Data driven reduced order model approach to inverse scattering

I will describe a construction of a reduced order model from wave scattering data collected by an array of sensors. The construction is based on interpreting the wave propagation as a dynamical system that is to be learned from the data.  The states of the dynamical system are the snapshots of the wave at discrete time intervals. We only know these snapshots at the sensors in the array.  The reduced order model is a Galerkin projection of the dynamical system that can be calculated from such knowledge. I will describe the construction and some properties of the reduced order model and I will show two imaging methods based on it.