Research On Partial Differential Equations In The Application Of Image Denoising

Images are often polluted by noise due to various reasons,thus how to find the methods which can effectively remove the noise in an image has been a big challenge for researchers.Although many methods have been proposed for image denoising in the past few decades,the research of image denoising techniques is still not out of date,there is no doubt that it has become a fundamental and important research topic in the field of digital image processing.The evolution diffusion method based on partial differential equation(PDE)is helpful to improve the quality of noise image,this method can process images in accordance with the desired diffusion behavior,therefore,since the PDE-based methods have been extended to image processing area,this research has been developed vigorously.The topic of this thesis is the research on PDEs in the application of image denoising,the main works are as follows:1.In the third chapter of this thesis,a hybrid image denoising model which combines the second-order and fourth-order PDEs is proposed.As known to all,it is a difficult issue to eliminate noise while avoiding the staircase effect and preserving edges in image denoising task.The Perona-Malik(PM)model and the Rudin-Osher-Fatemi(ROF)model are widely used in image denoising.However,a common disadvantage of these two models is that they tend to cause the staircase effect.In order to solve this problem,we propose a well-balanced anisotropic diffusion(WBAD)model by considering an adaptive balance parameter to improve both of them.The balance can be made in a selective way,meaning that it will alternate between the PM diffusion and ROF diffusion in accordance with the image features.However,in the flat area of an image,the PM model is used to perform the diffusion process,so the denoised image still appears slight staircase phenomenon.Considering that the You-Kaveh(YK)model can essentially reduce the staircasing effect,thus in the thsis we introduce a hybrid image restoration model based on an adaptive weight parameter to take advantage of the WBAD model and the fourth-order model,the hybrid model takes all the advantage of the ROF,PM,and YK models.From the quantitative comparison results such as peak signal-to-noise ratio(PSNR)and mean structure similarity(MSSIM),our hybrid model achieved the highest value in the comparative experiments of the relevant models.The visual experiment results also show that the hybrid model can effectively eliminate the image noise while avoiding the staircase effect,and the model still has a good ability to preserve image edges.2.In the fourth chapter of this thesis,an anisotropic fourth-order PDE-based image denoising model with texture presevation is proposed.Although the fourth-order YK model has a natural advantage in avoiding the staircase effect,it always tends to leave images with speckle artifacts.In addition,the classical second-order and fourth-order partial differential equations can not preserve the texture details of an image well,and the fourth-order YK model can also be seen as an isotropic diffusion model,therefore we provide an improvement to current fourth-order PDE-based image denoising model,the main idea is that we add a diffusion coefficient and replace the global fidelity term constraints in the previous model with an adaptive fidelity term.Compared with the related image denoising methods,it is found that the improved scheme can not only alleviate the speckle effect,but also it has certain advantages in the protection of image texture details.The experimental results show that our improvement scheme improve the quality of images which are polluted by noise both in terms of subjective visual and objective evaluation criteria.