Image Denoising Based On Partial Differential Equations

With the development of computer technology, image processing has been more and more popular in the last two decades. There are three kinds of basic research methods, which are based on probability and statistics, wavelets and PDEs respectively. Image processing based on PDEs has achieved great development in the last two decades, because of its strong adaptability, the anisotropy diffusion characteristic and the property of keeping the edge and texture details simultaneously. We made the following research in image denoising based on PDEs.On the solution of nonlinear partial differential equations, the check-board finite difference scheme is introduced. Solving the non-linear diffusion equations, generally adopt the explicit finite difference scheme, but a explicit difference scheme in order to ensure its stability, the time step is more limited, while the check-board finite difference scheme is the combination of explicit difference scheme and implicit difference scheme, and it is unconditional stability, so we can select a larger time step in order to speed up the processing of the images.On the basis of analyzing the shock filtering and non-linear diffusion equations, we propose a equation based on shock filter coupled to non-linear diffusion equation, that is, in shock filtering add a part of anisotropy diffusion, and add to the diffusion of weight function, both of image smoothing and edge-sharpening have achieved good results.