{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/23072"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/23072","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"High resolution signal and image recovery: Fast algorithms and analysis","abstract":"In this dissertation we address three issues arising in signal recovery problems: developing fast and efficient algorithms for convex set constrained signal recovery, analyzing resolution limits in signal recovery algorithms, and developing new regularization techniques for reducing the ill effects of noise in signal recovery algorithms.","abstract_html":"In this dissertation we address three issues arising in signal recovery problems: developing fast and efficient algorithms for convex set constrained signal recovery, analyzing resolution limits in signal recovery algorithms, and developing new regularization techniques for reducing the ill effects of noise in signal recovery algorithms.","abstract_has_math":false,"creators":["Dharanipragada, Satyanarayana"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Electrical Engineering","degree_department":null,"school":null,"contributors":["Arun, K.S."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-05-07T14:01:08Z","date_published":"2011-05-07T14:01:08Z","updated_at":"2026-07-22T22:25:21Z","subjects":["Engineering, Electronics and Electrical"],"languages":["eng"],"rights":["Copyright 1994 Dharanipragada, Satyanarayana"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9512345","(UMI)AAI9512345"],"render_values":[{"text":"AAI9512345","href":null,"code":true},{"text":"(UMI)AAI9512345","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/23072","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Arun, K.S."]},{"key":"dc:creator","label":"Author","values":["Dharanipragada, Satyanarayana"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-05-07T14:01:08Z","10000-01-01","1994"]},{"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":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 1994 Dharanipragada, Satyanarayana"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9512345","(UMI)AAI9512345","http://hdl.handle.net/2142/23072"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["In this dissertation we address three issues arising in signal recovery problems: developing fast and efficient algorithms for convex set constrained signal recovery, analyzing resolution limits in signal recovery algorithms, and developing new regularization techniques for reducing the ill effects of noise in signal recovery algorithms.","For convex set constrained signal recovery, we develop an approach that is well-suited for applications with a limited number of measurements. We show that convex set constraints do indeed improve resolution in signal recovery. Next, we develop a quadratically convergent Newton algorithm to compute the reconstruction that is consistent with the convex set constraints and measured data, and that is closest to a known nominal signal. We also suggest suitable modifications to the algorithm in order that it has the desired local and global convergence properties and is computation and memory efficient. We demonstrate the algorithm on several practical applications.","We next investigate the key issue of resolution limits in signal recovery. The classical Rayleigh limit serves only as a lower bound on the achievable resolution. We show that in the ideal situation in which infinitely many noise-free measurements are available, the resolution limit depends only on the intersample spacing and not on the shape and width of the sampling kernel. In the practical situation of finitely many noise-corrupted measurements, we show that details finer than the Rayleigh resolution limit can be recovered by simple linear processing. In the process, we derive an algorithm for high resolution signal recovery (from linear measurements) and show how one can precompute worst-case error bounds and resolution ability of the algorithm. We illustrate the results on one-dimensional and two-dimensional examples.","Most reconstruction algorithms require solution of a linear system of equations that is almost always highly ill-conditioned and, hence, very sensitive to noise. We investigate the reduced rank SVD-based regularization scheme and present a new technique for rank selection in this scheme. The selection is based on maximizing a similarity measure. The similarity measure is constructed by enforcing our belief that signals with large norms are less likely than ones with small norms. The method is tested extensively for the bandlimited extrapolation application with much success.","Made available in DSpace on 2011-05-07T14:01:08Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9512345.pdf: 4665325 bytes, checksum: 645a225e15d961f6ec5f2ce73119dc09 (MD5) Previous issue date: 1994","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T15:01:59Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:29:27-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission","ETDs are only available to UIUC Users without author permission","U of I Only"]},{"key":"dc:title","label":"Title","values":["High resolution signal and image recovery: Fast algorithms and analysis"]}]}],"canonical_facts":{"dc:contributor":["Arun, K.S."],"dc:creator":["Dharanipragada, Satyanarayana"],"dc:date":["2011-05-07T14:01:08Z","10000-01-01","1994"],"dc:description":["In this dissertation we address three issues arising in signal recovery problems: developing fast and efficient algorithms for convex set constrained signal recovery, analyzing resolution limits in signal recovery algorithms, and developing new regularization techniques for reducing the ill effects of noise in signal recovery algorithms.","For convex set constrained signal recovery, we develop an approach that is well-suited for applications with a limited number of measurements. We show that convex set constraints do indeed improve resolution in signal recovery. Next, we develop a quadratically convergent Newton algorithm to compute the reconstruction that is consistent with the convex set constraints and measured data, and that is closest to a known nominal signal. We also suggest suitable modifications to the algorithm in order that it has the desired local and global convergence properties and is computation and memory efficient. We demonstrate the algorithm on several practical applications.","We next investigate the key issue of resolution limits in signal recovery. The classical Rayleigh limit serves only as a lower bound on the achievable resolution. We show that in the ideal situation in which infinitely many noise-free measurements are available, the resolution limit depends only on the intersample spacing and not on the shape and width of the sampling kernel. In the practical situation of finitely many noise-corrupted measurements, we show that details finer than the Rayleigh resolution limit can be recovered by simple linear processing. In the process, we derive an algorithm for high resolution signal recovery (from linear measurements) and show how one can precompute worst-case error bounds and resolution ability of the algorithm. We illustrate the results on one-dimensional and two-dimensional examples.","Most reconstruction algorithms require solution of a linear system of equations that is almost always highly ill-conditioned and, hence, very sensitive to noise. We investigate the reduced rank SVD-based regularization scheme and present a new technique for rank selection in this scheme. The selection is based on maximizing a similarity measure. The similarity measure is constructed by enforcing our belief that signals with large norms are less likely than ones with small norms. The method is tested extensively for the bandlimited extrapolation application with much success.","Made available in DSpace on 2011-05-07T14:01:08Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9512345.pdf: 4665325 bytes, checksum: 645a225e15d961f6ec5f2ce73119dc09 (MD5) Previous issue date: 1994","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T15:01:59Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:29:27-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission","ETDs are only available to UIUC Users without author permission","U of I Only"],"dc:identifier":["AAI9512345","(UMI)AAI9512345","http://hdl.handle.net/2142/23072"],"dc:language":["eng"],"dc:rights":["Copyright 1994 Dharanipragada, Satyanarayana"],"dc:subject":["Engineering, Electronics and Electrical"],"dc:title":["High resolution signal and image recovery: Fast algorithms and analysis"],"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":"2026-07-22T22:25:21Z"}