Uniqueness and stability for a seismic-type generalized Radon transform

Abstract

In this paper, we consider a generalized seismic Radon transform that maps a given function to its integrals over a certain family of curves in the plane. Such transforms arise in many areas of mathematics, geophysics, and imaging science. This paper contains new explicit inversion formulas of this generalized seismic Radon transform for various families of curves based on their monotonicity. We derive an analogue of the Fourier slice theorem and present a Sobolev space to obtain a stability estimate for this Radon transform. Finally, we consider local uniqueness results for which we prove a sufficiency theorem.