Reconstruction of a vector field and a symmetric $2$-tensor field from the moment ray transforms in $\mathbb{R}^2$

TL;DR

This paper introduces a method to reconstruct a vector field and a symmetric 2-tensor field in the plane from their combined attenuated moment ray transforms, along with stability estimates for the recovery process.

Contribution

It presents a novel reconstruction technique and stability analysis for recovering vector and tensor fields from moment ray transforms in 2D.

Findings

Successful reconstruction method for vector and tensor fields.

Stability estimates for the inverse problem.

Applicable to fields supported in convex domains.

Abstract

We present a technique for recovering a vector field and a symmetric $2$-tensor field, both real-valued and compactly supported in some strictly convex bounded domain with smooth boundary in the Euclidean plane, from the sum of their attenuated moment ray transforms. In addition, we provide a stability estimate for recovering both the vector field and the symmetric $2$-tensor field from the aforementioned ray transform.