Image Denoising And Image Decomposition Based On Dual Method

First the paper aim at the disadvantage of the gradient decent time marching algo-rithm for the minimization of LLT model, and propose a dual method based on Legender-Fenchel transform to overcome the numerical di?culties related to the non-di?erentiabilityof LLT model. We have proofed the convergence of the dual method and demonstrated thespeed of convergence of the dual method is faster than the gradient decent time marchingalgorithm by numerical experiments.Second, we aim at shortcoming of the ROF( Rudin, Osher and Fatemi ) model andLLT model in denoising processing, combin decomposition model, TV-norm and Fourth-Order PDE, the article proposes the DD ( decomposition and denoising ) model basedon di?erence between texture and noise. In denoising, the new model decompose annoisy image into three parts, structure, texture and noise, so achieves the denoising anddecomposition goal. Further more, we testify rationality and validity of the DD modeland the algorithm through the experiments.In the end, to avoide the staircase e?ects of the structure from the TV-G model,Vese-Osher model and TV-H?1 model and so on, we proposed a two-steps method to overcomethis problem. In the first step, we propose a new space for the normal vector and proofsome properties of it. We use the dual method based on the Legender-Fenchel transformto solve it. In the second step, we use the original grade descent algorithm to solve it.