{"id":{"repo_id":"buffalo","oai_identifier":"oai:ubir.buffalo.edu:10477/79962"},"canonical_url":"https://search.dev.ndltd.org/etd/buffalo/oai:ubir.buffalo.edu:10477/79962","repository":{"repo_id":"buffalo","name":"Buffalo","base_url":"https://ubir.buffalo.edu/oai/request"},"display":{"title":"Gibbs-Free Reconstruction of Fourier Data with Fourier Continuation and Subvoxel Shift with High Order Approximation","abstract":"Ph.D.","abstract_html":"Ph.D.","abstract_has_math":false,"creators":["Shi, Ruonan"],"institution":"State University of New York at Buffalo","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Jung, Jae-Hun","Mathematics"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2019,"date_issued":"2019-07-30T15:11:26Z","date_published":"2019-07-30T15:11:26Z","updated_at":"2026-07-27T19:05:21Z","subjects":["applied mathematics"],"languages":["eng"],"rights":["Users of works found in University at Buffalo Institutional Repository (UBIR) are responsible for identifying and contacting the copyright owner for permission to reuse. University at Buffalo Libraries do not manage rights for copyright-protected works and cannot assist with permissions.","Copyright retained by author."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/10477/79962","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Jung, Jae-Hun","Mathematics"]},{"key":"dc:creator","label":"Author","values":["Shi, Ruonan"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2019-07-30T15:11:26Z","2019","2019-05-15 19:40:26"]},{"key":"dc:publisher","label":"Institution","values":["State University of New York at Buffalo"]},{"key":"dc:type","label":"Dc Type","values":["Text","Dissertation"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["applied mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Users of works found in University at Buffalo Institutional Repository (UBIR) are responsible for identifying and contacting the copyright owner for permission to reuse. University at Buffalo Libraries do not manage rights for copyright-protected works and cannot assist with permissions.","Copyright retained by author."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/10477/79962"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Ph.D.","This thesis is concerned with the study of reconstructing the underlying function from scattering data. In particular, I am interested in reducing the Gibbs oscillation [18 , 41] caused by reconstructing discontinuous functions from Fourier data. In some applications, such as Magnetic Resonance Imaging (MRI) [42], the real world data (Fourier coeffi­cients) are collected in the frequency space (k-space). Due to acquisition time limitations and noises, typically only a limited part of data is acquired, resulting in Gibbs ringing on the functions/images reconstructed by the Fourier partial sum algorithm. Moreover, if the underlying function/image is only piecewise smooth, i.e ., containing jump discontinuities, its Fourier reconstruction by the Fourier partial sum will suffer from the Gibbs phenomenon with spurious oscillations appearing near the discontinuities. It is then necessary and important to reduce the Gibbs oscillation, and simultaneously to preserve the properties (such as discontinuities) of the function/image during the reconstruction process. To achieve such a goal, I employ the Li regularization reconstruction method, which is a widely used technique for data reconstruction. Moreover, I will improve a recently proposed method using Li regularization of edge sparsity.","**To request an accessible version of the file(s) associated with this item, contact library@buffalo.edu. Please include the item's persistent URL [http://hdl.handle.net/. . .] in your request.**"]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Gibbs-Free Reconstruction of Fourier Data with Fourier Continuation and Subvoxel Shift with High Order Approximation"]}]}],"canonical_facts":{"dc:contributor":["Jung, Jae-Hun","Mathematics"],"dc:creator":["Shi, Ruonan"],"dc:date":["2019-07-30T15:11:26Z","2019","2019-05-15 19:40:26"],"dc:description":["Ph.D.","This thesis is concerned with the study of reconstructing the underlying function from scattering data. In particular, I am interested in reducing the Gibbs oscillation [18 , 41] caused by reconstructing discontinuous functions from Fourier data. In some applications, such as Magnetic Resonance Imaging (MRI) [42], the real world data (Fourier coeffi­cients) are collected in the frequency space (k-space). Due to acquisition time limitations and noises, typically only a limited part of data is acquired, resulting in Gibbs ringing on the functions/images reconstructed by the Fourier partial sum algorithm. Moreover, if the underlying function/image is only piecewise smooth, i.e ., containing jump discontinuities, its Fourier reconstruction by the Fourier partial sum will suffer from the Gibbs phenomenon with spurious oscillations appearing near the discontinuities. It is then necessary and important to reduce the Gibbs oscillation, and simultaneously to preserve the properties (such as discontinuities) of the function/image during the reconstruction process. To achieve such a goal, I employ the Li regularization reconstruction method, which is a widely used technique for data reconstruction. Moreover, I will improve a recently proposed method using Li regularization of edge sparsity.","**To request an accessible version of the file(s) associated with this item, contact library@buffalo.edu. Please include the item's persistent URL [http://hdl.handle.net/. . .] in your request.**"],"dc:format":["application/pdf"],"dc:identifier":["http://hdl.handle.net/10477/79962"],"dc:language":["eng"],"dc:publisher":["State University of New York at Buffalo"],"dc:rights":["Users of works found in University at Buffalo Institutional Repository (UBIR) are responsible for identifying and contacting the copyright owner for permission to reuse. University at Buffalo Libraries do not manage rights for copyright-protected works and cannot assist with permissions.","Copyright retained by author."],"dc:subject":["applied mathematics"],"dc:title":["Gibbs-Free Reconstruction of Fourier Data with Fourier Continuation and Subvoxel Shift with High Order Approximation"],"dc:type":["Text","Dissertation"]},"updated_at":"2026-07-27T19:05:21Z"}