Research Of Multiplicative Denoising Models Based On The Variational Methods

Image quality will be reduced for image information influenced by some external factors in the formation, transmission, storage and processing of the process, which brings inconvenience on image subsequent processing and application. In recent years, denosing has paid much attention by many researchers. The variational method and partial differential equation(PDE) active in the various fields of image processing. This thesis aims to research of multiplicative noise removal based on variation methods. First of all, reviewing the research status and methods of denoising. Next, discussing advantages and disadvantages of existing noise removal model based on variational method and PDE. Then, introducing the related variational theory and image denoising evaluation methods. To address issue on image edge blurring, accumulated blocks, and even producing ‘staircass effect', while the variational model applys to remove multiplicative noise. A variational model for removing multiple multiplicative noises and an efficient variational model for restoring noisy images with Gamma multiplicative noise are proposed, and the main research work is as follows:(1) To solve issue that some informations of image texture will be lost and model algorithm convergence rate is slow, when the existing model is to effectively remove multiplicative noise. This thesis proposes a variational model for removing multiple multiplicative noises with a new fidelity term based on Bayesian framework of maximum a posteriori probability(MAP) method and variational method. A numerical algorithm which has a fast convergence speed of the model is given, and the algorithm convergence has been proved with the relevant mathematical theory. Simulation results show that the proposed model can effectively remove Gamma noise and Rayleigh noise, well protects the image texture information, and improves the efficiency of the denoising. Denoising effect and efficiency are significantly better than model proposed by Y. Huang, et al.(2) Aiming at the image blurring of the edge details and producing ‘staircase effect' in removal of Gamma multiplicative noise, a fidelity term and a model for removing Gamma noise are proposed. This thesis gives an algorithm and discusses the convergence of improved algorithms with related mathematics theory. The experimental results of subjective visual display that the proposed model for removing noise is better than the existing model. Proposed model of this thesis can better protect the image edge, alleviate or even inhibit the ‘staircase effect'. The peak signal-to-noise ratio is improved and the relative error rate is decreased, so the proposed model has good denoising effect. Color image experiment results show that new model can also be applied to color image denoising, which can preserve the edge and texture information well.