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.
Inhaltsverzeichnis
The radiation therapy planning problem.- Mathematical models for medical imaging.- Articles by Workshop Speakers.-Tomography through the transport equation.- A general framework for iterative reconstruction algorithms in optical tomography, using a finite element method.- Scattered radiation in nuclear medicine: A case study on the Boltzmann transport equation.- Mathematical aspects of radiation therapy treatment planning: Continuous inversion versus full discretization and optimization versus feasibility.- Early results on general vertex sets and truncated projections in cone-beam tomography.- Mathematical problems in microwave medical imaging.- Image reconstruction from experimental data in diffusion tomography.- The Application of the x-ray transform to 3D conformal radio therapy.- Optimization methods for radiation therapy plans.- Fully three-dimensional reconstruction in electron microscopy.
