The Research Of Image Reconstruction Problem Based On The Smoothing Total Variation

As one of the classic models, the ROF model has been focused on the field of image processing. The main reason of this model is due to keeping the edge regions while restoring the degraded image. However, this model usually leads to the staircase effects in the smoothing regions. So in the dissertation we will propose a modified model based on smoothing the total variation term of the ROF model to consider the image reconstruction problem. We also propose a fast and robust numerical method to solve the Proposed model. Specifically, the arrangement of this dissertation is organized as follows:In chapter 1, we introduce some research backgrounds and methods of digital image processing and image reconstruction, introduces the main work and content arrangement of the paper.In chapter 2, we give some preliminary knowledge, including some classic models,the primal-dual method, the steepest descent method and some notation of mathematical symbols used in the dissertation.In chapter 3, we mainly put forward a new image reconstruction model, and give related theory analysis.In chapter 4, we propose a numerical method to solve the established model, that is to say, transferring the initial problem to the primal-dual problem so that we can solve it effectively. We verify the validity of the model and algorithm by some numerical comparisons.The fifth chapter summarizes some main results in this dissertation and points out future research direction.