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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.


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1569-3945
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Volume 27, Issue 4

Issues

Invertibility and stability for a generic class of radon transforms with application to dynamic operators

Siamak RabieniaHaratbar
Published Online: 2018-12-05 | DOI: https://doi.org/10.1515/jiip-2018-0014

Abstract

Let X be an open subset of â„ť2. We study the dynamic operator, đť’ś, integrating over a family of level curves in X when the object changes between the measurement. We use analytic microlocal analysis to determine which singularities can be recovered by the data-set. Our results show that not all singularities can be recovered as the object moves with a speed lower than the X-ray source. We establish stability estimates and prove that the injectivity and stability are of a generic set if the dynamic operator satisfies the visibility, no conjugate points, and local Bolker conditions. We also show this results can be implemented to fan beam geometry.

Keywords: Radon transform; integral geometry; microlocal analysis; Fourier integral operators,Bolker condition; pseudodifferential operators

MSC 2010: 44A12; 46F12; 53C65

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About the article

Received: 2018-03-31

Revised: 2018-10-31

Accepted: 2018-11-04

Published Online: 2018-12-05

Published in Print: 2019-08-01


Funding Source: Division of Mathematical Sciences

Award identifier / Grant number: 1600327

Partly supported by NSF Grant DMS 1600327.


Citation Information: Journal of Inverse and Ill-posed Problems, Volume 27, Issue 4, Pages 469–486, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/jiip-2018-0014.

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