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On the robustness of noise-blind low-rank recovery from rank-one measurements.
Linear Algebra Appl. 652, 37-81 (2022)
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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Publication type
Article: Journal article
Document type
Scientific Article
Keywords
Low-rank Matrix Recovery ; Noise-blind ; Nuclear Norm Minimization ; Phase Retrieval ; Quotient Property ; Robustness
ISSN (print) / ISBN
0024-3795
Quellenangaben
Volume: 652,
Pages: 37-81
Publisher
Elsevier
Publishing Place
New York, NY
Non-patent literature
Publications
Reviewing status
Peer reviewed
Institute(s)
Institute of Computational Biology (ICB)
Grants
Leibniz-Rechenzentrum
Helmholtz Association
Deutsche Forschungsgemeinschaft
Priority Program CoSIP
Helmholtz Association
Deutsche Forschungsgemeinschaft
Priority Program CoSIP