Phaseless sampling and reconstruction in shift-invariant spaces
Friday, August 18, 2017 - 10:00am - 10:30am
Cheng Cheng (University of Central Florida)
Phase retrieval (Phaseless sampling and reconstruction) plays important roles in signal/image/speech processing. It consists of reconstructing a signal of interest from its magnitude measurements. The underlying recovery problem is possible to solve only if we have additional information about the signal. In this talk, we consider phaseless sampling and reconstruction of real-valued signals in a shift-invariant space from their magnitude measurements on the Euclidean space and from their phaseless samples taken on a discrete set with ﬁnite sampling density. We ﬁnd an equivalence between nonseparability of signals in a shift-invariant space and their phase retrievability with phaseless samples taken on the Euclidean space. We also propose a reconstruction algorithm which provides a suboptimal approximation to the original signal when its noisy phaseless samples are available only.