The Missing Cone Problem in Computer Tomography and a Model for Interpolation in Synthetic Aperture Radar
Hayner, David Alan
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https://hdl.handle.net/2142/71970
Description
Title
The Missing Cone Problem in Computer Tomography and a Model for Interpolation in Synthetic Aperture Radar
Author(s)
Hayner, David Alan
Issue Date
1983
Department of Study
Electrical Engineering
Discipline
Electrical Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Physics, Electricity and Magnetism
Abstract
The first part of this thesis considers the missing cone or limited view angle problem in computer tomography. In this problem only an incomplete set of projection data is available from which an image must be reconstructed. The data are limited in the sense that projections are available only over a limited view angle, a restricted perspective. The object of the algorithms presented in this thesis is to reconstruct a higher quality image than that obtainable by treating the projections as the only source of information concerning the image to be generated. This is accomplished by treating the problem in terms of spectral extrapolation. With this interpretation, various assumptions concerning the image and other forms of a priori information can be included in the data set to increase the total information content available. This larger data set allows the generation a superior image. It is shown that with data spanning over a continuous arc of only 60 degrees, that a high resolution image can be recovered; the original reconstruction, from the projection data only, is unitelligible.
In order to understand the subtleties of these enhancement algorithms, the spectral extrapolation techniques employed must be well understood. The extrapolation techniques employed are those of Gerchberg and Papoulis. A result of studying these extrapolation techniques is that either can be characterized as a contraction mapping for any realizable discrete implementation. Further, it is theoretically derived and experimentally verified that these algorithms will in general obtain an optimal solution prior to converging to the unique fixed point. The norm of the error is minimized by this optimal solution, not by the fixed point.
In the second part of this thesis, a nearest-neighbor interpolation scheme for image generation in spotlight mode synthetic aperture radar is analyzed. A model reflecting the effects of nearest-neighbor interpolation is derived and simulations are provided to support these results. It is also shown that an adaptive presumming operation, performed on the collected azimuth data, will significantly reduce the effects of nearest-neighbor interpolation.
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