Inverse of the conic transformation of a function with a power weight

Abstract

We consider the Radon transformation defined on circular cones called the conical Radon transform. In the three-dimensional space $R^{3}$, it maps the functions to its surface integrals over a circular cone, and in $R^{2}$ to its integrals over two rays with a common vertex. In this paper, we present new formulas for inversion of k-weighted conical and X-ray Radon transformations under complete and incomplete data in $R^{2}$ and $R^{3}$.