The Radon Transform on a Family of Curves in the Plane
A. M. Cormack · Proceedings of the American Mathematical Society · 1981
Inversion formulas are given for Radon’s problem when the line integrals are evaluated along curves given, for a fixed $(p,\phi )$, by ${r^\alpha }\cos \left | {\alpha (\theta - \phi )} \right | = {p^\alpha }$, where $\alpha$ is real, $\alpha e 0$.