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. 2007:2007:92780.
doi: 10.1155/2007/92780.

The Mathematical Foundations of 3D Compton Scatter Emission Imaging

T T Truong  1 , M K Nguyen, H Zaidi
Affiliations

The Mathematical Foundations of 3D Compton Scatter Emission Imaging

T T Truong et al. Int J Biomed Imaging. 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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Figures

Figure 1
Figure 1
Two imaging modalities using scattered radiation with and without collimation.
Figure 2
Figure 2
Compton scattering differential cross-section.
Figure 3
Figure 3
Illustration of linear and conical projections.
Figure 4
Figure 4
𝒞 1-cone and 𝒞 1-conical Radon transform definition.
Figure 5
Figure 5
Principle of a Compton camera.
Figure 6
Figure 6
𝒞 2-cone and 𝒞 2-conical Radon transform definition.
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