Design of sampling and interpolation systems with applications to medical imaging
Willis, Nathaniel Parker
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Permalink
https://hdl.handle.net/2142/22626
Description
Title
Design of sampling and interpolation systems with applications to medical imaging
Author(s)
Willis, Nathaniel Parker
Issue Date
1992
Doctoral Committee Chair(s)
Bresler, Yoram
Department of Study
Electrical and Computer Engineering
Discipline
Electrical and Computer Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Electronics and Electrical
Language
eng
Abstract
Various aspects concerning the theory and design of sampling and interpolation systems are investigated in this dissertation. The first investigation is of time-sequential sampling. A novel theory of time-sequential sampling is developed which links time-sequential sampling with generalized multidimensional sampling. This theory includes conditions for time-sequential patterns, temporal uniformity, and bounds on temporal parameters. The behavior of time-sequential patterns is analyzed for the case of large space-spatial bandwidth products with the surprising result that the time-sequential constraint becomes irrelevant. The theory is also developed for arbitrary dimension with any spatial and spectral support. The theory is used to develop simple algorithms for designing time-sequential sampling patterns. Several examples of these algorithms are given. The application of time-sequential sampling to time-varying tomography is also investigated. It is shown that if the rapid temporal variation is concentrated in the center of the object being reconstructed then an improvement by up to a factor of four can be realized over conventional linear sampling. The time-sequential design algorithms are applied to this problem, and simulation results using these optimal sampling strategies are shown.
The norm-invariance property of minimax optimal interpolation is also presented. We show that the same interpolator is optimal for any norm which is finite over the class of input signals. For minimax optimality, this surprising result effectively ends the debate over which norm is relevant for a given application.
The last topic is minimax optimal interpolation in the presence of noise. A novel interpolator is derived which is optimal in both form and amount of regularization. This is significant because traditionally either the form or the amount of regularization is chosen on an ad hoc basis.
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