There has been considerable interest in reconstruction of remotely sensed imagery from incomplete frequency measurements for some time now. Given the nature of the collection process, it may be that portions of the spectrum are either missing or corrupted such that one is left with an incomplete representation of the original image. The advances in both the theory and available software for sparse signal reconstruction through function minimization make it an attractive approach for recreating the missing frequency data. It is the aim of this thesis to generalize the reconstruction technique known as Total Variation (TV) minimization from a signal processing perspective and to show that it is but one instance of a more general class of multi-filter operators. The approach will be demonstrated using freely avail- able third-party software, and the reconstruction accuracy of TV minimization will be compared to that of several of the developed alternative operators. Last, the relationship between these operators and the frequencies to be reconstructed will be examined.
","abstract_html":"<p>There has been considerable interest in reconstruction of remotely sensed imagery from incomplete frequency measurements for some time now. Given the nature of the collection process, it may be that portions of the spectrum are either missing or corrupted such that one is left with an incomplete representation of the original image. The advances in both the theory and available software for sparse signal reconstruction through function minimization make it an attractive approach for recreating the missing frequency data. It is the aim of this thesis to generalize the reconstruction technique known as Total Variation (TV) minimization from a signal processing perspective and to show that it is but one instance of a more general class of multi-filter operators. The approach will be demonstrated using freely avail- able third-party software, and the reconstruction accuracy of TV minimization will be compared to that of several of the developed alternative operators. Last, the relationship between these operators and the frequencies to be reconstructed will be examined.</p>","abstract_has_math":false,"creators":["Hagen, Michael"],"institution":null,"degree_name":"Master of Arts (MA)","degree_level":"Open Access Thesis","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Dr. Andrew Ross, Chair","Dr. Jayakumar Ramanathan","Dr. William Sverdlik"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2012,"date_issued":"2012-01-01T08:00:00Z","date_published":"2012-01-01T08:00:00Z","updated_at":"2026-07-24T02:16:51Z","subjects":["optical","radar","transformation","frequency","application","Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://commons.emich.edu/theses/450","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Dr. Andrew Ross, Chair","Dr. Jayakumar Ramanathan","Dr. William Sverdlik"]},{"key":"dc:creator","label":"Author","values":["Hagen, Michael"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2013-04-24T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Open Access Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Arts (MA)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["optical","radar","transformation","frequency","application","Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://commons.emich.edu/theses/450"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["There has been considerable interest in reconstruction of remotely sensed imagery from incomplete frequency measurements for some time now. Given the nature of the collection process, it may be that portions of the spectrum are either missing or corrupted such that one is left with an incomplete representation of the original image. The advances in both the theory and available software for sparse signal reconstruction through function minimization make it an attractive approach for recreating the missing frequency data. It is the aim of this thesis to generalize the reconstruction technique known as Total Variation (TV) minimization from a signal processing perspective and to show that it is but one instance of a more general class of multi-filter operators. The approach will be demonstrated using freely avail- able third-party software, and the reconstruction accuracy of TV minimization will be compared to that of several of the developed alternative operators. Last, the relationship between these operators and the frequencies to be reconstructed will be examined.
"]},{"key":"dc:title","label":"Title","values":["Image reconstruction through polyfiltered variation minimization"]}]}],"canonical_facts":{"dc:contributor":["Dr. Andrew Ross, Chair","Dr. Jayakumar Ramanathan","Dr. William Sverdlik"],"dc:creator":["Hagen, Michael"],"dc:date.available":["2013-04-24T07:00:00Z"],"dc:description.abstract":["There has been considerable interest in reconstruction of remotely sensed imagery from incomplete frequency measurements for some time now. Given the nature of the collection process, it may be that portions of the spectrum are either missing or corrupted such that one is left with an incomplete representation of the original image. The advances in both the theory and available software for sparse signal reconstruction through function minimization make it an attractive approach for recreating the missing frequency data. It is the aim of this thesis to generalize the reconstruction technique known as Total Variation (TV) minimization from a signal processing perspective and to show that it is but one instance of a more general class of multi-filter operators. The approach will be demonstrated using freely avail- able third-party software, and the reconstruction accuracy of TV minimization will be compared to that of several of the developed alternative operators. Last, the relationship between these operators and the frequencies to be reconstructed will be examined.
"],"dc:identifier":["https://commons.emich.edu/theses/450"],"dc:subject":["optical","radar","transformation","frequency","application","Mathematics"],"dc:title":["Image reconstruction through polyfiltered variation minimization"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Open Access Thesis"],"thesis:degree_name":["Master of Arts (MA)"]},"updated_at":"2026-07-24T02:16:51Z"}