The linearized Calder\'on problem for polyharmonic operators

TL;DR

This paper addresses a linearized inverse problem for polyharmonic operators, establishing uniqueness in determining coefficients up to gauge by inverting momentum ray transforms, extending Calderón's original work to higher-order operators.

Contribution

It introduces a uniqueness result for the linearized Calderón problem for polyharmonic operators of order 2m, using inversion of momentum ray transforms, which is a novel extension of classical results.

Findings

Proved uniqueness for coefficients of polyharmonic operators up to gauge.

Established a method based on inverting momentum ray transforms.

Extended Calderón's original inverse problem to higher-order operators.

Abstract

In this article we consider a linearized Calder\'on problem for polyharmonic operators of order $2m\ (m\ge 2)$ in the spirit of Calder\'on's original work [Cal80]. We give a uniqueness result for determining coefficients of order $\leq 2m-1$ up to gauge, based on inverting momentum ray transforms.