Open access
Datum
2018-04Typ
- Journal Article
ETH Bibliographie
no
Altmetrics
Abstract
We consider the recovery of a (real- or complex-valued) signal from magnitude-only measurements, known as phase retrieval. We formulate phase retrieval as a convex optimization problem, which we call PhaseMax. Unlike other convex methods that use semidefinite relaxation and lift the phase retrieval problem to a higher dimension, PhaseMax is a “non-lifting” relaxation that operates in the original signal dimension. We show that the dual problem to PhaseMax is basis pursuit, which implies that the phase retrieval can be performed using algorithms initially designed for sparse signal recovery. We develop sharp lower bounds on the success probability of PhaseMax for a broad range of random measurement ensembles, and we analyze the impact of measurement noise on the solution accuracy. We use numerical results to demonstrate the accuracy of our recovery guarantees, and we showcase the efficacy and limits of PhaseMax in practice. Mehr anzeigen
Persistenter Link
https://doi.org/10.3929/ethz-b-000454766Publikationsstatus
publishedExterne Links
Zeitschrift / Serie
IEEE Transactions on Information TheoryBand
Seiten / Artikelnummer
Verlag
IEEEOrganisationseinheit
09695 - Studer, Christoph / Studer, Christoph
Zugehörige Publikationen und Daten
Has part: https://doi.org/10.3929/ethz-b-000458686
ETH Bibliographie
no
Altmetrics