Image Denoising Based On Variational And Partial Differential Equations

Image denoising is one of the most important,basic studies in image pro-cessing.The presence of noise in images is unavoidable.It may be introduced by the image formation process,image transmission and image recording.Im-age denoising method based on variational partial differential equations is one of the most important methods in image denoising.Since it is not only has strong mathematical support,but also has flexibility,extendibility and stability.Since the general image contains the edge parts and smooth part,three characters like removing noise,preserving edges and recovering smooth parts are required in image denoising.Developing a variational model which is capable of restoring both edges and smooth parts is still a valid challenge in image denoising.The simple L2 model can keep image smooth,but it may seriously blur edges.The classical TV model can do well in preserving shape edges,but for image's smooth part,the solution to this model has the undesirable staircasing effect.The LLT model can avoid the staircasing effect,it is a high order model,it.is relatively difficult for solve,and it may be blur edge in some degree.The three major studies of this dissertation are put forward:Since the TV model can produce staircasing effect for smooth parts,we propose to make use of the L2 model to get a smooth primal sketch,and then get other meaningful signal by the TV model from the residual image.Numerical results show our method is able to keep edges as TV model,but also avoid the staircasing effect,and the restored image by our method is smooth and nature.Due to the convergence speed of the fixed point method with the observed image as the initial value to iteration for the LLT model is slow,we construct a homotopy equation based on gradually reducing the smooth parameter,and present a suitable curve tracking to improve the initial value to fixed point iteration.With the help of the homotopy method,the convergence of the fixed point method is enhanced efficiently.Since the larger regularization parameter is benefit for smooth,and the smaller regularization parameter can do well in image fit,we construct an im-proved LLT model to avoid the LLT model's blurring edges in some degree.Numerical results show our model can keep smooth as the LLT model,and greatly improve the quality of the image.