A uniqueness result for the inverse problem of identifying boundaries from weighted Radon transform

TL;DR

This paper proves a uniqueness theorem for an inverse problem involving the weighted Radon transform in odd-dimensional Euclidean spaces, specifically for identifying surfaces where the integrand is discontinuous.

Contribution

It establishes a new uniqueness result for determining discontinuity surfaces from weighted Radon transform data in odd dimensions.

Findings

Uniqueness of surface determination in weighted Radon transform

Applicable to functions with discontinuities on surfaces

Extends classical Radon transform results to weighted case

Abstract

We study the problem of the integral geometry, in which the functions are integrated over hyperplanes in the $n$-dimensional Euclidean space, $n=2m+1$. The integrand is the product of a function of $n$ variables called the density and weight function depending on $2n$ variables. Such an integration is called here the weighted Radon transform, which coincides with the classical one if the weight function is equal to one. It is proved the uniqueness for the problem of determination of the surface on which the integrand is discontinuous.