Department of Computational and Applied Mathematics

In numerical inverse scattering, fitting cross-correlations of wavefields rather than the wavefields themselves can be surprisingly robust with respect to the uncertainties of the forward scattering model. However, this approach raises new challenges: (i) 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 questions with lifting, semidefinite relaxation, and expander graphs. In the process, we solve a question posed by Candes et al. in 2011 on robust phase retrieval. This mix of ideas has also proved to be the right approach in the recent work of Singer et al. on angular synchronization. Joint work with Vincent Jugnon.