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On recovery guarantees for angular synchronization.
J. Fourier Anal. Appl. 27:31 (2021)
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,
Artikelnummer: 31
Verlag
Birkhäuser
Verlagsort
233 Spring Street, 6th Floor, New York, Ny 10013 Usa
Nichtpatentliteratur
Publikationen
Begutachtungsstatus
Peer reviewed
Institut(e)
Institute of Computational Biology (ICB)
Förderungen
German Science Foundation DFG