The Application Of Two Types Of Stochastic Differential Equation On Image Restoration

In the process of transmission, storage, measurements, images will appear thephenomenon of distortion. But in many areas, people often want distinct images,so it is necessary to have intensive research on image and the technology of imagerestoration. There are three methods to restore image, such as wavelet, probability,mathematical statistics and partial differential equation. Partial differentialequation was widely applied in the field of image restoration, this model has a lotof shortcomings because of the nature of the partial differential equation, butFeynman-Kac connect the partial differential equation with stochastic differentialequation, this paper use stochastic differential equation to recover the gray imagewith the noise pollution.The article research on the problem of gray image restoration affected by thegaussian noise. Firstly we get the information of the image, we can constructmathematical or probability model by the information, using the model to restorethe image along the opposition direction, so we can get a image with high quality.Image restoration can be viewed as the inverse process of image degradation, sowe can use stochastic differential equation to restore the gray image with noisepollution restoration.Firstly, we introduce the thermal diffusion model and the anisotropicdiffusion model belonged to the partial differential equation, Feynman-Kacformulas are used to get the thermal diffusion model based on stochasticdifferential equation and the anisotropic diffusion model; Secondly, reflectivestochastic differential equation can be regarded as a Skorokhod problem, in thispaper, we can prove the properties of reflective stochastic differential equations byusing the properties of Skorokhod problem and study the problems of backwardstochastic differential equations, we study the reflective stochastic differentialequation and backward stochastic differential equation as image restoration model.After the process of image restoration, we have image enhancement process, tomeet the needs of the people, it will be the result of image restoration processing.Finally we use Matlab to image restoration, and to evaluate the quality of imagerestoration.