Research And Application Of Image Denoising Methods Based On Variation And Partial Differential Equations

Along with the rapid development of computer and network technology,human beings have entered the digital image era.A digital images are usually unavoidable corrupted by many factors such as imaging equipment and the external environment during the acquisition,compression,transmission,and storage processes,which resulting in the image distortion.Image distortion mainly manifests as the structure information of the image is submerged by noise,and the distorted image can no longer truly reflect the information of the original image,which brings difficulties to image post-processing such as image enhancement,image segmentation and edge detection.Image denoising aims to faithfully reconstruct an image from its noise corrupted observation.It tends to provide more accurate and reliable information for subsequent processing of the image.Thus,image denoising is a fundamental problem and an important process for many image processing systems.In today's digital image age,people are increasingly demanding high-quality images,the quality of distorted images are effectively improved by image denoising technology,which make the improved images more suitable for daily life and scientific research applications.Therefore,it has important theoretical significance and practical application value to research and design of effective image denoising method.This paper deeply studies the image denoising methods based on variational and partial differential equation and theirs applications in low-dose computerized tomography(CT)post-processing.The main research works are summarized as follows:(1)An image denoising model based on variable order variation is proposed.The proposed model combines the advantages of the first-order variation model and the second-order variation model,which employs the edge indicator based on the fusion ofgradient modulus and local entropy to control the order of variation to achieve a different diffusion modes.Moreover,the proposed model is solved by fast Fourier transform(FFT)-based split Bregman algorithm to improve the operation speed of the model.The experimental results show that the proposed variable order variation model has a better denoising capability for natural images,and similarly,the model obviously improves the quality of low-dose computed tomography(LDCT)image and achieves a better visual effect similar to that of high-dose computed tomography(HDCT)image.Obviously,the proposed model is suitable for clinical diagnosis and has practical application value.(2)To overcome the shortcomings of the traditional partial differential equation Image denoising model,a hybrid second order partial differential equation image denoising model based on directed heat flow theory is proposed.The proposed model makes full use of the advantages of isotropic diffusion(ID)model,Perona-Malik(PM)model and second order directional derivative,and uses second-order directional derivative to improve ID model and PM model to achieve directional diffusion.At the same time,the patch similarity modulus is used as the edge detector of the PM Model,which further improves the edge-preserving performance of the improved PM model.In order to better maintain the edge structure information of the image,the original noise image is used as a reference to extract the structure information,so that the improved ID model and the improved PM model can diffuse directionally along the edge's tangential direction of the original noise image.In addition,considering the local structure information of the image,a new weighting function based on patch similarity modulus is used to balance the relative weights of the modified ID model and the modified PM model.Computer experiments on nature images demonstrate that the improved hybrid denoising model can not only effectively eliminate the noise in the flat area and he aliasing and the noise around edges,but also efficiently preserve the edges,textures,thin lines,weak edges and fine details,and avoid the staircase effects.In addition,the proposed model can be extended to the low-dose CT post-processing,and the computer experimental results show that the proposed model can effectively suppresse the speckle noise and streak artifacts of the LDCT image and retain the useful diagnostic information.(3)On the basis of in-depth study of the isotropic You and Kaveh(YK)model,an improved an improved isotropic fourth-order partial differential equation model based on CED(Coherence Enhancing Diffusion)priori is proposed for image smoothing and image denoising.The proposed method is an improved YK model that firstly performs a preprocessing using coherence-enhancing diffusion filter,and then uses the improved YK model for smoothing and denoising,instead of directly using the improved YK model.In the stage of smoothing and denoising,an adaptive edge-stopping function founded on the Tansig function is used to adaptively adjust the smoothing and denoising intensity,which can remove the noise and insignificant details without destruction of important edges and textures in the image.Experimental results show that the proposed model not only has good smoothing and denoising performance for natural images,but also can significantly improve the quality of LDCT images.(4)The traditional partial differential equation image denoising model has the problems of staircase effects and edge blurring,an improved fourth-order partial differential equation image denoising model based on structure tensor was proposed.The proposed model employed the determinant and the trace of the structure tensor of the image as the edge indicators and estimated the edge and gradient directions by the eigenvectors of the structure tensor matrix.In flat regions of the image,isotropic diffusion is performed;in the edges of the image,the diffusion is along the edge direction;in the cornersof the image,the diffusion is totally stopped,so the proposed model achieved anisotropic diffusion.The experimental results of natural images and LDCT images show that the improved model performs more effectively than some related models in removing noise,preserving edge details and avoiding staircase effects.