  We consider the inverse problem of quantitative reconstruction of properties
(e.g., bulk modulus, density) of visco-acoustic materials based on measurements
of responding waves after stimulation of the medium. Numerical reconstruction
is performed by an iterative minimization algorithm. Firstly, we investigate
the robustness of the algorithm with respect to attenuation model uncertainty,
that is, when different attenuation models are used to simulate synthetic
observation data and for the inversion, respectively. Secondly, to handle
data-sets with multiple reflections generated by wall boundaries around the
domain, we perform inversion using complex frequencies, and show that it offers
a robust framework that alleviates the difficulties of multiple reflections. To
illustrate the efficiency of the algorithm, we perform numerical simulations of
ultrasound imaging experiments to reconstruct a synthetic breast sample that
contains an inclusion of high-contrast properties. We perform experiments in
two and three dimensions, where the latter also serves to demonstrate the
numerical feasibility in a large-scale configuration.
