This PhD aims to develop a new class of ultrasonic focusing methods for phased-array imaging by combining deep learning, physics-based modeling, and optimal transport theory. The first research axis introduces a reweighted, probabilistic extension of the Total Focusing Method (TFM), where per-isochrone focusing weights are iteratively estimated by a shared convolutional network and normalized using a neural time-of-flight field. This iterative, differentiable framework enables more adaptive, interpretable, and robust imaging in heterogeneous or uncertain media.

The second axis proposes a full reformulation of TFM as a Wasserstein barycenter problem, in which each partial image is modeled as an empirical distribution in a joint space of spatial coordinates and ultrasonic amplitude. A physically meaningful transport cost, based on geodesic distances that minimize time-of-flight variations with respect to selected emitters, encodes the acoustic geometry directly in the metric. The resulting grid-free barycenters yield sharp, physically consistent reflector localization and open new opportunities at the interface between optimal transport and ultrasonic phased-array imaging. Overall, the thesis aims to merge physics, machine learning, and geometric optimal transport to formulate next-generation reconstruction methods for ultrasonic imaging.