A Class Of Research On Image Denoising Based On Partial Differential Equation

Currently, the image denoising technology has been widely used in many fields such as medical diagnosis, space project, industry, biological science and so on.However, the difficulty of image denoising is how to solve the contradiction between the effective removal of noise and the important details of the image. The image denoising algorithm based on partial differential equation (PDE) has attracted the interest of many researchers because of its local adaptability, formal specification and the flexibility of model building. In this paper, we start with the classical partial differential equation denoising model, make a deep research and analysis, and then improve it. Finally, the conclusion is obtained by simulation experiment.The main work of this paper is as follows:1. In view of the problems that PM flux for regions where the gradient magnitude is higher than smoothing threshold may lead to undesirable blurring effect and edge displacement,the image is divided into three segments based on the gradient magnitude: regions where the gradient is lower than the smoothing threshold, regions where the gradient is between the smoothing threshold and inflection point of flux,and regions where the gradient magnitude is higher than inflection point. We define the conditions that should be considered in these three segments.the PM diffusion coefficient at a part of its domain (s>k) does not work properly for denoising.Substitute this part by an appropriate function. To evaluate the proposed coefficient,use it to denoise several noisy images. Experimental results confirm the superiority of the proposed coefficient comparing with traditional PM coefficient.2. A novel PDE-based image denoising approach is proposed in this paper. It is based on a nonlinear fourth-order diffusion model. That nonlinear PDE scheme is described first. Then, a mathematical treatment is provided for this differential model,its well-posedness being investigated. Prove that the model is well-posed in some certain conditions and admits a weak solution. The weak solution of the obtained PDE is approximated by developing an explicit finite-difference based numerical discretization scheme.The successful results provided by this PDE-based denoising technique and the performed method comparisons are also described.3. A hybrid nonlinear fourth-order diffusion-based image denoising algorithm is presented. The proposed compund PDE-based model combines a fourth-order diffusion to a two-dimension gaussian kernel, also, the speckle noise removal algorithm integrated into the explicit finite difference method-based numerical approximation framework elaborated for the PDE. It shows that it provides an effective detail-preserving image denoising that overcomes the staircase effect and removes the speckle noise.