Special Session 43: Recent Advances in Inverse Problems, Imaging, and Their Applications

Effective sound speed estimation in ultrasound imaging
Josselin Garnier
Ecole polytechnique
France
Co-Author(s):    Laure Giovangigli, Quentin Goepfert, Pierre Millien
Abstract:
In this talk, we present a mathematical model and analysis for a new method to estimate the sound speed in ultrasound imaging. We first perform a detailed analysis of the point-spread function of an imaging system in the presence of a mismatch between the true sound speed in the medium and the speed used in the reverse-time imaging function. This analysis leads to an estimator of the sound speed in the presence of a point-like reflector (a guide star). In a second part, we consider a random multiscale medium (modeling biological tissue for instance) and use stochastic homogenization techniques to derive a representation formula for the scattered field. We then show that statistical moments of the imaging functional can be recovered from data corresponding to a single realization of the medium. We demonstrate that the point-spread function can be extracted directly from speckle patterns, making it possible to estimate the effective sound speed even in the absence of a point-like reflector.