Physics-driven structured cosparse modeling for source localization

Cosparse modeling is a recent alternative to sparse modeling, where the notion of dictionary is replaced by that of an analysis operator. When a known analysis operator is well adapted to describe the signals of interest, the model and associated algorithms can be used to solve inverse problems. Here we show how to derive an operator to model certain classes of signals that satisfy physical laws, such as the heat equation or the wave equation. We illustrate the approach on an acoustic inverse problem with a toy model of wave propagation and discuss its potential extensions and the challenges it raises.