{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/71970"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/71970","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"The Missing Cone Problem in Computer Tomography and a Model for Interpolation in Synthetic Aperture Radar","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.","abstract_html":"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.","abstract_has_math":false,"creators":["Hayner, David Alan"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Electrical Engineering","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-12-16T22:22:49Z","date_published":"2014-12-16T22:22:49Z","updated_at":"2026-07-22T22:26:05Z","subjects":["Physics, Electricity and Magnetism"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(UMI)AAI8324571"],"render_values":[{"text":"(UMI)AAI8324571","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/71970","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Hayner, David Alan"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-12-16T22:22:49Z","10000-01-01","1983"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Electrical Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Physics, Electricity and Magnetism"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/71970","(UMI)AAI8324571"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["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.","Made available in DSpace on 2014-12-16T22:22:49Z (GMT). No. of bitstreams: 1 8324571.pdf: 5733936 bytes, checksum: 2d2f7bee0818f1df27168047a846f21f (MD5) Previous issue date: 1983","Embargo set by: Seth Robbins for item 72136 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","165 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1983."]},{"key":"dc:title","label":"Title","values":["The Missing Cone Problem in Computer Tomography and a Model for Interpolation in Synthetic Aperture Radar"]}]}],"canonical_facts":{"dc:creator":["Hayner, David Alan"],"dc:date":["2014-12-16T22:22:49Z","10000-01-01","1983"],"dc:description":["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.","Made available in DSpace on 2014-12-16T22:22:49Z (GMT). No. of bitstreams: 1 8324571.pdf: 5733936 bytes, checksum: 2d2f7bee0818f1df27168047a846f21f (MD5) Previous issue date: 1983","Embargo set by: Seth Robbins for item 72136 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","165 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1983."],"dc:identifier":["http://hdl.handle.net/2142/71970","(UMI)AAI8324571"],"dc:subject":["Physics, Electricity and Magnetism"],"dc:title":["The Missing Cone Problem in Computer Tomography and a Model for Interpolation in Synthetic Aperture Radar"],"dc:type":["text"],"thesis:degree_discipline":["Electrical Engineering"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:26:05Z"}