Partial Differential Equations-based Image Recovery

Image restoration is always one of the concems in image processing and is still a necessary preprocessing step for many high level applications. Traditional ways suffer from the loss of edge, lines and texture when restoring images. Since PDE-based methods can restore images when keep images' details well, they have gotten more and more concerns recently.The dissertation focuses on the research of image modeling and corresponding image restoration algorithms. From different views, it studies three image restoration models of different types. Firstly, the dissertation discussed the models based on the scale space theory. It focuses on the anisotropic diffusion equations. Secondly, models based on calculus of variations are discussed here. TV and a fourth order model are studied here. Lastly, the dissertation discussed a hyperbolic equation called shock filter. This model can used for enhancement or deblur.Main creativies of the dissertation are: (1) Proposing a complex image restoration model by coupling P-M with medium filter. (2) Proposing a selective diffusion models based on a time weighted function. (3) Proposing an image restoration model by coupling second order with fourth order models. (4) For the convenience of the further research, I develop a PDEs-based image restoration platform.