Several new results are presented for applications involving the restoration of coherent signals and images from incomplete Fourier data. A closed form solution is derived for a class of iterative restoration algorithms. The closed form result may be used as a non-iterative implementation of the iterative algorithm. The closed form solution is also used to develop a simple, effective termination rule for the iterative algorithm. The utility of the new termination rule is demonstrated using simulated and experimental data. A solution technique is proposed for efficient restoration of bounded signals. The efficiency of the proposed technique is demonstrated via a one-dimensional slab dielectric profile inversion example. Finally, a difference image approach is proposed as a way to reduce the data requirements for 4-D magnetic resonance imaging of the cardiac cycle. The proposed technique is successfully applied to experimental MRI data, and future prospects for the approach are discussed.
| Identifer | oai:union.ndltd.org:arizona.edu/oai:arizona.openrepository.com:10150/282433 |
| Date | January 1997 |
| Creators | Walsh, David Oliver, 1966- |
| Contributors | Marcellin, Michael W. |
| Publisher | The University of Arizona. |
| Source Sets | University of Arizona |
| Language | en_US |
| Detected Language | English |
| Type | text, Dissertation-Reproduction (electronic) |
| Rights | Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author. |
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