Image De-noised Based On Partial Difference Equation

The goal of denoising is to remove the noise and to retain the important signal features as much as possible.The traditional denoising methods blur the edges while removing the noise.With the study of partial differential equation,it has been widely used in image enhancement,image segment,image denoising etc.,and satisfactory results are obtained.Based on the detailed analysis of tensor-driven curvature-preserving PDE,this method is further improved to improve the image denoising effect,this paper make some researches on it.Also the idea of non-local filtering is applied in the filtering methods based on PDE,better denoising result is obtained by combining non-local with variation method.A weighted curvature-preserving partial differential equation(PDE)based filtering method is proposed.The tensor-driven curvature-preserving PDE filtering method(TCPDE)shows excellent performance in image denoising,however,the method does not consider the integral curves may experience different image structures,and the diffusion tensor is constructed by using linear structure tensor,these two factors result the method can not preserve image edge very well.Then,a new construct diffusion tensor is constructing by using non-linear structure tensor and weight coefficients id designed by employing local image directional information for different integral curves,a new tensor-driven curvature-preserving PDE filtering method is proposed in this paper.Total variation model can remove noise effectively,but it will bring in staircase effect,to improve this disadvantage,second order total generalized variation(TGV)is used as regularization term in the new denoising model.Also nonlocal differential operators are applied to the TV model and TGV model,the nonlocal operators are constructed by using the idea of the nonlocal means filtering algorithm,the new methods makes use of the global information of the image to remove noise.Combining the nonlocal Patch similarity regularization with nonlocal TV regularization and nonlocal TGV respectively,two new nonlocal Patch self-similarity regularized image denoising models are proposed.A new kernel function is constructed by using the similarity measure of the pixels in the images to instead the Gaussian kernel used in TCPDE,the denoising ability and the ability of preserving structure information of the algorithm are enhanced.