Einführung in die Computertomographie
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Einführung in die Computertomographie: Mathematisch-physikalische Grundlagen der Bildrekonstruktion

Einführung in die Computertomographie: Mathematisch-physikalische Grundlagen der Bildrekonstruktion

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About the Book

Das Buch deckt neben den Themen der Entstehung, der Eigenschaften sowie Detektion von Röntgenstrahlen, die Entwicklungshistorie der Computertomographie, die elementaren Methoden der Signalverarbeitung und insbesondere die Signalverarbeitungsverfahren der Computertomographie ab. Hierbei wird Wert auf die ausführliche Darstellung der Mathematik der zwei- und dreidimensionalen Rekonstruktionsverfahren gelegt. Neben der ausführlichen Erklärung der theoretischen Konzepte wird auf die praktischen Randbedingungen der technischen Realisierung sowie auf die auftretenden Bildartefakte besonders eingegangen.

Table of Contents:
1 Einleitung.- 2 Röntgenstrahlung.- 2.1 Erzeugung von Röntgenstrahlung.- 2.2 Absorption und Streuung von Röntgenstrahlung.- 2.3 Detektion von Röntgenstrahlung.- 2.4 Statistik der Röntgenquanten.- 3 Historie der Computertomographie.- 3.1 Tomosynthese.- 3.2 Rotation-Translation des Nadelstrahls (1. Generation).- 3.3 Rotation-Translation des Fächerstrahls (2. Generation).- 3.4 Rotation-Rotation in Einzelschichten (3. Generation).- 3.5 Rotation-Fix mit geschlossenem Detektorring (4. Generation).- 3.6 Fix-Fix mit geschlossenem Detektorring (EBCT).- 3.7 Rotation-Rotation in der Spiralbahn.- 3.8 Rotation-Rotation in Kegelstrahlgeometrie.- 3.9 Micro-CT.- 3.10 PET-CT Kombinationsgeräte.- 3.11 Optisch-fotografische Rekonstruktionstechnik.- 4 Elementare Methoden der Signalverarbeitung.- 4.1 Signale.- 4.2 Räumliche Elementarsignale.- 4.3 Systeme.- 4.4 Signalübertragung.- 4.5 Diracsto?.- 4.6 Dirackamm.- 4.7 Sto?antwort.- 4.8 Übertragungsfunktion.- 4.9 Fouriertransformation.- 4.10 Faltungssatz.- 4.11 Parseval-Theorem.- 4.12 Filtern im Frequenzraum.- 4.13 Hankel-Transformation.- 4.14 Abel-Transformation.- 4.15 Hilbert-Transformation.- 4.16 Abtasttheorem und Nyquist-Kriterium.- 4.17 Wiener-Khintchine-Theorem.- 4.18 Fouriertransformation diskreter Signale (DFT).- 4.19 Finite diskrete Fouriertransformation.- 4.20 z-Transformation.- 4.21 Chirp-z-Transformation.- 5 Zweidimensionale Rekonstruktionsverfahren.- 5.1 Radontransformation.- 5.2 Inverse Radontransformation und Fourier-Slice-Theorem.- 5.3 Implementation der direkten inversen Radontransformation.- 5.4 Linogramm-Methode.- 5.5 Rückprojektion.- 5.6 Gefilterte Rückprojektion.- 5.7 Vergleich von Rückprojektion und gefilterter Rückprojektion.- 5.8 Filtered Layergram: Filterung nach der Rückprojektion.- 5.9 GefilterteRückprojektion und Radonsche Lösung.- 5.10 Cormack-Transformation.- 5.11 Algebraische Rekonstruktionsverfahren.- 5.12 Lösung durch Singulärwertzerlegung.- 5.13 Iterative Rekonstruktion mit ART.- 5.14 Maximum-Likelihood-Verfahren.- 5.15 Zusammenfassung der zweidimensionalen Verfahren.- 6 Technische Realisierung.- 6.1 Rekonstruktion mit realen Signalen.- 6.2 Praktische Implementation der gefilterten Rückprojektion.- 6.3 Minimale Anzahl der Detektorelemente.- 6.4 Minimale Anzahl der Projektionen.- 6.5 Geometrie des Fächerstrahlsystems.- 6.6 Bildrekonstruktion für die Fächerstrahlgeometrie.- 6.7 Detektorviertelversatz und Abtasttheorem.- 7 Dreidimensionale Rekonstruktionsverfahren.- 7.1 Sekundärrekonstruktion aus 2D Schichtenfolgen.- 7.2 Spiral-CT.- 7.3 Rekonstruktion in Parallelstrahlgeometrie.- 7.4 Exakte Rekonstruktionsverfahren in Kegelstrahlgeometrie.- 7.5 Approximative Rekonstruktionen in Kegelstrahlgeometrie.- 7.6 Helix-Kegelstrahlrekonstruktionsverfahren.- 8 Beurteilung der Bildqualität.- 8.1 Die Modulationstransferfunktion in der Bildgebung.- 8.2 Modulationstransferfunktion und Point-Spread-Function.- 8.3 Die Modulationstransferfunktion bei der Computertomographie.- 8.4 SNR, DQE und ROC.- 8.5 2D-Artefakte.- 8.6 3D-Artefakte.- 8.7 Rauschen in rekonstruierten Bildern.- 9 Praktische Aspekte der Computertomographie.- 9.1 Aufnahmeplanung.- 9.2 Datendarstellung.- Literatur.


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Product Details
  • ISBN-13: 9783540208082
  • Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
  • Publisher Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Height: 279 mm
  • No of Pages: 420
  • Returnable: Y
  • Width: 210 mm
  • ISBN-10: 3540208089
  • Publisher Date: 30 Apr 2004
  • Binding: Hardback
  • Language: German
  • Returnable: Y
  • Sub Title: Mathematisch-physikalische Grundlagen der Bildrekonstruktion


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Einführung in die Computertomographie: Mathematisch-physikalische Grundlagen der Bildrekonstruktion
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