Structure Tensor Based Hybrid Order PDE For Image Denoising

Digital image is vulnerable to a variety of noise pollution in the whole process of acquisition,transmission and storage,resulting in degradation of image quality,affecting the visual effect and further analysis of the image.Therefore,noise reduction of digital image is a hot topic in the field of machine vision and digital image processing.Image denoising is to restore the damaged image with noise to the original image without noise.The denoising process requires preserving and repairing the edge and texture of the image as much as possible.The image denoising model based on variational method and partial differential equation can effectively balance the contradiction between image smoothing and protecting image structure information.In this thesis,we focus on additive white Gaussian noise which obeys normal distribution,and study the image denoising method based on partial differential equation and variational method,mainly including the following two aspects :For the second-order and fourth-order partial differential equations used for image denoising,although both of them can effectively protect the edge details while denoising,they also have different defects.The image after denoising by the second-order model will have‘staircase effect’,while the fourth-order partial differential equation is prone to spot after denoising.In order to neutralize the advantages of both,and with the advantage of structural tensor in analyzing image structure information,this thesis proposes a hybrid order partial differential equation denoising model based on structural tensor.The model uses the determinant and trace of structural tensor to control diffusion and adaptively diffuses along the gradient direction and tangent direction,which can not only ensure the integrity of image edge texture information,but also realize denoising.The experimental results show that the proposed model has better ability to remove noise and edge details than the related models in terms of subjective visual and objective evaluation indexes.Although the total variation denoising model has the advantage of edge preserving,it is easy to produce ‘staircase effect’ in the smooth region.In this thesis,a weighted mixed-order total variation denoising model based on structural tensor is proposed.The model uses the determinant or trace of structural tensor as diffusion parameters to control the smoothness in different regions of the image according to different noise densities.The split Bregman iterative algorithm is used to numerically solve the corresponding discrete problems.In each iteration,the coherent enhanced diffusion filter is used for preprocessing;then,the denoising model proposed in this thesis is used for denoising.The numerical experiment results demonstrate that the model in this thesis has better protection ability for details such as texture edges and can effectively eliminate noise.