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Biomedical Imaging

Book Description

Covering both physical as well as mathematical and algorithmic foundations, this graduate textbook provides the reader with an introduction into modern biomedical imaging and image processing and reconstruction. These techniques are not only based on advanced instrumentation for image acquisition, but equally on new developments in image processing and reconstruction to extract relevant information from recorded data. To this end, the present book offers a quantitative treatise of radiography, computed tomography, and medical physics.

Contents
Introduction
Digital image processing
Essentials of medical x-ray physics
Tomography
Radiobiology, radiotherapy, and radiation protection
Phase contrast radiography
Object reconstruction under nonideal conditions

Table of Contents

  1. Cover
  2. Title Page
  3. Copyright
  4. Contents
  5. Preface and Acknowledgements
  6. 1 Introduction
    1. 1.1 X-ray radiography as an example
    2. 1.2 Summary of biomedical techniques covered herein
  7. 2 Digital image processing
    1. 2.1 Image representation and point operations
    2. 2.2 Geometric transformations and interpolation
    3. 2.3 Convolution and filtering
      1. 2.3.1 Linear filters
      2. 2.3.2 Filtering in Fourier space
      3. 2.3.3 Nonlinear or rank filters
    4. 2.4 The Hough transform
    5. 2.5 Theory of linear imaging systems
      1. 2.5.1 Introduction and definitions
      2. 2.5.2 Point spread function (PSF)
      3. 2.5.3 Modulation transfer function (MTF)
      4. 2.5.4 Example: cosine grating and Gaussian PSF
      5. 2.5.5 Measurement of PSF and MTF
    6. 2.6 Measures of image quality
      1. 2.6.1 Contrast
      2. 2.6.2 Resolution
      3. 2.6.3 Image noise
      4. 2.6.4 Power spectral density
    7. 2.7 Fourier transformation: fundamentals
      1. 2.7.1 Definitions and notations
      2. 2.7.2 Properties and examples of Fourier pairs
    8. 2.8 Digital data and sampling
      1. 2.8.1 Sampling continuous functions
      2. 2.8.2 The sampling theorem
      3. 2.8.3 Discrete Fourier transformation (DFT)
    9. References
    10. Symbols and abbreviations used in Chapter 2
  8. 3 Essentials of medical x-ray physics
    1. 3.1 Electromagnetic spectrum
    2. 3.2 Interactions of x-rays and matter
      1. 3.2.1 Beer–Lambert law
      2. 3.2.2 Differential and integral cross sections
      3. 3.2.3 Photoelectric absorption
      4. 3.2.4 Thomson scattering
      5. 3.2.5 Compton scattering
      6. 3.2.6 Pair production and annihilation
      7. 3.2.7 Photonuclear reactions
    3. 3.3 Generation of x-rays
      1. 3.3.1 Bremsstrahlung spectrum of an x-ray tube
      2. 3.3.2 Characteristic spectrum of an x-ray tube
      3. 3.3.3 Synchrotron radiation
    4. 3.4 Detection of x-rays
    5. 3.5 Statistics of counting x-ray and gamma quanta
    6. 3.6 Summary and implications for clinical applications
    7. References
    8. Symbols and abbreviations used in Chapter 3
  9. 4 Tomography
    1. 4.1 Tomography in a nutshell
    2. 4.2 Mathematical fundamentals of tomography
      1. 4.2.1 Radon transformation (RT)
      2. 4.2.2 Fourier slice theorem (FST)
      3. 4.2.3 Backprojection operator
      4. 4.2.4 General inversion formula
      5. 4.2.5 Different reconstruction methods by choice of α
      6. 4.2.6 Dimensionality of reconstruction and relation to the Hilbert transform
      7. 4.2.7 Reconstruction as a convolution problem
      8. 4.2.8 Problems of discretization and speed
    3. 4.3 Reconstruction based on Chebyshev series and orthogonal polynomial expansion
      1. 4.3.1 Chebyshev polynomials
      2. 4.3.2 Chebyshev backprojection
      3. 4.3.3 Chebyshev expansion
    4. 4.4 Tomographic projection geometries
      1. 4.4.1 X-ray transform, Fresnel scaling theorem and cone beam reconstruction
      2. 4.4.2 Tomography based on the 3d Radon transform
    5. 4.5 Tomography artifacts and algebraic reconstruction
      1. 4.5.1 Tomography artifacts and corrections
      2. 4.5.2 Algebraic reconstruction techniques (ART) and Helgason–Ludwig consistency conditions
    6. References
    7. Symbols and abbreviations used in Chapter 4
  10. 5 Radiobiology, radiotherapy, and radiation protection
    1. 5.1 Interactions of ionizing particles with matter
      1. 5.1.1 Introductory remarks
      2. 5.1.2 Energy transfer from photons to charged secondary particles
      3. 5.1.3 Energy loss of charged particles in matter
    2. 5.2 Dose calculation and measurement
      1. 5.2.1 Analytical example: proton Bragg peak
      2. 5.2.2 Algorithms for external photon beams
      3. 5.2.3 Principles of ionization dosimetry
    3. 5.3 Radiobiology
      1. 5.3.1 The cell cycle
      2. 5.3.2 Ionizing radiation and biological organisms
      3. 5.3.3 Radiation damage to DNA
      4. 5.3.4 Linear energy transfer and relative biological effectiveness
      5. 5.3.5 Cell survival after irradiation: linear quadratic model
    4. 5.4 Fundamentals of radiotherapy
      1. 5.4.1 Motivation
      2. 5.4.2 Steps in radiotherapy
      3. 5.4.3 Radiation modalities and treatment techniques
      4. 5.4.4 Fractionation
      5. 5.4.5 Tumor control and normal tissue complication probability
    5. 5.5 Elements of radiation protection
      1. 5.5.1 Deterministic and stochastic effects
      2. 5.5.2 Equivalent and effective dose
      3. 5.5.3 Natural and man made radiation exposure
    6. References
    7. Symbols and abbreviations used in Chapter 5
  11. 6 Phase contrast radiography
    1. 6.1 Radiography beyond geometrical optics
      1. 6.1.1 Limits of geometrical optics
      2. 6.1.2 The x-ray index of refraction and phase shift in matter
    2. 6.2 Wave equations and coherence
      1. 6.2.1 The stationary wave equation and diffraction integrals
      2. 6.2.2 The optical far field and the phase problem
      3. 6.2.3 Coherence
      4. 6.2.4 Paraxial wave equation (parabolic wave equation)
      5. 6.2.5 Projection approximation of the object transmission function
    3. 6.3 Propagation imaging
      1. 6.3.1 The illumination wavefront: cone beam and plane wave
      2. 6.3.2 Contrast transfer by free space propagation
      3. 6.3.3 Transport of intensity equation (TIE)
      4. 6.3.4 Propagation imaging in the TIE regime
      5. 6.3.5 Propagation imaging in the holographic regime
      6. 6.3.6 Iterative algorithms for reconstruction
    4. 6.4 Grating based phase contrast
      1. 6.4.1 Refraction, wavefront tilts and phase gradient
      2. 6.4.2 Talbot effect and grating based x-ray phase imaging
      3. 6.4.3 Talbot effect with object in the beam path
      4. 6.4.4 Coded apertures
    5. References
    6. Symbols and abbreviations used in Chapter 6
  12. 7 Object reconstruction under nonideal conditions
    1. 7.1 Inverse problems
      1. 7.1.1 Regularization techniques for inverse problems
      2. 7.1.2 Maximum likelihood approach
      3. 7.1.3 Bayesian inference techniques
    2. 7.2 Reconstruction of two-dimensional images
      1. 7.2.1 Images as Markov random fields
      2. 7.2.2 Image deconvolution by the Wiener filter
      3. 7.2.3 Total variation denoising
    3. References
    4. Symbols and abbreviations used in Chapter 7
  13. Index