Title :
An Efficient Method for an Ill-Posed Problem — Band-Limited Extrapolation by Regularization
Author_Institution :
Dept. of Math., Kansas State Univ., Manhattan, KS
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;
Journal_Title :
Signal Processing, IEEE Transactions on
DOI :
10.1109/TSP.2006.881255
