Study On PDE Based Denoising Methods For Flash X-ray Radiographic Image

The edges are very important information in the X-ray images. Smoothing X-ray images should balance the removing noises against preserving edges. So, the smoothing has to be adaptively controlled with two principles: (1) less smoothing in the locations with image edges, and more smoothing in the locations with other regions; and (2) minimal smoothing in the directions across image edges and maximal smoothing in the directions along image edges.The image denoising methods based on the Partial Differential Equations (call PDE for short) is a kind of nonlinear diffusion filtering methods. The methods use a nonlinear diffusion with a directional distribution of coefficient function instead of isotropic diffusion of Gaussian convolution. Thus, the method can protect the image edges while eliminating the noises. So, the methods are appropriate to our task.In the paper, the source of the PDE's methods in the image processing is discussed in the paper. By solving the linear conduction equation, we can get the smoothed results which are equivalent to the results of Gaussian convolution. Then, we discuss the adaptive mechanism of the nonlinear diffusion filtering. By selecting the proper diffusion coefficient function (also call edge stopping function), the nonlinear diffusion filtering methods can control the different degree of the diffusion in the different region of the image. That is to say, the diffusion is weak in the edges to protect the edges and the diffusion is strong in the flat region to smooth the noises. The different effects of the different nonlinear diffusion filters are also discussed in the paper. We then unify all kinds of diffusion filters with one formula. The formula takes all factors in the diffusion problem into account. The selection of all parameters is discussed in detail. So, we can get the absolute adaptive nonlinear diffusion filter. Further more, we propose a nonlinear diffusion filter which is based on the directions of the image edges. The new method is constructed on the orthogonal coordinate of the image edges. The direction of diffusion is sufficiently considered in the method. The diffusion is weak in the orthogonal direction of the image edges to protect the edges and strong in the parallel direction of the image edges to eliminate the noises efficiently. The advantage of the new method is to illustrate the mechanism of the nonlinear diffusion filter with no complex analysis in theory.There are many impulse noises with large amplitude in the CCD (Charge Coupled Device) images of flash X-ray radiography. It increases the difficulty of our task because nonlinear diffusion filtering is not efficient to the noises. To solve the problem, a median-anisotropicdiffusion filtering (call MADF for short) method is proposed in the paper. The new method overcomes the shortage of the traditional method which can not eliminate the impulse noises. It is shown that the application of the new method to CCD images can get good results.Moreover, the methods based on the variational problem are also discussed in the paper. Diffusion equations can come from the variational approach. The variational approach can unify various nonlinear filtering methods in theory and the different variational integral function (energy functional) is equivalent to different PDE, and derives different nonlinear diffusion filtering methods. We also propose two hybrid diffusion filtering methods by the variatinal approach. The hybrid methods eliminate the stair-effect of the TV (total variation) method. The numerical results show that the hybrid methods are more reasonable in the image denoising.