based on variational technique. The common routine is to construct PDE models by the variation of continuous energy functional and to discretize the obtained PDEs to denoising images.In this thesis, we discretize a generic continuous energy functional and construct denoising model by variational calculus.Explicit iteration scheme for solving the nonlinear system of equations is derived.Numerical experiments are carried out to verify the effectiveness of the generalized model and the efficiency compared with PDE models.