Unification, H-duality, and data truncation in image reconstruction from divergent beam projections

Guang-Hong Chen

doi:10.1117/12.560178

26 October 2004 Unification, H-duality, and data truncation in image reconstruction from divergent beam projections

Guang-Hong Chen

Proceedings Volume 5535, Developments in X-Ray Tomography IV; (2004) https://doi.org/10.1117/12.560178
Event: Optical Science and Technology, the SPIE 49th Annual Meeting, 2004, Denver, Colorado, United States

Abstract

In this paper, a unified framework of image reconstruction from both fan-beam and cone-beam projections is formulated by using intermediate functions. The intermediate function has an imaginary part and a real part. The causality principle is used to prove that the imaginary and real part is mutually linked by a Hilbert transform. Using this link, it is shown that image can be reconstructed by using either the real part or the imaginary part of the intermediate function. Thus there exist two fundamental image reconstruction schemes in image reconstruction from divergent beam projections. One scheme only uses the imaginary part of the intermediate function, while the other scheme only uses the real part. Two schemes are dual to each other by Hilbert transform in intermediate functions. Thus this dual nature is called H-duality. One of the paired dual formulas explicitly allows data truncation, while the other one does not. However, they are equivalent in the sense that both of them are mathematically exact image reconstruction formulas provided the measured data is sufficient for both formulas and is free from noise. Practically, a fan-beam image reconstruction formula is identified to solve the fan-beam data truncation problem.

Citation Download Citation

Guang-Hong Chen "Unification, H-duality, and data truncation in image reconstruction from divergent beam projections", Proc. SPIE 5535, Developments in X-Ray Tomography IV, (26 October 2004); https://doi.org/10.1117/12.560178

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