Codes and Expansions (CodEx) Seminar
Matthias Wellershoff (University of Maryland)
Uniqueness of phase retrieval from sampled Gabor measurements: a short overview
Phase retrieval is a term applied to mathematical problems in which one tries to recover the phases of a large, structured collection of complex numbers from measurements of their moduli. If there is enough redundancy in the structured collection, then recovery of the complex phases is possible. In this talk, we consider measurements generated by the Gabor (or short-time Fourier) transform and explore setups in which recovery is impossible and ones in which recovery is possible. To do so, we touch upon subjects ranging from complex analysis to sampling theory and we demonstrate (among other things) that i) there can be no uniqueness result for sampled Gabor phase retrieval with lattice measurements which holds for all square-integrable signals and ii) there are uniqueness results which hold for bandlimited signals.