Research On Image Restoration Models,Algorithms And Applications Based On Non-convex High-order Total Variation

Images are an important source of information for human beings and play an important role in production and life.On account of the backwardness of imaging technology or the interference of external interference factors,most of the images what they see are degraded,such as blurred images,noise pollution and so on,and these factors sharp image definition.The degraded images can lose part of the information,at the same time people cannot obtain much more information,and the degraded images also bring some difficulties for the research work.Thus,how to restore high quality images accurately and efficiently has become a hot issue in the field of image processing.With the help of the mathematical theory of image restoration,base on the direction of total variation regularization,this paper set up a non-convex high-order image restoration model for degraded images with different blur and noise corruption,and propose the corresponding algorithm.Then,the validity of the proposed method was verified by numerical experiments.Then,numerical experiments are carried out to verify the effectiveness of the proposed method.The main research contents is as follows.(1)Aiming at the disadvantage of convex total variation regularization model which is easy to produce staircase effects,we propose a non-convex high-order total variation regularization model with constraints.Based on the generalized iterative contraction algorithm and the alternating direction of multipliers method,we also propose a new alternating minimization algorithm is proposed.Using the new algorithm to restore the image,we only need three simple sub-problems.The three sub-problems are solved by generalized threshold shrinkage operator,fast Fourier transform and projection operator respectively.Numerical experiments show that the new model and algorithm can effectively restore degraded images with different kinds of blur and different degrees of Gauss white noise.(2)In order to make full use of the prior information of the image,the sparse prior information of the image is introduced into the image restoration problem in this paper.Considering that wavelet transform can effectively represent sparse images,we set up a hybrid regularization model with non-convex constraints based on high-order total variation regularization and wavelet regularization in this paper.Aiming at this model,a new alternating iteration algorithm is proposed,and the acceleration technique is used in the new algorithm to improve the computational efficiency.Numerical experiments show that the new model and algorithm are effective not only for slightly blurred degraded images,but also for seriously blurred degraded images.