{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/69291"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/69291","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Tomographic Image Reconstruction via a Hankel Transform Approach and a Low-Noise Digital Filter Structure (Processing, Fourier-Bussel, Roundoff Errors)","abstract":"We considered two independent problems.","abstract_html":"We considered two independent problems.","abstract_has_math":false,"creators":["Higgins, William Evan"],"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":"2014-12-15T19:04:49Z","date_published":"2014-12-15T19:04:49Z","updated_at":"2026-07-22T22:26:00Z","subjects":["Engineering, Electronics and Electrical"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(UMI)AAI8502173"],"render_values":[{"text":"(UMI)AAI8502173","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/69291","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Higgins, William Evan"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-12-15T19:04:49Z","10000-01-01","1984"]},{"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":["Engineering, Electronics and Electrical"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/69291","(UMI)AAI8502173"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["We considered two independent problems.","In the first, we studied a relatively unexplored algorithm for reconstructing a two dimensional quantity (an "image") from a set of its projections. The algorithm, which we dubbed the "Hankel transform reconstruction (HTR) algorithm," took two steps to develop.","The first involved deriving an algorithm for computing a general integer-order Hankel transform. The algorithm gives reliable integer-order Hankel transforms for many typical well-behaved functions.","The second step of the development concerned studying the HTR algorithm. This work, which incorporated the aforementioned Hankel transform algorithm, demonstrated that the HTR algorithm can give acceptable reconstructions and compares favorably in terms of reconstruction quality and computational complexity to the popular convolution-back-projection algorithm.","The second problem dealt with reducing roundoff error in fixed-point cascade-form digital filters. We applied a technique known as error spectrum shaping (ESS) to this class of filters. We derived the optimal coefficients for the ESS circuitry and also considered suboptimal possibilities. This work showed that not only can ESS reduce roundoff error considerably without overly complicating the filter structure, but that it also compares favorably to low-noise structures derived via linear state-space techniques.","Made available in DSpace on 2014-12-15T19:04:49Z (GMT). No. of bitstreams: 1 8502173.pdf: 4286195 bytes, checksum: f6127b10908a88265646b523d55f1215 (MD5) Previous issue date: 1984","Embargo set by: Seth Robbins for item 69457 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","146 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1984."]},{"key":"dc:title","label":"Title","values":["Tomographic Image Reconstruction via a Hankel Transform Approach and a Low-Noise Digital Filter Structure (Processing, Fourier-Bussel, Roundoff Errors)"]}]}],"canonical_facts":{"dc:creator":["Higgins, William Evan"],"dc:date":["2014-12-15T19:04:49Z","10000-01-01","1984"],"dc:description":["We considered two independent problems.","In the first, we studied a relatively unexplored algorithm for reconstructing a two dimensional quantity (an "image") from a set of its projections. The algorithm, which we dubbed the "Hankel transform reconstruction (HTR) algorithm," took two steps to develop.","The first involved deriving an algorithm for computing a general integer-order Hankel transform. The algorithm gives reliable integer-order Hankel transforms for many typical well-behaved functions.","The second step of the development concerned studying the HTR algorithm. This work, which incorporated the aforementioned Hankel transform algorithm, demonstrated that the HTR algorithm can give acceptable reconstructions and compares favorably in terms of reconstruction quality and computational complexity to the popular convolution-back-projection algorithm.","The second problem dealt with reducing roundoff error in fixed-point cascade-form digital filters. We applied a technique known as error spectrum shaping (ESS) to this class of filters. We derived the optimal coefficients for the ESS circuitry and also considered suboptimal possibilities. This work showed that not only can ESS reduce roundoff error considerably without overly complicating the filter structure, but that it also compares favorably to low-noise structures derived via linear state-space techniques.","Made available in DSpace on 2014-12-15T19:04:49Z (GMT). No. of bitstreams: 1 8502173.pdf: 4286195 bytes, checksum: f6127b10908a88265646b523d55f1215 (MD5) Previous issue date: 1984","Embargo set by: Seth Robbins for item 69457 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","146 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1984."],"dc:identifier":["http://hdl.handle.net/2142/69291","(UMI)AAI8502173"],"dc:subject":["Engineering, Electronics and Electrical"],"dc:title":["Tomographic Image Reconstruction via a Hankel Transform Approach and a Low-Noise Digital Filter Structure (Processing, Fourier-Bussel, Roundoff Errors)"],"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":"2026-07-22T22:26:00Z"}