Locating rare and weak material anomalies by convex demixing of propagating wavefields

This paper considers the problem of detecting and localizing material anomalies in solid structures, given spatiotemporal observations at a pre-defined grid of points that collectively describe the material displacement resulting from an induced, propagating acoustic surface wave. We propose an approach that seeks to separate or demix each temporal snapshot of the propagating wavefield into its constituent components, which are assumed to be morphologically dissimilar in the vicinity of material defects. We cast this demixing approach as a group lasso regression task, characterized by morphologically dissimilar dictionaries, and establish conditions under which material anomalies may be accurately identified using this approach. We demonstrate and validate the performance of this approach on synthetic data as well as real-world data.