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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

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Volume 24, Issue 3


A Radon-type transform arising in photoacoustic tomography with circular detectors

Sunghwan Moon
  • Department of Mathematical Sciences, Ulsan National Institute of Science and Technology (UNIST), Ulsan 689-798, Republic of Korea
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Published Online: 2015-01-10 | DOI: https://doi.org/10.1515/jiip-2014-0008


Photoacoustic tomography is the most well-known example of a hybrid imaging method. In this article, we define a Radon-type transform arising in a version of photoacoustic tomography that uses integrating circular detectors and describe how the Radon transform integrating over all circles with a fixed radius is determined from this Radon-type transform. We consider three situations in which the centers of the circular detectors are located on a cylinder, on a plane, and on a sphere. This transform is similar to a toroidal Radon transform, which maps a given function to its integrals over a set of tori. We also study this object.

Keywords: Photoacoustic; theromoacoustic; tomography; Radon; toroidal

MSC: 44A12; 65R10; 92C55

About the article

Received: 2014-01-31

Revised: 2014-12-03

Accepted: 2014-12-10

Published Online: 2015-01-10

Published in Print: 2016-06-01

Funding Source: NSF

Award identifier / Grant number: DMS 0908208

Funding Source: NSF

Award identifier / Grant number: DMS 1211463

This work was partly supported by NSF grants DMS 0908208 and DMS 1211463.

Citation Information: Journal of Inverse and Ill-posed Problems, Volume 24, Issue 3, Pages 233–244, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/jiip-2014-0008.

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