  Generalized Abel equations have been employed in the recent literature to
invert Radon transforms which arise in a number of important imaging
applications, including Compton Scatter Tomography (CST), Ultrasound Reflection
Tomography (URT), and X-ray CT. In this paper, we present novel injectivity
results and inversion methods for Generalized Abel operators. We apply our
theory to a new Radon transform, $\mathcal{R}_j$, of interest in URT, which
integrates a square integrable function of compact support, $f$, over ellipsoid
and hyperboloid surfaces with centers on a plane. Using our newly established
theory on generalized Abel equations, we show that $\mathcal{R}_j$ is injective
and provide an inversion method based on Neumann series. In addition, using
algebraic methods, we present image phantom reconstructions from
$\mathcal{R}_jf$ data with added pseudo random noise.
