NDLI: Derandomizing Restricted Isometries via the Legendre Symbol

Content Provider	Springer Nature Link
Author	Moreira, Joel Fickus, Matthew Mixon, Dustin G. Bandeira, Afonso S.
Copyright Year	2015
Abstract	The restricted isometry property (RIP) is an important matrix condition in compressed sensing, but the best matrix constructions to date use randomness. This paper leverages pseudorandom properties of the Legendre symbol to reduce the number of random bits in an RIP matrix with Bernoulli entries. In this regard, the Legendre symbol is not special—our main result naturally generalizes to any small-bias sample space. We also conjecture that no random bits are necessary for our Legendre symbol-based construction.
Ending Page	424
Page Count	16
Starting Page	409
File Format	PDF
ISSN	01764276
e-ISSN	14320940
Journal	Constructive Approximation
Issue Number	3
Volume Number	43
Language	English
Publisher	Springer US
Publisher Date	2015-09-24
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Sampling theory Restricted isometry property Numerical Analysis Analysis Linear codes, general Probabilistic methods Small-bias sample space Derandomization Compressed sensing Legendre symbol
Content Type	Text
Resource Type	Article
Subject	Analysis Computational Mathematics

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Derandomizing Restricted Isometries via the Legendre Symbol