Image Denoising Based On Primal-dual Algorithm

Digital image is often polluted by noise in the process of collection and transmission,the purpose of image denoising is to reduce or eliminate interference and noise, and remain the useful information in the image, which is the foundation for subsequent higher level image processing such as image segmentation, feature extraction and target recognition,ect. Therefore, e?ectively removing the noise of the image becomes an important issue in the ?eld of digital image processing.The ?rst chapter of this thesis introduces the background, existing methods in the?eld of digital image processing and image denoising. It also gives a brief description of the main idea of the research paper.The second chapter gives some preliminary knowledge. The knowledge consists the related models, primal-dual method, Chambolle projection algorithm, and some notations of mathematical symbols.The third chapter is based on TV-Stokes model, the ?rst step is to modify the tangent vector of the noised image. Then, we introduce the minimizing energy functional and free divergence condition. Afterword, making use of the dual variable of tangent vector and the orthogonal projection to the constraint set, then we can convert the minimizing energy functional to an unconstrained problem, the numerical experience use Chambolle projection algorithm. When reconstrcting image that matched with tangent vector in the second step, we also use dual variable. In the numerical experiments, we use primal-dual algorithm, which we then record the results, the thesis will present the e?ect of parameter selection for di?erent denoising result and the validity of the algorithm.The fourth chapter is based on the classical TV model with primal-dual projection gradient method, which adds projection algorithm on the basis of the original algorithm and terminates the iteration by convergence conditions, numerical experiments prove that this algorithm is not only e?cient in image denoising, but also decrease CPU calculating time.In the appendix part of this paper, I attached what I have achieved during my master study. In 2013 I applied for the scienti?c research ability promotion projects for science and technology which is hosted by China association, my paper was published in April2014 of the second issue of Science Popularization, the paper was titled ”Investigation and Analysis of the University Teachers’ Popular Science Creation Attitude”, which is as part of the thesis attached in the appendix.