Research On Theory And Algorithms Of Image Denoising Based On Non-Local Similarity

Images are inevitably polluted by different types of noise during image acquisition,transmission and storage.The noise degrades image quality and further affects subsequen-t image processing tasks,such as edge detection,image enhancement,segmentation and classification.Image denoising aims at removing noise while preserving image details as much as possible.As an important and fundamental image processing task,image denoising remains a research hotspot in the field of computer vision.Among the existing denoising methods,non-local means and its improved versions attract considerable attention.Con-sidering the weaknesses and limitations of existing denoising methods,this paper proposes several improved denoising methods based on analysis and research on the non-local simi-larity of image.The main works are summarized as follows:（1）Due to the limitations of Euclidean distance and fixed weight,we propose the unbiased distance non-local adaptive means（UD-NLAM）.UD-NLAM introduces three un-biased distances to measure the similarity between noisy image patch and the correspond-ing denoised image patch.The three unbiased distances are pixel-pixel,patch-patch and coupled unbiased distances,respectively.Compared with Euclidean distance,the unbiased distances keep more structure information of the original image.In addition,UD-NLAM updates weight value according to the denoised image in each iteration.This reduces the errors caused by calculating weight using only noisy image.Experiment results show that UD-NLAM outperforms some existing NLM-based methods in both quantitative evalua-tions and visual effects.（2）Owing to the weaknesses of single patch size and pure spatial domain denois-ing methods,we propose the multipatch unbiased distance non-local adaptive means with wavelet shrinkage（MUD-NLAM-WS）for grayscale image denoising.To enhance noise robustness,MUD-NLAM-WS automatically assigns different weights to different image patch sizes according to the noise level of image.Furthermore,MUD-NLAM-WS alter-nately adopts multipatch unbiased distance non-local adaptive means in spatial domain and wavelet shrinkage in transform domain to improve performance in edge preservation.Both quantitative and qualitative results demonstrate that MUD-NLAM-WS further improves the denoising performance of UD-NLAM.（3）Many existing image denoising methods fail to fully exploit non-local and local correlations in color images,and ignore the fact that realistic noise level varies among dif-ferent image patches and color channels.These always lead to unpleasant denoising results.To solve these problems,we propose the 3-dimensional non-local total variation with plug-and-play prior（3DNLTVP³）.Embedding a 3-dimensional total variation regularizer and a self-adaptive weight matrix into the plug-and-play framework,3DNLTVP³not only catch-es the similarity information within and cross image patches,but also adaptively controls the denoising strength on each image patch and each color channel.Experiments on syn-thetic and real-world noisy color images verify the superior performance of 3DNLTVP³in reducing noise and keeping details.（4）To capture the non-local,local and cross-channel correlations of the color image,we propose a quaternion-based non-local low rank and 3D total variation（QNLR3DTV）model for mixed noise removal in color images.Based on quaternion representation of color image,QNLR3DTV applies a quaternion-based 3D total variation regularization to catch the within-patch,cross-patch and cross-channel correlations.In addition,QNLR3DTV intro-duces a quaternion-based self-adaptive weight matrix and quaternion-based L₁-regularized minimization model to automatically adapt the denoising strength on each image patch and each color channel.Experiment results in mixed noise removal demonstrate the conver-gence and robustness of QNLR3DTV.Besides,QNLR3DTV outperforms the competing methods in terms of denoising effectiveness.