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The mathematics of medical imaging : a beginner's guide

Author: Timothy G Feeman
Publisher: New York : Springer, 2010.
Series: Springer undergraduate texts in mathematics and technology
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

Medical imaging is a major part of twenty-first century health care. This introduction explores the mathematical aspects of imaging in medicine to explain approximation methods in addition to  Read more...

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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Timothy G Feeman
ISBN: 9780387927114 0387927115 9780387927121 0387927123
OCLC Number: 587869652
Description: 141 p : ill.
Contents: Preface.- 1 X-rays.- 1.1 Introduction.- 1.2 X-ray behavior and Beer's law.- 1.3 Lines in the plane.- 1.4 Exercises.- 2 The Radon Transform.- 2.1 Definition.- 2.2 Examples.- 2.3 Linearity.- 2.4 Phantoms.- 2.5 The domain of R.- 2.6 Exercises.- 3 Back Projection.- 3.1 Definition and properties.- 3.2 Examples.- 3.3 Exercises.- 4 Complex Numbers.- 4.1 The complex number system.- 4.2 The complex exponential function.- 4.3 Wave functions.- 4.4 Exercises.- 5 The Fourier Transform.- 5.1 Definition and examples.- 5.2 Properties and applications.- 5.3 Heaviside and Dirac d.- 5.4 Inversion of the Fourier transform.- 5.5 Multivariable forms.- 5.6 Exercises.- 6 Two Big Theorems.- 6.1 The central slice theorem.- 6.2 Filtered back projection.- 6.3 The Hilbert transform.- 6.4 Exercises.- 7 Filters and Convolution.- 7.1 Introduction.- 7.2 Convolution.- 7.3 Filter resolution.- 7.4 Convolution and the Fourier transform.- 7.5 The Rayleigh-Plancherel theorem.- 7.6 Convolution in 2-dimensional space.- 7.7 Convolution, B, and R.- 7.8 Low-pass filters.- 7.9 Exercises.- 8 Discrete Image Reconstruction.- 8.1 Introduction.- 8.2 Sampling.- 8.3 Discrete low-pass filters.- 8.4 Discrete Radon transform.- 8.5 Discrete functions and convolution.- 8.6 Discrete Fourier transform.- 8.7 Discrete back projection.- 8.8 Interpolation.- 8.9 Discrete image reconstruction.- 8.10 Matrix forms.- 8.11 FFT-the fast Fourier transform.- 8.12 Fan beam geometry.- 8.13 Exercises.- 9 Algebraic Reconstruction Techniques.- 9.1 Introduction.- 9.2 Least squares approximation.- 9.3 Kaczmarz's method.- 9.4 ART in medical imaging.- 9.5 Variations of Kaczmarz's method.- 9.6 ART or the Fourier transform?.- 9.7 Exercises.- 10 MRI-An Overview.- 10.1 Introduction.- 10.2 Basics.- 10.3 The Bloch equation.- 10.4 The RF field.- 10.5 RF pulse sequences; T1 and T2 .- 10.6 Gradients and slice selection.- 10.7 The imaging equation.- 10.8 Exercises.- Appendix A Integrability.- A.1 Improper integrals.- A.2 Iterated improperintegrals.- A.3 L1 and L2 .- A.4 Summability.- Appendix B Topics for Further Study.- References.- Index
Series Title: Springer undergraduate texts in mathematics and technology
Responsibility: Timothy G. Feeman.

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From the reviews: "It is a textbook that presents a compact, rigorous treatment of basic tomographic image reconstruction at a level suitable for an undergraduate who is strong in math. ... This book Read more...

 
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