The Regularization P-M Image Denoising Method Based On Gradient Fidelity Term

With the development of computer processing capability and multi-media information processing requirements of information society, the image processing has become a very active field. Image denoising improves the quality of image to make it more suitable for practical applications. Therefore, research on it is of great value.This thesis studied the method of denoising in the framework of partial differential equations, especially in the method of introduce gradient fidelity term in low gradient nonlinear diffusion model.Firstly, we introduced the background and significance of this thesis, and described the research situation of the image denoising based on the partial differential equation. And then, two types of diffuse filtering model, isotropic diffuse model and the anisotropic diffuse model were proposed. A classical P-M denoising model was mainly studied by analyzing the behavior of P-M equation. It was pointed out the advantage and disadvantage of P-M denoising model. At the same time, the reason of P-M equation has ill-conditioning and why it is easy to produce ?ladder effect? were analyzed. A regularized P-M model that can eliminate ill-conditioning was derived and proved by numerical experiment. Finally, the generally used method of dealing with ?ladder effect?, high order partial differential denoising method, was introduced. By considering similarity of intensity and change of grayscale between original image and denoising image, a gradient fidelity constraint model was formulated. It was proofed that the functional constraints is a convex function and integrable in the space of bounded variation function, which theoretically ensures that it can maintain more information of the image edge.Combining the gradient fidelity term with regularized P-M model, a low order diffuse denoising model based on the gradient fidelity term was proposed. Subsequent experiments demonstrated that it can significantly restrain ?ladder effect? and has no disadvantage of original model that producing sub-constant result. Moreover, comparing with high order diffuse denoising model, the new model has a lower order partial derivative. That made it is efficient and stable for numerical solving. Meanwhile, the new model also overcomes the problem that high order diffuse denoising model leads ambiguous boundary. Since the constrained fidelity term will not change the existence and uniqueness of global optimal solution of denoising model, the model proposed in this paper can eliminate the ill-conditioning of P-M model while improving the ?ladder effect? of denoised image.