How to solve inverse scattering problems without knowing the source term: a three-step strategy

Marie Graff (1) , Marcus J. Grote (2) , Frédéric Nataf (3, 4) , Franck Assous (5)

1 Department of Mathematics [Auckland]
2 Department of Mathematics [Basel]
3 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
4 ALPINES - Algorithms and parallel tools for integrated numerical simulations
5 Department of Computer Science and Mathematics [Ariel university]

The solution of inverse scattering problems always presupposed knowledge of the incident wave-field and require repeated computations of the forward problem, for which knowing the source term is crucial. Here we present a three-step strategy to solve inverse scattering problems when the time signature of the source is unknown. The proposed strategy combines three recent techniques: (i) wave splitting to retrieve the incident and the scattered wavefields, (ii) time-reversed absorbing conditions (TRAC) for redatuming the data inside the computational domain, (iii) adaptive eigenspace inversion (AEI) to solve the inverse problem. Numerical results illustrate step-by-step the feasibility of the proposed strategy.

Mots clés: Inverse scattering; Imaging; Adaptive eigenspace inversion; Unknown source term; Time-reversed absorbing conditions; Wave splitting; Redatuming

Domaines: Mathématiques [math]; Analyse numérique [math.NA]

Marie Graff, Marcus J. Grote, Frédéric Nataf, Franck Assous. How to solve inverse scattering problems without knowing the source term: a three-step strategy. Inverse Problems, 2019, 35 (10), pp.104001. ⟨10.1088/1361-6420/ab2d5f⟩. ⟨hal-02002931⟩