Study On Adaptive Regularization Model Denoising Algorithm Based On L~q Norm

Image is the most important information carrier in human cognitive activities.With the rapid development of digital information and the popularity of electronic imaging devices,human perception systems receive more and more external infor-mation,about 80%of in which is from the images.Since images are often affected by various noises during the process of generation,transmission and reception,people cannot obtain accurate feature information from degraded images in time,which will affect the subsequent processing of images,so how to denoise image has become especially important.This thesis mainly focused on the basic theories of image de-noising,denoise modeling and denoising algorithms.The main work and innovations are as follows:Firstly,the basic knowledge such as functional analysis and operator in image denoising is introduced in detail.The Split Bregman iterative method and the aug-mented Lagrangian multiplier method(ALMM)in image denoising are introduced.The relaxation optimization method was first proposed by TSUTSU et al.It is a fast algorithm for iteratively solving the lp(0<p<2)regularization problem in compressed sensing.In this part,it is briefly analyzed and applied to the denoising model;Secondly,the adaptive weighted TVq model based on the difference of curva-ture can effectively keep the characteristics of image edges and details,and prevent the staircase effect.This work firstly given the FP-Jacobi and FP-PCG;further proposed ALMM method based on the lq relaxation function to solve TVq model,and analyzed the convergence of the algorithm.Experimental results show that this algorithm has good performance in denoising;Finally,the LLT model(ALLT model)based on a high order adaptive regu-lariser with lq norm is given,and the numerical implementation of the ALLT model using ALMM method based on the lq relaxation function is proposed.Numerical experiments show that the new high order adaptive model and numerical algorithm can effectively remove the noise in the image and maintain its edge details.