Arnoldi Projection Fractional Tikhonov for Large Scale Ill-Posed Problems  

作　　者：Wang Zhengsheng Mu Liming Liu Rongrong Xu Guili Wang Zhengsheng;Mu Liming;Liu Rongrong;Xu Guili(college of science,nanjing university of aeronautics and astronautics,Nanjing 210016,P.R.China;institute of automation,nanjing university of aeronautics and astronautics,Nanjing 210016,P.R.China)

机构地区：College of Science,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,P.N.China 2.Institute of Automation,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,P.N.China

出　　处：《Transactions of Nanjing University of Aeronautics and Astronautics》2018年第3期395-402,共8页南京航空航天大学学报（英文版）

基　　金：supported by the National Natural Science Foundations of China(Nos.11571171and 61473148)

摘　　要：It is well known that Tikhonov regularization in standard form may determine approximate solutions that are too smooth for ill-posed problems,so fractional Tikhonov methods have been introduced to remedy this shortcoming.And Tikhonov regularization for large-scale linear ill-posed problems is commonly implemented by determining apartial Arnoldi decomposition of the given matrix.In this paper,we propose a new method to compute an approximate solution of large scale linear discrete ill-posed problems which applies projection fractional Tikhonov regularization in Krylov subspace via Arnoldi process.The projection fractional Tikhonov regularization combines the fractional matrices and orthogonal projection operators.A suitable value of the regularization parameter is determined by the discrepancy principle.Numerical examples with application to image restoration are carried out to examine that the performance of the method.It is well known that Tikhonov regularization in standard form may determine approximate solutions that are too smooth for ill-posed problems,so fractional Tikhonov methods have been introduced to remedy this shortcoming.And Tikhonov regularization for large-scale linear ill-posed problems is commonly implemented by determining apartial Arnoldi decomposition of the given matrix.In this paper,we propose a new method to compute an approximate solution of large scale linear discrete ill-posed problems which applies projection fractional Tikhonov regularization in Krylov subspace via Arnoldi process.The projection fractional Tikhonov regularization combines the fractional matrices and orthogonal projection operators.A suitable value of the regularization parameter is determined by the discrepancy principle.Numerical examples with application to image restoration are carried out to examine that the performance of the method.

关 键 词：ill-posed problems fractional matrix Tikhonov regularization orthogonal projection operator image restoration 

分 类 号：O241.6[理学—计算数学]