Analysis and Algorithms for the Phase Retrieval Problem

Analysis and Algorithms for the Phase Retrieval Problem

-
Radu Balan , University of Maryland
Fine Hall 214

The phase retrieval problem presents itself in many applications is physics and engineering. Recent papers on this topic present examples ranging from X-Ray crystallography to audio and image signal processing, classification with deep networks, quantum information theory, and fiber optics data transmission. The problem is to reconstruct a vector in a Hilbert space, up to a global phase factor, from magnitudes of inner products with vectors of a given frame. Two fundamental problems are: (i) analysis of frame sets when inversion is possible; and (ii) efficient algorithms to perform inversion, when possible. In this talk I will describe recent results regarding these problems including descriptions of the Cramer-Rao lower bound as well as other robustness measures for any inversion algorithm.