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Microlocal analysis in tomography. 2nd edition. (English) Zbl 1395.94042

Scherzer, Otmar (ed.), Handbook of mathematical methods in imaging. In 3 volumes. New York, NY: Springer (ISBN 978-1-4939-0789-2/print; 978-1-4939-0790-8/ebook; 978-1-4939-0791-5/print+ebook; 978-3-642-27795-5/online (updated continuously)). Springer Reference, 847-902 (2015).
Summary: Several limited data problems in tomography will be presented in this chapter, including ones for X-ray tomography, electron microscopy, and radar imaging. First, reconstructions from limited data will be evaluated to observe their strengths and weaknesses. Then, the basic analytic properties of the transforms will be presented. The concept of microlocal analysis will be introduced to make the notion of singularity precise. Finally, the microlocal properties of the tomographic transforms are given and then used to explain the observed strengths and limitations of the reconstructions. This will show that these limitations are intrinsic to these limited data problems themselves.
For the entire collection see [Zbl 1322.68001].

MSC:

94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
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