  Speed-of-sound (SoS) is an emerging ultrasound contrast modality, where
pulse-echo techniques using conventional transducers offer multiple benefits.
For estimating tissue SoS distributions, spatial domain reconstruction from
relative speckle shifts between different beamforming sequences is a promising
approach. This operates based on a forward model that relates the sought local
values of SoS to observed speckle shifts, for which the associated image
reconstruction inverse problem is solved. The reconstruction accuracy thus
highly depends on the hand-crafted forward imaging model. In this work, we
propose to learn the SoS imaging model based on data. We introduce a
convolutional formulation of the pulse-echo SoS imaging problem such that the
entire field-of-view requires a single unified kernel, the learning of which is
then tractable and robust. We present least-squares estimation of such
convolutional kernel, which can further be constrained and regularized for
numerical stability. In experiments, we show that a forward model learned from
k-Wave simulations improves the median contrast of SoS reconstructions by 63%,
compared to a conventional hand-crafted line-based wave-path model. This
simulation-learned model generalizes successfully to acquired phantom data,
nearly doubling the SoS contrast compared to the conventional hand-crafted
alternative. We demonstrate equipment-specific and small-data regime
feasibility by learning a forward model from a single phantom image, where our
learned model quadruples the SoS contrast compared to the conventional
hand-crafted model. On in-vivo data, the simulation- and phantom-learned models
respectively exhibit impressive 7 and 10 folds contrast improvements over the
conventional model.
