Image Denoising Models Based On Variation And Partial Differential Equations

Image quality will be affected when the unpredictable noise is brought into theimage information in the process of acquisition, transmission, storage and processing.The presence of the noise makes it difficult to complete the subsequent processing andthe practical applications. Image denoising has been one of the hot issues in the field ofimage processing research. Based on the variational method and modern partialdifferential equations (PDE), this thesis proposes a novel total variational model withstrict convexity to remove multiplicative noise. The main research work is as follows:First of all, a novel total variational model with strict convexity is proposed to theremove the multiplicative noise obeying to the Gamma distribution. The model isconstructed by the fidelity term which is derived with the maximum a-posterioriprobability (MAP), a fitting term and a novel hybrid measurement. According to themathematical characteristics of the Gamma noise and the properties of this model, thisthesis has discussed the selection of the regularization parameters in the model.Secondly, converting the new variational model into two minimization problem,and using the Newton iterative method and variational method respectively to get thesolutions, then a kind of alternating iterative optimization algorithm can be built. As aresult, the corresponding iterative sequence is concluded and the convergence of theiterative sequence has been proved by the related theory of the variational method andthe modern PDE.Finally, using the alternating iterative optimization algorithm, the thesis completesa series of simulation experiments to demonstrate the effectiveness, advancementand robustness of the model. The analysis of the experiment results shows that thedenoising effect of the model is better than the present similar models. It can not onlyrestrain multiplicative noise better, but also have more natural visual effect. The detailcharacteristics of the image edges are kept well, the image blur is alleviated, and‘step-casing effect’ is suppressed greatly. The proposed model can also be applied toremove the noise in the medical image, and its effect is better than some of the majormodels at present.