Research On Image Denoising And Decomposition Using PDE Based Methods

Image denoising and decomposition are two main tasks in the image processing field. Since the end of the 1980's, PDE(partial differential equations) and variational methods have raised a strong interest, and also have gotten a rapid development. In this thesis, we concentrate on the research on image denoising and decomposition using variational and PDE-based methods. The main works of this thesis are as follows:(1) By analyzing the anisotropic diffusion equation, we propose a new denoising model which smooth the noisy image and write the information into the second derivatives of the image in the gradient direction and its orthogonal to prevent the unstableness when the noise is too large. And we adjust the diffusion coefficients in the direction of the isophotes and the direction of the gradient to prevent the oversmoothing in the smooth areas. The new model has strong ability of denoising and can reduce the staircasing effect very well.(2)A new image decomposition model for gray level images is proposed. To overcome the caveat of TV-based methods which are apt to cause staircasing effect in the recovered images, a high-order energy is introduced into the functional. And we model the oscillatory parts using Hilbert space, and use Gabor functions to extract the textures. Compared with some classical image decomposition model, the new model gives better results that more edges are protected and staircasing effect is reduced.(3)A decomposition model for RGB color image is proposed. We add constraint into the Beltrami Flow to make it extract the textures more precisely. And inspired by Gilboa's work, we also introduced the Forward-and-Backward diffusion to enhance some singularities such as edges while smoothing the image.