Quantitative localization of small obstacles in acoustic media
Résumé
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.