Time-harmonic inverse wave problem in linear viscoelasticity
Résumé
We consider the quantitative inverse problem in which the physical properties of a viscoelastic medium are reconstructed from wave measurements. The inversion and direct modeling are carried out in the frequency domain to facilitate working with different attenuation models, which are frequency-dependent. The hybridizable discontinuous Galerkin (HDG) method is employed in forward modeling to discretize the time-harmonic linear viscoelastic equations, as well as in inversion. The inversion follows a minimization algorithm in which the elastic moduli are iteratively updated. We carry out reconstructions with attenuation model uncertainty and illustrate the performance of the method in ultrasound imaging experiment to reconstruct synthetic breast samples.
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