Ebook: Computational Radiology and Imaging: Therapy and Diagnostics
- Tags: Physiological Cellular and Medical Topics, Analysis
- Series: The IMA Volumes in Mathematics and its Applications 110
- Year: 1999
- Publisher: Springer-Verlag New York
- Edition: 1
- Language: English
- pdf
The articles collected in this volume are based on lectures given at the IMA Workshop, "Computational Radiology and Imaging: Therapy and Diagnostics", March 17-21, 1997. Introductory articles by the editors have been added. The focus is on inverse problems involving electromagnetic radiation and particle beams, with applications to X-ray tomography, nuclear medicine, near-infrared imaging, microwave imaging, electron microscopy, and radiation therapy planning. Mathematical and computational tools and models which play important roles in this volume include the X-ray transform and other integral transforms, the linear Boltzmann equation and, for near-infrared imaging, its diffusion approximation, iterative methods for large linear and non-linear least-squares problems, iterative methods for linear feasibility problems, and optimization methods. The volume is intended not only for mathematical scientists and engineers working on these and related problems, but also for non-specialists. It contains much introductory expository material, and a large number of references. Many unsolved computational and mathematical problems of substantial practical importance are pointed out.
Content:
Front Matter....Pages i-x
The Radiation Therapy Planning Problem....Pages 1-16
Mathematical Models for Medical Imaging....Pages 17-32
Tomography Through the Transport Equation....Pages 33-44
A General Framework for Iterative Reconstruction Algorithms in Optical Tomography, Using a Finite Element Method....Pages 45-70
Scattered Radiation in Nuclear Medicine: A Case Study on the Boltzmann Transport Equation....Pages 71-100
Mathematical Aspects of Radiation Therapy Treatment Planning: Continuous Inversion Versus Full Discretization and Optimization Versus Feasibility....Pages 101-112
Early Results on General Vertex Sets and Truncated Projections in Cone-Beam Tomography....Pages 113-135
Mathematical Problems in Microwave Medical Imaging....Pages 137-156
Image Reconstruction from Experimental Data in Diffusion Tomography....Pages 157-181
The Application of the X-ray Transform to 3D Conformal Radiotherapy....Pages 183-227
Optimization Methods for Radiation Therapy Plans....Pages 229-249
Fully Three-Dimensional Reconstruction in Electron Microscopy....Pages 251-281
Back Matter....Pages 282-288
Content:
Front Matter....Pages i-x
The Radiation Therapy Planning Problem....Pages 1-16
Mathematical Models for Medical Imaging....Pages 17-32
Tomography Through the Transport Equation....Pages 33-44
A General Framework for Iterative Reconstruction Algorithms in Optical Tomography, Using a Finite Element Method....Pages 45-70
Scattered Radiation in Nuclear Medicine: A Case Study on the Boltzmann Transport Equation....Pages 71-100
Mathematical Aspects of Radiation Therapy Treatment Planning: Continuous Inversion Versus Full Discretization and Optimization Versus Feasibility....Pages 101-112
Early Results on General Vertex Sets and Truncated Projections in Cone-Beam Tomography....Pages 113-135
Mathematical Problems in Microwave Medical Imaging....Pages 137-156
Image Reconstruction from Experimental Data in Diffusion Tomography....Pages 157-181
The Application of the X-ray Transform to 3D Conformal Radiotherapy....Pages 183-227
Optimization Methods for Radiation Therapy Plans....Pages 229-249
Fully Three-Dimensional Reconstruction in Electron Microscopy....Pages 251-281
Back Matter....Pages 282-288
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