Nonreciprocal broken ray transforms with applications to fluorescence imaging

作者：Florescu Lucia^*; Markel Vadim A; Schotland John C

来源：Inverse Problems, 2018, 34(9): 094002.

DOI：10.1088/1361-6420/aacec7

• Broken ray transform
• star transform
• fluorescence imaging
• Compton scattering

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.

• 出版日期2018-9