Codes and Expansions (CodEx) Seminar

Arun Suresh (University of Missouri):
On the Generic Crystallographic Phase Retrieval Problem

We consider the problem of recovering a real signal from its power spectrum assuming that the signal is sparse with respect to a generic basis for \(R^N\). Our main result is that if the sparsity level is \(\sim N/2\) in this basis, then the generic sparse vector is uniquely determined up to sign from its power spectrum. We also prove that if the sparsity level is at most \(\sim N/4\), then every sparse vector is determined up to sign from its power spectrum. Analogous results are also obtained for the power spectrum of a complex signal, which extend earlier results in the literature.