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.

Short bio

马世琪，吉林大学数学学院副教授。马世琪博士2019年博士毕业于香港浸会大学，之后前往芬兰于韦斯屈莱大学从事博士后研究。2022年入职吉林大学。马世琪博士主要从事反问题领域的研究，成果主要集中于随机反问题，流形上的反问题以及固定角度反散射问题。目前在Comm. Math. Phys., Inverse Problems, SIAM J. Math. Anal., Math. Z.等期刊发表多篇文章