An Efficient Method for an Ill-Posed Problem — Band-Limited Extrapolation by Regularization

Author

Chen, Weidong

Author_Institution

Dept. of Math., Kansas State Univ., Manhattan, KS

Volume

54

Issue

12

fYear

2006

Firstpage

4611

Lastpage

4618

Abstract

In this paper, a regularized spectral estimation formula and a regularized iterative algorithm for band-limited extrapolation are presented. The ill-posedness is taken into account. First the Fredholm equation is regularized. Then it is transformed to a differential equation in the case where the time interval is R. A fast algorithm to solve the differential equation is given by the finite difference and a regularized spectral estimation formula is obtained. Then a regularized iterative extrapolation algorithm is introduced and compared with the Papoulis and Gerchberg algorithm

Keywords

Fredholm integral equations; differential equations; extrapolation; finite difference methods; iterative methods; spectral analysis; Fredholm equation; Gerchberg algorithm; Papoulis algorithm; differential equation; finite difference; ill-posed problem band-limited extrapolation; regularized iterative extrapolation algorithm; regularized spectral estimation; Convergence; Differential equations; Distortion; Extrapolation; Finite difference methods; Helium; Image analysis; Iterative algorithms; Signal processing algorithms; Spectral analysis; Extrapolation of band-limited signal; ill-posedness; regularization;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/TSP.2006.881255

Filename

4014399