The missing cone problem in computer tomography and a model for interpolation in synthetic aperture radar

The first part of this thesis considers the missing cone problem in computer tomography. In this problem, an incomplete set of projection data is available from which an image must be reconstructed. 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 available. In order to understand the subtleties of these enhancement algorithms, the spectral extrapolation techniques exployed must be well understood. A result of studying the Gerchberg and Papoulis extrapolation techniques is that either can be characterized as a contraction mapping for any realizable discrete implementation. Furthermore, 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.