2015, Guo, Yukun, Hömberg, Dietmar, Hu, Guanghui, Li, Jingzhi, Liu, Hongyu

This work concerns the inverse scattering problems of imaging unknown/inaccessible scatterers by transient acoustic near-field measurements. Based on the analysis of the migration method, we propose efficient and effective sampling schemes for imaging small and extended scatterers from knowledge of time-dependent scattered data due to incident impulsive point sources. Though the inverse scattering problems are known to be nonlinear and ill-posed, the proposed imaging algorithms are totally direct involving only integral calculations on the measurement surface. Theoretical justifications are presented and numerical experiments are conducted to demonstrate the effectiveness and robustness of our methods. In particular, the proposed static imaging functionals enhance the performance of the total focusing method (TFM) and the dynamic imaging functionals show analogous behavior to the time reversal inversion but without solving time-dependent wave equations.

2014, Hu, Guanghui, Liu, Xiaodong

In this paper, we prove uniqueness in determining a sound-soft ball or polyhedral scatterer in the inverse acoustic scattering problem with a single incident point source wave in RN (N = 2, 3). Our proofs rely on the reflection principle for the Helmholtz equation with respect to a Dirichlet hyperplane or sphere, which is essentially a 'point-to-point extension formula. The method has been adapted to proving uniqueness in inverse scattering from sound-soft cavities with interior measurement data incited by a single point source. The corresponding uniqueness for sound-hard balls or polyhedral scatterers has also been discussed.