The Mathematical Foundations of 3D Compton Scatter Emission Imaging

Truong, T. T.; Nguyen, M. K.; Zaidi, H.

doi:https://doi.org/10.1155/2007/92780

International Journal of Biomedical Imaging

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Mathematics in Biomedical Imaging

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Research Article | Open Access

Volume 2007 | Article ID 092780 | https://doi.org/10.1155/2007/92780

The Mathematical Foundations of 3D Compton Scatter Emission Imaging

T. T. Truong,¹M. K. Nguyen,²and H. Zaidi³

Academic Editor: Zhaotian Zhang

Received27 Sept 2006

Accepted20 Feb 2007

Published30 Apr 2007

Abstract

The mathematical principles of tomographic imaging using detected (unscattered) X- or gamma-rays are based on the two-dimensional Radon transform and many of its variants. In this paper, we show that two new generalizations, called conical Radon transforms, are related to three-dimensional imaging processes based on detected Compton scattered radiation. The first class of conical Radon transform has been introduced recently to support imaging principles of collimated detector systems. The second class is new and is closely related to the Compton camera imaging principles and invertible under special conditions. As they are poised to play a major role in future designs of biomedical imaging systems, we present an account of their most important properties which may be relevant for active researchers in the field.

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Copyright

Copyright © 2007 T. T. Truong et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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