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An efficient method for an ill-posed problem [three dashes]band-limited extrapolation by regularization

by Chen, Weidong

Abstract (Summary)
In this paper a regularized spectral estimation formula and a regularized iterative algorithm

for band-limited extrapolation are presented. The ill-posedness of the problem is taken into account. First

a 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

by the finite differences is given and a regularized spectral estimation formula is obtained.

Then a regularized iterative extrapolation algorithm is introduced and compared with the

Papoulis and Gerchberg algorithm. A time-frequency regularized extrapolation algorithm

is presented in the two-dimensional case. The Gibbs phenomenon is analyzed.

Then the time-frequency regularized extrapolation algorithm is applied to image restoration

and compared with other algorithms.

Bibliographical Information:

Advisor:

School:Kansas State University

School Location:USA - Kansas

Source Type:Master's Thesis

Keywords:extrapolation of band limited signal ill posedness regularization mathematics 0405

ISBN:

Date of Publication:01/01/2007

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