While most of Radon transform applications to imaging involve integrations over smooth sub-
manifolds of the ambient space, lately important situations have appeared where the …

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 …

Since Compton cameras were introduced in the use of single photon emission computed
tomography, various types of conical Radon transforms, which integrate the emission …

Classical computed tomography assumes that x-rays propagate without scattering. The data
is modeled as the two-dimensional Radon transform of the attenuation coefficient of the …

For more than three decades, the exploitation of Compton scattering has led to significant
progress in imaging the inner parts of an optically opaque object. In this imaging process …

We investigate the idealized mathematical model of single scatter in PET for a detector
system possessing excellent energy resolution. The model has the form of integral …

In this dissertation, we focus on analytic and numerical inversion of an integral transform
(cone or Compton transform) that maps a function to its integrals over conical surfaces with a …