Convex recovery from interferometric measurements
In seismic and SAR imaging, fitting cross-correlations of wavefields rather than the wavefields themselves can result in much improved robustness vis-a-vis model uncertainties. This approach however raises two challenges: (i) new spurious local minima may complicate the inversion, and (ii) one must find a good subset of cross-correlations to make the problem well-posed. I will explain how to address these two problems with lifting, semidefinite relaxation, and expander graphs. This mix of ideas has recently proved to be the right approach in other contexts as well, such as angular synchronization (Singer et al.) and phase retrieval (Candes et al.). Joint work with Vincent Jugnon.