A Novel Time-Domain Direct Sampling Approach for Inverse Scattering Problems in Acoustics

SIAM Journal on Applied Mathematics, Volume 84, Issue 5, Page 2152-2174, October 2024.
Abstract. This work is concerned with an inverse scattering problem of determining unknown scatterers from time-dependent acoustic measurements. A novel time-domain direct sampling method is developed to efficiently determine both the locations and shapes of inhomogeneous media. In particular, our approach is very easy to implement since only cheap space-time integrations are involved in the evaluation of the imaging functionals. Using the Fourier–Laplace transform, we establish an inherent connection between the time-domain and frequency-domain direct sampling methods. Furthermore, rigorous theoretical justifications and extensive numerical experiments are provided to verify the validity and feasibility of the proposed methods.



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