Application Research Of Fractional-order Total Variation Regularization Model In Image Processing

This thesis studies the application of fractional order total variation regularization model in image processing,which focus on image restoration.Based on the existing forms of total variation regularization models and algorithms,we explore new models and other forms of algorithm.Firstly,we briefly introduce the research background and significance of this thesis,the evaluation index related to image restoration,the research status at home and abroad;then introduce the selection and evolution of regularization parameters;then,introduce the different regularization models of scholar,especially different solving algorithms and processes for fractional-order total variation regularization models,such as gradient descent method,MM algorithm,PD algorithm,ADMM algorithm,split Bregman algorithm,adaptive PDHG algorithm.And we compare the advantages and disadvantages of various algorithms.Secondly,we use the feature that the fractional derivative has longer memory function than the integer order,and adopt a different algorithm than the previous one,that is,we transform the fractional-order total variation regularization model into a saddle point problem,and then use the adaptive PDHG algorithm to solve it.A number of numerical experiments show that the fractional-order total variation regularization model can better protect the edge information and texture details,and the adaptive PDHG algorithm is superior to several other algorithms in dealing with the fractional-order total variation regularization model.The peak signal-to-noise ratio(PSNR)and structural similarity index measure SSIM are used to evaluate the restoration effect.The recovery results of this method are better.Furthermore,we consider that the image contains many different features,but the fractional derivative operator has the same penalty along the x-axis and y-axis directions,and the two sub-variables of a fractional derivative operator with the same weight cannot be effectively coupled with local features.In order to better take care of local features,we add different weights to each component of the fractional derivative operator.so we construct an adaptive weight matrix and propose adaptive fractional total variational regularization(AFOTV model).Then we introduce auxiliary variables and solve them with ADMM algorithm.The PSNR value and SSIM value are used to evaluate the restoration results.Experimental results show that,compared with the ATV model,the AFOTV model is significantly better than the ATV model with the same noise level.In addition,the convergence analysis of the ADMM algorithm solving model is carried out.Finally,the last chapter is the summary,the brief introduction of further unsolved problem and prospects.