Doctor of Philosophy / Department of Mathematics / Robert B. Burckel / 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.
| Identifer | oai:union.ndltd.org:KSU/oai:krex.k-state.edu:2097/474 |
| Date | January 1900 |
| Creators | Chen, Weidong |
| Publisher | Kansas State University |
| Source Sets | K-State Research Exchange |
| Language | en_US |
| Detected Language | English |
| Type | Dissertation |
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