A Case Study of the Regularization Methods for Ill-Posed Inverse Problems

Inverse problem,as a branch of mathematics,is associated with the reversal of the cause-effect sequence and consists of finding the unknown causes of known consequences.A case study,which is based on the characterizations of the ill-posedness with inverse problems and the essence behind the regularization method for ill-posed inverse problem solving,is presented in this paper.The Tikhonov regularization method and the Landweber iteration are introduced.The spectral filters for the corresponding regularization methods are also discussed.