One-Bit Compressed Sensing by Linear Programming

We give the first computationally tractable and almost optimal solution to the problem of one‐bit compressed sensing, showing how to accurately recover an s‐sparse vector \input amssym $x \in {\Bbb R}^n$ from the signs of $O(s \log^2(n/s))$ random linear measurements of x. The recovery is achieved b...

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Vydané v:Communications on pure and applied mathematics Ročník 66; číslo 8; s. 1275 - 1297
Hlavní autori: Plan, Yaniv, Vershynin, Roman
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Hoboken Wiley Subscription Services, Inc., A Wiley Company 01.08.2013
John Wiley and Sons, Limited
Predmet:
Linear programming
Mathematical problems
Measurement
Probability distribution
Vector space
ISSN:0010-3640, 1097-0312
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Popis
Shrnutí:We give the first computationally tractable and almost optimal solution to the problem of one‐bit compressed sensing, showing how to accurately recover an s‐sparse vector \input amssym $x \in {\Bbb R}^n$ from the signs of $O(s \log^2(n/s))$ random linear measurements of x. The recovery is achieved by a simple linear program. This result extends to approximately sparse vectors x. Our result is universal in the sense that with high probability, one measurement scheme will successfully recover all sparse vectors simultaneously. The argument is based on solving an equivalent geometric problem on random hyperplane tessellations.
Bibliografia:istex:88EF71FF4DE8B44BBA77AF51C72D2B3C173CA0D3
ArticleID:CPA21442
ark:/67375/WNG-FS64H2S6-V
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:0010-3640
1097-0312
DOI:10.1002/cpa.21442