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Filbir, F. ; Krahmer, F.* ; Melnyk, O.

On recovery guarantees for angular synchronization.

J. Fourier Anal. Appl. 27:31 (2021)
Verlagsversion DOI
Open Access Gold (Paid Option)
Creative Commons Lizenzvertrag
The angular synchronization problem of estimating a set of unknown angles from their known noisy pairwise differences arises in various applications. It can be reformulated as an optimization problem on graphs involving the graph Laplacian matrix. We consider a general, weighted version of this problem, where the impact of the noise differs between different pairs of entries and some of the differences are erased completely; this version arises for example in ptychography. We study two common approaches for solving this problem, namely eigenvector relaxation and semidefinite convex relaxation. Although some recovery guarantees are available for both methods, their performance is either unsatisfying or restricted to the unweighted graphs. We close this gap, deriving recovery guarantees for the weighted problem that are completely analogous to the unweighted version.
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Publikationstyp Artikel: Journalartikel
Dokumenttyp Wissenschaftlicher Artikel
Schlagwörter Angular Synchronization ; Eigenvector Relaxation ; Graph Laplacian ; Ptychography ; Semidefinite Programming Relaxation; Complex Quadratic Optimization; Phase Retrieval
ISSN (print) / ISBN 1069-5869
Quellenangaben Band: 27, Heft: 2, Seiten: , Artikelnummer: 31 Supplement: ,
Verlag Birkhäuser
Verlagsort 233 Spring Street, 6th Floor, New York, Ny 10013 Usa
Begutachtungsstatus Peer reviewed
Förderungen German Science Foundation DFG
Helmholtz Association