Nonreciprocal broken ray transforms with applications to fluorescence imaging

Inverse Problems
Lucia FlorescuJohn C Schotland

Abstract

Broken ray transforms (BRTs) are typically considered to be reciprocal, meaning that the transform is independent of the direction in which a photon travels along a given broken ray. However, if the photon can change its energy (or be absorbed and re-radiated at a different frequency) at the vertex of the ray, then reciprocity is lost. In optics, non-reciprocal BRTs are applicable to imaging problems with fluorescent contrast agents. In the case of x-ray imaging, problems with single Compton scattering also give rise to non-reciprocal BRTs. In this paper, we focus on tomographic optical fluorescence imaging and show that, by reversing the path of a photon and using the non-reciprocity of the data function, we can reconstruct simultaneously and independently all optical properties of the medium (the intrinsic attenuation coefficients at the excitation and the fluorescence frequency and the concentration of the contrast agent). Our results are also applicable to inverting BRTs that arise due to single Compton scattering.

References

Apr 28, 2009·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Lucia FlorescuVadim A Markel
Apr 7, 2010·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Lucia FlorescuJohn C Schotland
Aug 14, 2010·International Journal of Biomedical Imaging·M MorvidoneH Zaidi
May 15, 2015·Physics in Medicine and Biology·R Krylov, A Katsevich
Aug 25, 2015·Radiology·Cynthia H McColloughJoel G Fletcher

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Citations

May 19, 2020··Vadim A. MarkelJohn C. Schotland

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Methods Mentioned

BETA
fluorescence imaging
x-ray imaging
three-ray
BRT
x-ray tomography

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