A Regularized Sampling Method for Solving Three-Dimensional Inverse Scattering Problems
SIAM Journal on Scientific Computing
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Domain reconstruction using photothermal techniques
Journal of Computational Physics
Exact non-reflecting boundary conditions
Journal of Computational Physics
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An inverse problem is considered where the structure of multiple sound-soft planar obstacles is to be determined given the direction of the incoming acoustic field and knowledge of the corresponding total field on a curve located outside the obstacles. A local uniqueness result is given for this inverse problem suggesting that the reconstruction can be achieved by a single incident wave. A numerical procedure based on the concept of the topological derivative of an associated cost functional is used to produce images of the obstacles. No a priori assumption about the number of obstacles present is needed. Numerical results are included showing that accurate reconstructions can be obtained and that the proposed method is capable of finding both the shapes and the number of obstacles with one or a few incident waves.