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LOCAL SINGULARITY RECONSTRUCTION FROM INTEGRALS OVER CURVES IN R-3
Stockholm University, Faculty of Science, Department of Mathematics.
2013 (English)In: Inverse Problems and Imaging, ISSN 1930-8337, E-ISSN 1930-8345, Vol. 7, no 2, 585-609 p.Article in journal (Refereed) Published
Abstract [en]

We define a general curvilinear Radon transform in R-3, and we develop its microlocal properties. We prove that singularities can be added (or masked) in any backprojection reconstruction method for this transform. We use the microlocal properties of the transform to develop a local backprojection reconstruction algorithm that decreases the effect of the added singularities and reconstructs the shape of the object. This work was motivated by new models in electron microscope tomography in which the electrons travel over curves such as helices or spirals, and we provide reconstructions for a specific transform motivated by this electron microscope tomography problem.

Place, publisher, year, edition, pages
2013. Vol. 7, no 2, 585-609 p.
Keyword [en]
Electron microscopy, curvilinear Radon transform, Fourier integral operator, microlocal analysis
National Category
Mathematics Physical Sciences
Identifiers
URN: urn:nbn:se:su:diva-91532DOI: 10.3934/ipi.2013.7.585ISI: 000319204400014OAI: oai:DiVA.org:su-91532DiVA: diva2:634601
Funder
The Wenner-Gren Foundation
Note

AuthorCount:2;

Available from: 2013-07-01 Created: 2013-06-28 Last updated: 2017-12-06Bibliographically approved

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