Fixed angle inverse scattering for sound speeds close to constant

TL;DR

This paper demonstrates that a sound speed close to constant can be stably reconstructed from a single fixed angle scattering measurement, using a linearized approach related to photoacoustic imaging techniques.

Contribution

It introduces a novel stable method for the inverse scattering problem with near-constant sound speeds, adapting the time-reversal technique for the linearized problem.

Findings

Stable reconstruction of near-constant sound speeds from one measurement

Relation of the linearized problem to photoacoustic imaging

Application of modified time-reversal method for stability

Abstract

We study the fixed angle inverse scattering problem of determining a sound speed from scattering measurements corresponding to a single incident wave. The main result shows that a sound speed close to constant can be stably determined by just one measurement. Our method is based on studying the linearized problem, which turns out to be related to the acoustic problem in photoacoustic imaging. We adapt the modified time-reversal method from [P. Stefanov and G. Uhlmann, Thermoacoustic tomography with variable sound speed, Inverse Problems 25 (2009), 075011] to solve the linearized problem in a stable way, and we use this to give a local uniqueness result for the nonlinear inverse problem.