6533b884fe1ef96bd12de750

RESEARCH PRODUCT

Fixed angle inverse scattering for sound speeds close to constant

Shiqi MaLeyter Potenciano-machadoMikko Salo

subject

FOS: Mathematics35R30 35Q60 35J05 31B10 78A40Analysis of PDEs (math.AP)

description

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 use this to give a local uniqueness result for the nonlinear inverse problem.

yearjournalcountryeditionlanguage
2021-01-01
10.48550/arxiv.2109.07761https://doi.org/10.48550/arxiv.2109.07761