Recovery of the sound speed for the Acoustic wave equation from phaseless measurements

TL;DR

This paper develops a new method to recover higher order terms in the acoustic wave equation using phaseless measurements, by establishing stability results for a Hamiltonian flow transform, advancing inverse boundary problem techniques.

Contribution

It introduces a novel stability analysis for the Hamiltonian flow transform, enabling the recovery of higher order coefficients from phaseless acoustic measurements.

Findings

New stability results for Hamiltonian flow transform

Successful recovery of higher order terms in the wave equation

Differentiates from geodesic X-ray transform approaches

Abstract

We recover the higher order terms for the acoustic wave equation from measurements of the modulus of the solution. The recovery of these coefficients is reduced to a question of stability for inverting a Hamiltonian flow transform, not the geodesic X-ray transform encountered in other inverse boundary problems like the determination of conformal factors. We obtain new stability results for the Hamiltonian flow transform, which allow to recover the higher order terms.