Krishnan, Venkateswaran P.; Quinto, Eric Todd 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]. Cited in 31 Documents MSC: 94A08 Image processing (compression, reconstruction, etc.) in information and communication theory Keywords:limited data problems in tomography; microlocal analysis PDFBibTeX XMLCite \textit{V. P. Krishnan} and \textit{E. T. Quinto}, in: Handbook of mathematical methods in imaging. In 3 volumes. New York, NY: Springer. 847--902 (2015; Zbl 1395.94042) Full Text: DOI References: This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.