By Christoph Börgers (auth.), Christoph Börgers, Frank Natterer (eds.)
The articles gathered during this quantity are in line with lectures given on the IMA Workshop, "Computational Radiology and Imaging: remedy and Diagnostics", March 17-21, 1997. Introductory articles via the editors were extra. the focal point is on inverse difficulties related to electromagnetic radiation and particle beams, with functions to X-ray tomography, nuclear medication, near-infrared imaging, microwave imaging, electron microscopy, and radiation treatment making plans. Mathematical and computational instruments and versions which play very important roles during this quantity contain the X-ray rework and different critical transforms, the linear Boltzmann equation and, for near-infrared imaging, its diffusion approximation, iterative tools for giant linear and non-linear least-squares difficulties, iterative equipment for linear feasibility difficulties, and optimization tools. the amount is meant not just for mathematical scientists and engineers engaged on those and comparable difficulties, but additionally for non-specialists. It includes a lot introductory expository fabric, and a lot of references. Many unsolved computational and mathematical difficulties of considerable sensible significance are pointed out.
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Extra info for Computational Radiology and Imaging: Therapy and Diagnostics
1) is in a deplorable state. There exist some Russian papers on uniqueness . General methods have been developed, too, but apparently they have been applied to 1D problems only . Nothing seems to be known about stability. The numerical methods which have become known are of the Newton type, either applied directly to the transport equation or to the so-called diffusion approximation . The diffusion approximation is an approximation to the transport equation by a parabolic differential equation.
The principal problem that arises in Optical Tomography is the dominance of scattering, which causes light to propagate diffusely in tissue and thus prohibits the ~pplication of direct reconstruction methods using the Radon transform. Various reconstruction methods, including ad hoc backprojection [11, 37] and semi-analytic  schemes have been proposed, but increasingly attention is turning to iterative, model-based reconstruction methods [6, 18,30]. Data acquisition for Optical Tomography is not limited to steadystate attenuation measurements.
A taxonomy of algorithms is given, with an analysis of their spatial and temporal complexity. Key words. Optical Tomography, Diffusion, Inverse Problems, Finite Elements. 1. Introduction. By Optical Tomography we mean the methodology of using light in a narrow wavelength band in the near-infrared (",700nmlOOOnm), to transilluminate tissue, and to use the resulting measurements of intensity on the tissue boundary to reconstruct a map of the optical properties within the tissue. This quite complex field is relatively new, yet has attracted considerable interest from theoreticians, experimental scientists, and clinicians.