The Application Of Partial Differential Equation To Denoise X-ray

Images play an important role in exchanging information and dealing with accident in dalily life. Especially with the development of medical technology, medical image processing make a great cotributions to improve the quality of life as well as the whole life of mankind.Since the discovery of X-ray in1985,it have been used more and more widely in medical treatment,and also explore a new way to disease diagnosis.In recent years,new methods were used to disease diagnosis such as CT、PETCT、MRI which were developed basis on X-ray.Medical images can very intuitive to show the internal orgnization structure which makes post-processing of medical images become very important research direction in the entire diagnostic processing.Medical image processing mainly means to the obtained tissue or organ image to further processing, such as the denoising. Analysis, enhancement, segmentation, feature extraction, in order to determine the needed part be enhanced or feature extraction, to reached the blurred image became clearly or highlight a particular position.This paper reviews the history and current situation of image processing.Based on the theory of mathematical:good mathematical model can be recovered in good treatment results.Several commonly used image model and noise model were introduced. At the same time, explains most of the images are suitable for the BV concept. For example, the international standard test lena pictures. ntroduce the relationship between the heat conduction model and denosing of images,at the view of thermodynamic.At the same time,the relationship was proved from the view of discrete and continuous.In addition a brief description of the solution with regularization can improve the ill problem of p-m model.through the ralation of variational paritial differential will solve the PDE equation problem is reduced to solving the Eular-lagrange equation.While solving the Eular-lagrange equation by solving its corresponding gradient flow,that is seeking the minimum of the energy functional to obtain the minimum.In solving the gradient descent flow, finite difference method was used to discretize, the function can be divided into explicit, implicit, and semi-implicit approximation for solving first-order and second order derivative. When make the discretization of divergence, in order to achieve the best results, the slightest discretization discretized was used. In addition, basis on the PM model, Rudin, Osher and the Fatime proposed a new method based on the TV model of the diffusion coefficient (?), can realize the image denoising.In this paper, the basic TV-based model will produce "block effect", and based on (?) the diffusion does not produce sub-block effect, but will produce blurred edges under the premise,a new adaptive diffusion coefficient, meet on the smooth (flat image) region can be achieved similar to the effect of the second norm, at the edge (rapid change) area, can achieve the effect similar to the TV model (first-order norm), this method can be called adaptive TV model adaptive adjustment of the diffusion coefficient according to the local characteristics of the image.Results:Through the adjustment of the TV mode makes the mode with adaptive ability and the result close to the original image,This article, a standard pneumoconiosis image was used to plus Gaussian noise, and median filtering, and basic TV model for denoising compared with the effect of adaptive TV model. At last,it can be drawn that the result was produced by adaptive model was excellent than they wre. Finally, the TV model in denoising coupled with the enhanced role can demonstrate the flexibility of the TV model.