Medical Image Processing:
The Mathematics of Medical Imaging
by James A. Green, Greenwood Research.
[ ] Small hardback, ISBN-13: 978-1-890121-80-8 (ISBN 1-890121-80-0), 2nd edition, 49.20 dollars.

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Image reconstruction from projections in computerized tomography, CT, PET, ECT, ultrasound, NMR image techniques, methods, and fundamental data. Improved attenuation correction compensation algorithms for PET and SPECT. Contains superior cone beam algorithms for CT and a new 90 degree scanning algorithm, CRUX, in addition to treatments of advanced architectures and methods. Also contains extensive tables of the relevant tissue constants for the design engineer. 2nd edition edited by industry experts.

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Contents
Acknowledgements
List of Illustrations

Introduction

Chapter 1. CAT: Computerized Axial Tomography.
Chapter 2. Backprojections.
Chapter 3. The Radon Reconstruction.
Chapter 4. Methods for Reconstruction from Projections.
Chapter 5. Emission Computed Tomography.
Chapter 6. Ultrasonic Imaging.
Chapter 7. Nuclear Magnetic Resonance Imaging.

Appendix A. Websites for Medical Imaging.
Appendix B. Natural Constants and Measures.
Appendix C. C++ Code for ECT.

Bibliography
Index

About the Author
Books by the Author

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0.1 The Radon Transform
1.1 Computed Tomography by Parallel Projection.
1.2 Reconstruction by Back-Projection.
1.3 Beer's Law.
1.4 The Radon Transform Again.
1.5 Alternative Radon Transform.
1.6 The Fourier Slice Theorem.
1.7 The Fourier Slice.
1.8 The Fourier Slice Theorem II.
2.1 Backprojection 1/r Artifact Noise.
2.2 Projection Scanners.
2.3 Ray Geometry for Projective Scanning.
2.4 Star Artifacts.
2.5 Reconstruction of Phantoms from Projections.
3.1 The Radon Transform for Reconstruction.
3.2 Ray Geometry.
4.0 Reconstruction of an Ellipse from Projections.
4.1 Simple Backprojection.
4.2 Reflection & Refraction at an Interface.
4.3 Fourier Slice Theorem Along an Axis.
4.4 Crux Algorithm 90 degree scan.
4.5 The Imatron Electron Beam CT System.
4.6 Radon Transform in Cylindrical Coordinates.
4.7 Projection & Filtered Backprojection, Annulus.
4.8 Fan Beam Geometry.
4.9 Geometry for Computing Fan Unit Vector.
4.10 A Cone Beam Scanning Geometry.
4.11 Reconstruction of an Ellipse from Projections.
5.0 Architectures for ECT.
5.1 ECT Projection for an Ellipsoid, constant mu and C.
5.2 Right Half of an ECT Disk Projection.
5.3 ECT Disk Projection with C*exp[-mu*r] modeling.
5.4 Projection Shapes for Perfect Reconstruction.
5.5 Optimal ECT Compensation Filters.
5.6 Optimal ECT Filtering.
5.7 The ideal filter f(x)/p(x).
5.8 Cubic Section Approximation to f(x)/p(x).
5.9 Projection Prefiltering with poly(x).
5.10 Radon Transform Geometry for ECT.
6.1 Percentage of Beam Remaining after x centimeters.
6.2 Angles of Incidence, Reflection, & Refraction.
6.3 Depth of US Penetration in Centimeters.
6.4 A-mode scan of pulse reflections.
6.5 M-mode scan with time-scale.
6.6 B-mode, or backscatter mode slice images.
6.7 B-scan of a human eye.
6.8a B-scan of fully distended dog bladder.
6.8b Diagram of a mechanical scan arm.
6.9 Doppler Shifts for blood velocity.
6.10 The Fourier Diffraction Projection Theorem.
6.11 Fourier Diffraction Projection Theorem II.
7.1 Two MRI scans of the Brain.
7.2 Nomenclature Map of Brain Central Region.
7.3 Model Spinning Proton.
7.4 Top Precession.
7.5 Proton Precession.
7.6 Torque Moment on a Current Loop.
7.7 The Magnetization.
7.8 Nutation of the Magnetization into the Plane.
7.9 Bflip resolved into counter-rotating vectors.
7.10 Flipping the Magnetization Vector.
7.11 The FID, or Free Induction Decay.
7.12 Fourier Transform NMR Concepts.
7.13 The dephasing of the Magnetization Vector.
7.14 the formation of spin echoes.
7.15 The Original Hahn Spin-Echo Experiment.
7.16 The Measurement of T1.
7.17 A Technique for Measuring T2.
7.18 Saddle-Shaped Magnetic Field for f.o.n.a.r.
7.19 Spin-Echo Decays and Contrast.
7.20 Field Geometry in NMR.
7.21 Fourier Transform NMR Gradient Sequence.
7.22 An Alternative Method for Gradient Fields.
7.23 Line Scanning.
7.24 Radon Transform for NMR Reconstruction.

Tables
Table 6.1 The speed of Ultrasound in Materials.
Table 6.2 Frequency Attenuation of Ultrasound.
Table 6.3 Haemodynamic Parameters.
Table 6.4 Reflection at Tissue Interfaces.
Table 7.1 NMR Sensitivities of Biomedical Import.
Table 7.2 T1 Relaxation Times in Viscous Liquids.
Table 7.3 T1 & T2 in Abdominal Tissues.
Table 7.4 T1 in Normal and Malignant Tissues.
Table 7.5 The Effect of Electric Currents in Tissue.
Table 7.6 Comparison of CT, NMR, US, and ECT.
Table A.1 Principal Manufacturers of NMR Systems.
Table B.1 Linear Attenuation in CT.
Table B.2 Beam Hardening.
Table B.3 Tracer Radionuclides, in Vitro Studies.
Table B.4 Tracer Radionuclides, in Vivo Studies.
Table B.5 Positron Emitters.
Table B.6 Applications of Radiotracers.
Table B.7 Ultrasound Constants.
Table B.8 Radiotracer Dosage.
Table B.9 NMR Constants.
Table B.10 Basic Physical Constants.

WSU Textbooks
Lynn N. McKinnis, Fundamentals of Musculoskeletal Imaging, 3rd edition, (with CD-rom), 2010, F.A.Davis Company.
___[Links/Musculoskeletal Imaging, Images, Papers, Books, Amazon].

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Includes code in C for applications in Emission Computed Tomography.

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