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Synopsis
Reconstruction from projections has revolutionized radiology and has now become one of the most important tools of medical diagnosis The E. M. I. Scanner is one example. In this text, some fundamental theoretical and practical questions are resolved. Despite recent research activity in the area, the crucial subject of the uniqueness of the reconstruction and the effect of noise in the data posed some unsettled fundamental questions. In particular, Kennan Smith proved that if we describe an object by a C^inf_o function, i.e., infinitely differentiable with compact support, then there are other objects with the same shape, i.e., support, which can differ almost arbitrarily and still have the same projections in finitely many directions. On the other hand, he proved that objects in finite dimensional function spaces are uniquely determined by a single projection for almost all angles, i.e., except on a set of measure zero. Along these lines, Herman and Rowland in "Three Methods for reconstructing objects from x-rays: a comparative study" (1973) showed that reconstructions obtained from the commonly used algorithms can grossly misrepresent the object and that the algorithm which produced the best reconstruction when using noiseless data gave unsatisfactory results with noisy data. Equally important are reports in Science, and personal communications by radiologists indicating that in medical practice failure rates of reconstruction vary from four to twenty percent. within this work, the mathematical dilemma posed by Kennan Smith's result is discussed and clarified.
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- ÉditeurSpringer Berlin Heidelberg
- Date d'édition1978
- ISBN 10 3540090878
- ISBN 13 9783540090878
- ReliureBroché
- Langueanglais
- Nombre de pages192
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Questions of uniqueness and resolution in reconstruction from projections.
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Berlin, Springer-Verlag, 1987
ISBN 10 : 3540090878
ISBN 13 : 9783540090878
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Questions of Uniqueness and Resolution in Reconstruction from Projections. (= Lecture Notes in Biomathematics, Vol. 26).
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Berlin, Heidelberg, New York: Springer, 1978
ISBN 10 : 3540090878
ISBN 13 : 9783540090878
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Softcover/Paperback. Etat : Gut. IX, 175 pages with fig.; 25 cm. Good. Former library copy with usual markings. Apart from that inside clean. Cover slightly used. Sprache: Englisch Gewicht in Gramm: 399. N° de réf. du vendeur 24161
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Questions of Uniqueness and Resolution in Reconstruction from Projections (Lecture Notes in Biomathematics, 26, Band 26)
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Springer Berlin Heidelberg, 1978
ISBN 10 : 3540090878
ISBN 13 : 9783540090878
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Questions of Uniqueness and Resolution in Reconstruction from Projections.
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New York: Springer, 1978
ISBN 10 : 3540090878
ISBN 13 : 9783540090878
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Paperback. Etat : Good. Series: Lecture Notes in Biomathematics 175p green paperback, this copy from a Cambridge college library with laminated cover, text clean, binding firm Language: English. N° de réf. du vendeur 161610
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Questions of Uniqueness and Resolution in Reconstruction from Projections
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Springer-Verlag GmbH, 1997
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ISBN 13 : 9783540090878
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Broschiert. Etat : Gut. 175 Seiten Versand sofort weltweit. Rechnung mit ausgewiesener MwSt. Bibliotheksexemplar. Worldwide shipping with invoice. Ex library Sprache: Englisch Gewicht in Gramm: 550. N° de réf. du vendeur 191437
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Questions of Uniqueness and Resolution in Reconstruction from Projections. (= Lecture Notes in Biomathematics, Band 26).
Edité par
Springer Berlin Heidelberg, 1978
ISBN 10 : 3540090878
ISBN 13 : 9783540090878
Ancien ou d'occasion
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8° , Softcover/Paperback. 1.Auflage,. 192 Seiten Einband etwas berieben, Bibl.Ex., innen guter und sauberer Zustand 9783540090878 Sprache: Englisch Gewicht in Gramm: 315. N° de réf. du vendeur 150553
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Questions of Uniqueness and Resolution in Reconstruction from Projections
Edité par
Springer Berlin Heidelberg, 1978
ISBN 10 : 3540090878
ISBN 13 : 9783540090878
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Etat : New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Reconstruction from projections has revolutionized radiology and has now become one of the most important tools of medical diagnosis The E. M. I. Scanner is one example. In this text, some fundamental theoretical and practical questions are resolved. Des. N° de réf. du vendeur 4880319
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Questions of Uniqueness and Resolution in Reconstruction from Projections
Edité par
Springer Berlin Heidelberg, 1978
ISBN 10 : 3540090878
ISBN 13 : 9783540090878
Neuf
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Taschenbuch. Etat : Neu. Druck auf Anfrage Neuware - Printed after ordering - Reconstruction from projections has revolutionized radiology and has now become one of the most important tools of medical diagnosis The E. M. I. Scanner is one example. In this text, some fundamental theoretical and practical questions are resolved. Despite recent research activity in the area, the crucial subject of the uniqueness of the reconstruction and the effect of noise in the data posed some unsettled fundamental questions. In particular, Kennan Smith proved that if we describe an object by a C^inf_o function, i.e., infinitely differentiable with compact support, then there are other objects with the same shape, i.e., support, which can differ almost arbitrarily and still have the same projections in finitely many directions. On the other hand, he proved that objects in finite dimensional function spaces are uniquely determined by a single projection for almost all angles, i.e., except on a set of measure zero. Along these lines, Herman and Rowland in 'Three Methods for reconstructing objects from x-rays: a comparative study' (1973) showed that reconstructions obtained from the commonly used algorithms can grossly misrepresent the object and that the algorithm which produced the best reconstruction when using noiseless data gave unsatisfactory results with noisy data. Equally important are reports in Science, and personal communications by radiologists indicating that in medical practice failure rates of reconstruction vary from four to twenty percent. within this work, the mathematical dilemma posed by Kennan Smith's result is discussed and clarified. N° de réf. du vendeur 9783540090878
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Questions of Uniqueness and Resolution in Reconstruction from Projections (Lecture Notes in Biomathematics, 26)
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Questions of Uniqueness and Resolution in Reconstruction from Projections
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Springer Berlin Heidelberg, Springer Berlin Heidelberg Nov 1978, 1978
ISBN 10 : 3540090878
ISBN 13 : 9783540090878
Neuf
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Taschenbuch. Etat : Neu. This item is printed on demand - Print on Demand Titel. Neuware -Reconstruction from projections has revolutionized radiology and has now become one of the most important tools of medical diagnosis The E. M. I. Scanner is one example. In this text, some fundamental theoretical and practical questions are resolved. Despite recent research activity in the area, the crucial subject of the uniqueness of the reconstruction and the effect of noise in the data posed some unsettled fundamental questions. In particular, Kennan Smith proved that if we describe an object by a C^inf_o function, i.e., infinitely differentiable with compact support, then there are other objects with the same shape, i.e., support, which can differ almost arbitrarily and still have the same projections in finitely many directions. On the other hand, he proved that objects in finite dimensional function spaces are uniquely determined by a single projection for almost all angles, i.e., except on a set of measure zero. Along these lines, Herman and Rowland in 'Three Methods for reconstructing objects from x-rays: a comparative study' (1973) showed that reconstructions obtained from the commonly used algorithms can grossly misrepresent the object and that the algorithm which produced the best reconstruction when using noiseless data gave unsatisfactory results with noisy data. Equally important are reports in Science, and personal communications by radiologists indicating that in medical practice failure rates of reconstruction vary from four to twenty percent. within this work, the mathematical dilemma posed by Kennan Smith's result is discussed and clarified.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 192 pp. Englisch. N° de réf. du vendeur 9783540090878
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