Quantitative localization of small obstacles in acoustic media

Hélène Barucq 1 Ha Pham 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 present inversion results using full-waveform inversion (FWI) in frequency-domain to locate small circular obstacles in a homogeneous medium. This type of questions arises in non-destructive testing in material imaging, geophysical exploration and medical imaging. We assume that the number, size, and type (hard or soft-scattering, and non-overlapping) of obstacles are known. The correct position are obtained by correcting iteratively an initial guess, via a non-linear optimization procedure which minimizes the difference between observed scattered data and simulated ones. In our approach, the positions are obtained directly, compared to others, in which positions are inferred from reconstructed medium contrast. Another novelty of our work resides in considering backscattered data generated from a limited number of fixed incident angles, and constant number of data point (irrespective of frequencies and angles). In addition, the initial guesses are allowed to be different in nature from the true configuration. Frequency hopping and recycling are used to mitigate the ill-posedness of the inverse problem. The calculation cost of iterative inversion, due to the need of solving a large number of direct problems, is alleviated by using a method based on single-layer potentials. The results of the work comprise first of a compatibility investigation (in the setting of localization problem) of several line search algorithms with nonlinear conjugate gradient and quasi-Newton search directions. This is carried out for 6-obstacle configuration using noisy backscattered data. The best combination are then tested on configuration with 12 obstacle with noisy and 24 obstacles with noise-free data.
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https://hal.archives-ouvertes.fr/hal-01928469
Contributor : Ha Pham <>
Submitted on : Tuesday, November 20, 2018 - 3:25:14 PM
Last modification on : Friday, July 12, 2019 - 7:08:01 PM

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  • HAL Id : hal-01928469, version 1

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Hélène Barucq, Ha Pham, Florian Faucher. Quantitative localization of small obstacles in acoustic media. GDR MecaWave - 1er colloque du GdR MecaWave, Nov 2018, Fréjus, France. ⟨hal-01928469⟩

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