Correlation imaging in inverse scattering is tomography on probability distributions

TL;DR

This paper explores how correlation imaging in inverse scattering can be viewed as tomography on probability distributions, establishing conditions for recovering stochastic moments and identifying when different random fields produce identical data.

Contribution

It introduces a novel perspective linking inverse scattering with probability distribution tomography and provides conditions for the uniqueness of stochastic field recovery.

Findings

Derived conditions for recovering stochastic moments from amplitude correlations.

Proved that identical data implies identical laws for certain random fields.

Established a connection between inverse scattering and probability distribution tomography.

Abstract

Scattering from a non-smooth random field on the time domain is studied for plane waves that propagate simultaneously through the potential in variable angles. We first derive sufficient conditions for stochastic moments of the field to be recovered from correlations between amplitude measurements of the leading singularities, detected in the exterior of a region where the potential is almost surely supported. The result is then applied to show that if two sufficiently regular random fields yield the same data, they have identical laws as function-valued random variables.