Questions of Uniqueness and Resolution in Reconstruction from Projections:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1978
|
| Schriftenreihe: | Lecture Notes in Biomathematics
26 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Reconstruction from projections has revolutionized radiology and as now become one of the most important tools of medical diagnosi- he E. M. I. Scanner is one example. In this text, some fundamental heoretical and practical questions are resolved. Despite recent research activity in the area, the crucial subject ·f the uniqueness of the reconstruction and the effect of noise in the ata posed some unsettled fundamental questions. In particular, Kennan mith proved that if we describe an object by a C~ function, i. e. , nfinitely differentiable with compact support, then there are other bjects with the same shape, i. e. , support, which can differ almost rhitrarily and still have the same projections in finitely many direc ions. On the other hand, he proved that objects in finite dimensional unction spaces are uniquely determined by a single projection for almost 11 angles, i. e. , except on a set of measure zero. Along these lines, erman and Rowland in [41) showed that reconstructions obtained from he commonly used algorithms can grossly misrepresent the object and hat the algorithm which produced the best reconstruction when using oiseless data gave unsatisfactory results with noisy data. Equally mportant are reports in Science, [67, 68) and personal communications y radiologists indicating that in medical practice failure rates of econstruction vary from four to twenty percent. within this work, the mathematical dilemma posed by Kennan Smith's esult is discussed and clarified |
| Beschreibung: | 1 Online-Ressource (X, 180 p) |
| ISBN: | 9783642455070 9783540090878 |
| ISSN: | 0341-633X |
| DOI: | 10.1007/978-3-642-45507-0 |
Internformat
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Datensatz im Suchindex
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| any_adam_object | |
| author | Katz, Myron Bernard |
| author_facet | Katz, Myron Bernard |
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| author_sort | Katz, Myron Bernard |
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| dewey-ones | 510 - Mathematics |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-45507-0 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:11Z |
| institution | BVB |
| isbn | 9783642455070 9783540090878 |
| issn | 0341-633X |
| language | English |
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| series2 | Lecture Notes in Biomathematics |
| spelling | Katz, Myron Bernard Verfasser aut Questions of Uniqueness and Resolution in Reconstruction from Projections by Myron Bernard Katz Berlin, Heidelberg Springer Berlin Heidelberg 1978 1 Online-Ressource (X, 180 p) txt rdacontent c rdamedia cr rdacarrier Lecture Notes in Biomathematics 26 0341-633X Reconstruction from projections has revolutionized radiology and as now become one of the most important tools of medical diagnosi- he E. M. I. Scanner is one example. In this text, some fundamental heoretical and practical questions are resolved. Despite recent research activity in the area, the crucial subject ·f the uniqueness of the reconstruction and the effect of noise in the ata posed some unsettled fundamental questions. In particular, Kennan mith proved that if we describe an object by a C~ function, i. e. , nfinitely differentiable with compact support, then there are other bjects with the same shape, i. e. , support, which can differ almost rhitrarily and still have the same projections in finitely many direc ions. On the other hand, he proved that objects in finite dimensional unction spaces are uniquely determined by a single projection for almost 11 angles, i. e. , except on a set of measure zero. Along these lines, erman and Rowland in [41) showed that reconstructions obtained from he commonly used algorithms can grossly misrepresent the object and hat the algorithm which produced the best reconstruction when using oiseless data gave unsatisfactory results with noisy data. Equally mportant are reports in Science, [67, 68) and personal communications y radiologists indicating that in medical practice failure rates of econstruction vary from four to twenty percent. within this work, the mathematical dilemma posed by Kennan Smith's esult is discussed and clarified Mathematics Mathematics, general Mathematik Projektion Mathematik (DE-588)4175877-8 gnd rswk-swf Biomathematik (DE-588)4139408-2 gnd rswk-swf Computertomografie (DE-588)4113240-3 gnd rswk-swf Bildrekonstruktion (DE-588)4145435-2 gnd rswk-swf Mustererkennung (DE-588)4040936-3 gnd rswk-swf Biomathematik (DE-588)4139408-2 s Projektion Mathematik (DE-588)4175877-8 s Bildrekonstruktion (DE-588)4145435-2 s 1\p DE-604 Mustererkennung (DE-588)4040936-3 s Computertomografie (DE-588)4113240-3 s 2\p DE-604 https://doi.org/10.1007/978-3-642-45507-0 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Katz, Myron Bernard Questions of Uniqueness and Resolution in Reconstruction from Projections Mathematics Mathematics, general Mathematik Projektion Mathematik (DE-588)4175877-8 gnd Biomathematik (DE-588)4139408-2 gnd Computertomografie (DE-588)4113240-3 gnd Bildrekonstruktion (DE-588)4145435-2 gnd Mustererkennung (DE-588)4040936-3 gnd |
| subject_GND | (DE-588)4175877-8 (DE-588)4139408-2 (DE-588)4113240-3 (DE-588)4145435-2 (DE-588)4040936-3 |
| title | Questions of Uniqueness and Resolution in Reconstruction from Projections |
| title_auth | Questions of Uniqueness and Resolution in Reconstruction from Projections |
| title_exact_search | Questions of Uniqueness and Resolution in Reconstruction from Projections |
| title_full | Questions of Uniqueness and Resolution in Reconstruction from Projections by Myron Bernard Katz |
| title_fullStr | Questions of Uniqueness and Resolution in Reconstruction from Projections by Myron Bernard Katz |
| title_full_unstemmed | Questions of Uniqueness and Resolution in Reconstruction from Projections by Myron Bernard Katz |
| title_short | Questions of Uniqueness and Resolution in Reconstruction from Projections |
| title_sort | questions of uniqueness and resolution in reconstruction from projections |
| topic | Mathematics Mathematics, general Mathematik Projektion Mathematik (DE-588)4175877-8 gnd Biomathematik (DE-588)4139408-2 gnd Computertomografie (DE-588)4113240-3 gnd Bildrekonstruktion (DE-588)4145435-2 gnd Mustererkennung (DE-588)4040936-3 gnd |
| topic_facet | Mathematics Mathematics, general Mathematik Projektion Mathematik Biomathematik Computertomografie Bildrekonstruktion Mustererkennung |
| url | https://doi.org/10.1007/978-3-642-45507-0 |
| work_keys_str_mv | AT katzmyronbernard questionsofuniquenessandresolutioninreconstructionfromprojections |