• Description

    This book surveys the main mathematical ideas and techniques behind some well-established imaging modalities such as X-ray CT and emission tomography, as well as a variety of newly developing coupled-physics or hybrid techniques, including thermoacoustic tomography.

    The Radon Transform and Medical Imaging emphasizes mathematical techniques and ideas arising across the spectrum of medical imaging modalities and explains important concepts concerning inversion, stability, incomplete data effects, the role of interior information, and other issues critical to all medical imaging methods.

    For nonexperts, the author provides appendices that cover background information on notation, Fourier analysis, geometric rays, and linear operators. The vast bibliography, with over 825 entries, directs readers to a wide array of additional information sources on medical imaging for further study.

CHAPTERS

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Front Matter

pp. i–xvi
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Chapter 1: Why Use Mathematics in Medical Imaging?

pp. 3–5
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Chapter 2: A Brief and Incomplete History of CT

pp. 7–9
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Chapter 3: Some Major CT Modalities and Their Features to Watch for

pp. 11–14
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Chapter 4: Organization of the Book

pp. 15–17
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Chapter 5: “Standard” CT and X-ray and Radon Transforms

pp. 21–51
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Chapter 6: Emission Tomography

pp. 53–63
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Chapter 7: Artifacts, Incomplete Data, Microlocal Analysis, and Such

pp. 65–75
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Chapter 8: More about 3D Radon and X-ray Transforms

pp. 77–81
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Chapter 9: A Brief Overview of Numerical Methods

pp. 83–86
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Chapter 10: MRI, EIT, OT, Elastography, UT

pp. 87–92
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Chapter 11: Thermo-, Photo-, and Optoacoustic Tomography (TAT/PAT/OAT)

pp. 97–139
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Chapter 12: Ultrasound Modulation in EIT and OT

pp. 141–149
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Chapter 13: Inverse Problems with Interior Information

pp. 151–156
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Appendix A: Notation

pp. 159–163
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Appendix B: Brief Notes on the Fourier Transform and Harmonic Analysis

pp. 165–180
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Appendix C: Geometric Rays, Trapping, Energy Decay

pp. 181–182
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Appendix D: Some Classes of Linear Operators and Operator Functions

pp. 183–189
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Appendix E: Recommended Books and Surveys

pp. 191–192
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Back Matter

pp. 193–240
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cover image CBMS-NSF Regional Conference Series in Applied Mathematics
Published:2013
ISBN:978-1-61197-328-0
eISBN:978-1-61197-329-7
Book Series Name:CBMS-NSF Regional Conference Series in Applied Mathematics
Book Code:CB85
Book Pages:xiv + 224