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Tomography

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Book cover Handbook of Mathematical Methods in Imaging

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Abstract

We define tomography as the process of producing an image of a distribution (of some physical property) from estimates of its line integrals along a finite number of lines of known locations. We touch upon the computational and mathematical procedures underlying the data collection, image reconstruction, and image display in the practice of tomography. The emphasis is on reconstruction methods, especially the so-called series expansion reconstruction algorithms.

We illustrate the use of tomography (including three-dimensional displays based on reconstructions) both in electron microscopy and in x-ray computerized tomography (CT), but concentrate on the latter. This is followed by a classification and discussion of reconstruction algorithms. In particular, we discuss how to evaluate and compare the practical efficacy of such algorithms.

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References and Further Reading

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Author information

Authors and Affiliations

  1. The Graduate Center of the City University of New York, New York, NY, USA

    Gabor T. Herman

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  1. Gabor T. Herman
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Editor information

Editors and Affiliations

  1. Computational Science Center, University of Vienna, Nordbergstrasse 15, Vienna, Austria

    Otmar Scherzer

  2. RICAM, Austrian Academy of Sciences, Linz, Austria

    Otmar Scherzer

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© 2011 Springer Science+Business Media, LLC

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Herman, G.T. (2011). Tomography. In: Scherzer, O. (eds) Handbook of Mathematical Methods in Imaging. Springer, New York, NY. https://doi.org/10.1007/978-0-387-92920-0_16

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