Image reconstruction from radially incomplete spherical Radon data

We study inversion of the spherical Radon transform with centers on a sphere (the data acquisition set). Such inversions are essential in various image reconstruction problems arising in medical, radar and sonar imaging. In the case of radially incomplete data, we show that the spherical Radon trans...

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Published in:arXiv.org 2017-09
Main Authors: Ambartsoumian, Gaik, Rim Gouia-Zarrad, Krishnan, Venkateswaran P, Roy, Souvik
Format: Article
Language:English
Subjects:
Algorithms
Image acquisition
Image reconstruction
Inversions
Radar imaging
Radon transformation
Robustness (mathematics)
Spherical shells
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Rim Gouia-Zarrad
Krishnan, Venkateswaran P
Roy, Souvik
description We study inversion of the spherical Radon transform with centers on a sphere (the data acquisition set). Such inversions are essential in various image reconstruction problems arising in medical, radar and sonar imaging. In the case of radially incomplete data, we show that the spherical Radon transform can be uniquely inverted recovering the image function in spherical shells. Our result is valid when the support of the image function is inside the data acquisition sphere, outside that sphere, as well as on both sides of the sphere. Furthermore, in addition to the uniqueness result our method of proof provides reconstruction formulas for all those cases. We present a robust computational algorithm based on our inversion formula and demonstrate its accuracy and efficiency on several numerical examples.
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subjects Algorithms
Image acquisition
Image reconstruction
Inversions
Radar imaging
Radon transformation
Robustness (mathematics)
Spherical shells
title Image reconstruction from radially incomplete spherical Radon data
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