Quantitative localization of small obstacles with single-layer potential fast solvers

Ha Pham 1 Hélène Barucq 1 Florian Faucher 1
1 Magique 3D - Advanced 3D Numerical Modeling in Geophysics
LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau], Inria Bordeaux - Sud-Ouest
Abstract : In this work, we numerically study the inverse problem of locating small circular obstacles in a homogeneous medium using noisy backscattered data collected at several frequencies. The main novelty of our work is the implementation of a single-layer potential based fast solver (called FSSL) in a Full-Waveform inversion procedure, to give high quality reconstruction with lowtime cost. The efficiency of FSSL was studied in our previous works [7, 6]. We show reconstruction results with up to 12 obstacles in structured or random configurations with several initial guesses, all allowed to be far and different in nature from the target. This last assumption is not expected in results using nonlinear optimization schemes in general. For results with 6 obstacles, we also investigate several optimization methods, comparing between nonlinear gradient descent and quasi- Newton, as well as their convergence with different line search algorithms.
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Ha Pham, Hélène Barucq, Florian Faucher. Quantitative localization of small obstacles with single-layer potential fast solvers. [Research Report] RR-9137, Inria Bordeaux Sud-Ouest; Magique 3D; Universite de Pau et des Pays de l'Adour. 2017. ⟨hal-01673475v2⟩

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