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Krahmer, F.* ; Kümmerle, C.* ; Melnyk, O.

On the robustness of noise-blind low-rank recovery from rank-one measurements.

Linear Algebra Appl. 652, 37-81 (2022)
Postprint DOI
Open Access Green
We prove new results about the robustness of well-known convex noise-blind optimization formulations for the reconstruction of low-rank matrices from an underdetermined system of random linear measurements. Specifically, our results address random Hermitian rank-one measurements as used in a version of the phase retrieval problem; that is, each measurement can be represented as the inner product of the unknown matrix and the outer product of a given realization of the standard complex Gaussian random vector. We obtain our results by establishing that with high probability the measurement operator consisting of independent realizations of such a random rank-one matrix exhibits the so-called Schatten-1 quotient property, which corresponds to a lower bound for the inradius of their image of the nuclear norm (Schatten-1) unit ball. We complement our analysis by numerical experiments comparing the solutions of noise-blind and noise-aware formulations. These experiments confirm that noise-blind optimization methods exhibit comparable robustness to noise-aware formulations.
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Publikationstyp Artikel: Journalartikel
Dokumenttyp Wissenschaftlicher Artikel
Korrespondenzautor
Schlagwörter Low-rank Matrix Recovery ; Noise-blind ; Nuclear Norm Minimization ; Phase Retrieval ; Quotient Property ; Robustness
ISSN (print) / ISBN 0024-3795
Zeitschrift Linear Algebra and its Applications
Quellenangaben Band: 652, Heft: , Seiten: 37-81 Artikelnummer: , Supplement: ,
Verlag Elsevier
Verlagsort New York, NY
Nichtpatentliteratur Publikationen
Begutachtungsstatus Peer reviewed
Institut(e) Institute of Computational Biology (ICB)
Förderungen Leibniz-Rechenzentrum
Helmholtz Association
Deutsche Forschungsgemeinschaft
Priority Program CoSIP