Gaussian beam Radon transform for tensor fields in ${\mathbb{R}}^2$

Abstract

In this article, we introduce and study a set of generalized Gaussian beam Radon transforms (GbRt) acting on tensor fields in ${\mathbb{R}}^2$. The operators considered include longitudinal, transverse, mixed GbRts, along with their integral moments. These operators extend the corresponding notions of the classical generalized Radon transforms for tensor fields. We establish reconstruction results for vector and symmetric 2-tensor fields using appropriate combinations of the defined transforms. This work extends a recent study on the recovery of scalar functions from their GbRt to the recovery of vector and tensor fields from analogously defined generalized GbRts.

17pages