High-order Adaptive Variational And PDE Image Denoising Model

Limited by the devices and the transmission channels, the noise is introduced during the periods of image capture and transmission. The occurring of the noise produces a bad effect on the visual feeling of the image and hampers the recognition by the human and computer. Therefore, image denoising is a very important and basic task in image processing. The denoising results give a direct effect on some sequence processing tasks, including edge detection、object recognition and image segmentation.Thus, to improve the image quality and make it feasible for the high level processing tasks, it is necessary to remove noise from the noisy image data.The partial differential equation methods for image processing remove noise by a time depending evolution equation, with the noisy image as initial values. These methods can preserve some features as task requires. As a typical second order PDE model, total variation model can produce a piecewise linear image, therefore promising a better edge preserving ability. However, this model recoveries a blocky effect image for some piecewise smoothing region. This undesired effect is named “staircase effect”.Now it is have come to an common that high order model is one of the effective way to relieve staircase effect as the solution of the high order model have more smoothing character. In practice, speckle may occur in the denoised image by high order model.This thesis introduces the principle and related knowledge of PDE methods for image denoising. Some typical models are also discussed. Some theory backgrounds,such as variation, scale space and gradient descent flow, and the discrete schemes which are necessary when implemented with computer, are both given. To research the key of denoising, especially for its edge preserving ability, local coordinate decomposition is presented.For the unsatisfactory edge preserving ability of current high order models, a new high-order variation energy function is proposed by introduce the gradient information after convolution as the weighting function of second derivative and leads to a fourth order diffusion model. In the procedure of construct the weighting coefficients, a scheme that making weighting function have the ability to preserve a certain edges isgiven based on the analysis of the classical second-order total variation diffusion model.This weighting function can determine local structure region of the image and adaptive the diffusion rate, as well as good retention properties of the detail in the diffusion.To remove speckle effect produced by high-order model, a relaxed median filter method is introduced into it.This method takes into account the pixel information of the image,using the mean and variance information of the pixels classify the pixels,smoothing noise pixels with relaxation median filtering.The use of relaxation median filter for image processing does not destroy the structure information of the image while eliminating speckles.Combination the merits of guide filtering and total variation model,an new method is propose. Guide filtering requires the help of a well-structured guide image. With the increasing of noise,the edge and the structure of the guide image is destroy, which can not provide effective guidance information,and seriously affect the denoising effect. The classic total variation model can obtain piece constant image and maintain good performance of boundaries and structure,which can provide robust guidance information to guide filter.