The inverse scattering problem from the multi-frequency backscattering data is a long-standing open problem. We advance the theory by proving a uniqueness result. Moreover, we introduce a direct sampling method for quantitatively reconstructing unknown inhomogeneities. Comprehensive numerical experiments validate the robustness, accuracy, and computational effectiveness of the proposed quantitative direct sampling method.

Publication:

INVERSE PROBLEMS

http://dx.doi.org/10.1088/1361-6420/ae963b

Author:

Yukun Guo

School of Mathematics, Harbin Institute of Technology, Harbin, People’s Republic of China

E-mail: ykguo@hit.edu.cn

Xiaodong Liu

State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, People’s Republic of China

Author to whom any correspondence should be addressed.

E-mail: xdliu@amt.ac.cn