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