Research On Image Processing Methods Based On Geometric Variation And Multiscale

In this thesis, we focus on the research of image denoising and image enhancement bysynthetically using several kinds of modern mathematical theories, such as functional analysis,multiscale analysis, variational method, partial differential equation (PDE), optimization theory etc.Firstly, with the comprehensive consideration of image geometric structure features and humanvision features, a new threshold parameter and time estimation and optimization method in P-Mnonlinear diffusion model is proposed, then combining wavelet transform(WT) with PDE, a waveletmultiscale-based image nonlinear diffusion model with fidelity item is established. Secondly,according to Weber-Fechner’s law, by introducing image frequency based on gradient into totalvariation(TV), an improved varaitional regularization image denoising and restoration model basedon frequency is proposed. Thirdly, an image structure saliency function according to structure tensorand its eigen values is firstly constructed, and then it is used to replace the lagrangian multiplier intraditional TV model,thus a frequency-based texture image denoising model combining tensorvoting with TV minimization is established. Fourthly, wavelet localization feature is introduced intoimage diffusion filter and an image geometric structure feature operator which is independent ofgradient is constructed by WT energy spectrum, based on it, a new WT-based nonlinear imageenhancement model is set up. Finally, by theory analysis and computer simulation, we make anoverall illustration about the advantages of the above new methods compared with other TV modelsin image denoising and enhancement.