Phaseless reconstruction: A frame theoretical approach, Part 1
Friday, October 27, 2017 - 9:30am - 11:00am
Nonlinearity causes information loss. In the phaseless reconstruction problem (a.k.a. phase retrieval), we seek to reconstruct a signal from the magnitudes of linear measurements. Phaseless reconstruction is an old problem in x-ray imaging, but also finds applications in acoustic signal processing and quantum information. For the case in which the signal is finite dimensional, frame theory proves to be a useful tool for analyzing phase retrievability. In general, there are three questions we are interested in: 1. What are sufficient and necessary conditions for a frame to be phase retrievable? 2. Is there a stable reconstruction algorithm for the phaseless reconstruction problem? 3. What is the relation between retrievability and stability? In the series of two talks, I am going to review important existing results and conjectures on these questions, as well as our recent work addressing the global stability of phaseless reconstruction.