NDLI: On the minimal number of measurements in low-rank matrix recovery

Content Provider	IEEE Xplore Digital Library
Author	Kabanava, M. Rauhut, H. Terstiege, U.
Copyright Year	2015
Description	Author affiliation: Dept. of Math., RWTH Aachen Univ., Aachen, Germany (Kabanava, M.; Rauhut, H.; Terstiege, U.)
Abstract	In this paper we present a new way to obtain a bound on the number of measurements sampled from certain distributions that guarantee uniform stable and robust recovery of low-rank matrices. The recovery guarantees are characterized by a stable and robust version of the null space property and verifying this condition can be reduced to the problem of obtaining a lower bound for a quantity of the form $inf_{xϵT}\|\|Ax\|\|2.$ Gordon's escape through a mesh theorem provides such a bound with explicit constants for Gaussian measurements. Mendelson's small ball method allows to cover the significantly more general case of measurements generated by independent identically distributed random variables with finite fourth moment.
File Size	203270
Page Count	5
Starting Page	382
Ending Page	386
File Format	PDF
ISBN	9781467373531
DOI	10.1109/SAMPTA.2015.7148917
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2015-05-25
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Atmospheric measurements Measurement uncertainty Null space Minimization Particle measurements Robustness Standards
Content Type	Text
Resource Type	Article

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On the minimal number of measurements in low-rank matrix recovery