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

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dc.contributor.author Chen, Weidong
dc.date.accessioned 2007-12-10T15:28:53Z
dc.date.available 2007-12-10T15:28:53Z
dc.date.issued 2007-12-10T15:28:53Z
dc.identifier.uri http://hdl.handle.net/2097/474
dc.description.abstract 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. en
dc.language.iso en_US en
dc.publisher Kansas State University en
dc.subject Extrapolation of band-limited signal en
dc.subject ill-posedness, regularization en
dc.title An efficient method for an ill-posed problem [three dashes]band-limited extrapolation by regularization en
dc.type Dissertation en
dc.description.degree Doctor of Philosophy en
dc.description.level Doctoral en
dc.description.department Department of Mathematics en
dc.description.advisor Robert B. Burckel en
dc.subject.umi Mathematics (0405) en
dc.date.published 2007 en
dc.date.graduationmonth December en


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