On the determination of a function from an elliptical Radon transform

Abstract

In recent years, Radon-type transforms that integrate functions over various sets of ellipses/ellipsoids have been considered in synthetic aperture radar, ultrasound reflection tomography, and radio tomography. In this paper, we consider the transform that integrates a given function in Rn over a set of solid ellipses (when n = 2) or solid ellipsoids of rotation (when n ≥ 3) with a fixed eccentricity and foci restricted to a hyperplane. Inversion formulas are obtained for appropriate classes of functions that are even with respect to the hyperplane. Stability estimates and local uniqueness results are also provided.