The restricted isometry property for random matrices with ϕ-subgaussian entries

2015 ◽  
Vol 23 (3) ◽  
Author(s):  
Yuriy Kozachenko ◽  
Viktor Troshki
Keyword(s):  
Random Matrices ◽  
Restricted Isometry Property

AbstractThe aim of this article is to construct the generalized random matrices, which satisfies the restricted isometry property (as introduced by Candes and Tao). Let the data be presented as a product of a vector with not more than

Restricted isometry property for random matrices with heavy-tailed columns

2014 ◽  
Vol 352 (5) ◽  
pp. 431-434 ◽  
Author(s):  
Olivier Guédon ◽  
Alexander E. Litvak ◽  
Alain Pajor ◽  
Nicole Tomczak-Jaegermann
Keyword(s):  
Random Matrices ◽  
Restricted Isometry Property ◽  
Heavy Tailed

scholarly journals A Simple Proof of the Restricted Isometry Property for Random Matrices

2008 ◽  
Vol 28 (3) ◽  
pp. 253-263 ◽  
Author(s):  
Richard Baraniuk ◽  
Mark Davenport ◽  
Ronald DeVore ◽  
Michael Wakin
Keyword(s):  
Random Matrices ◽  
Simple Proof ◽  
Restricted Isometry Property

scholarly journals The restricted isometry property for time–frequency structured random matrices

2012 ◽  
Vol 156 (3-4) ◽  
pp. 707-737 ◽  
Author(s):  
Götz E. Pfander ◽  
Holger Rauhut ◽  
Joel A. Tropp
Keyword(s):  
Random Matrices ◽  
Restricted Isometry Property ◽  
Time Frequency

The Restricted Isometry Property for Banded Random Matrices

2014 ◽  
Vol 62 (19) ◽  
pp. 5073-5084 ◽  
Author(s):  
Juan Castorena ◽  
Charles D. Creusere
Keyword(s):  
Random Matrices ◽  
Restricted Isometry Property

scholarly journals Isometric sketching of any set via the Restricted Isometry Property

2018 ◽  
Vol 7 (4) ◽  
pp. 707-726 ◽  
Author(s):  
Samet Oymak ◽  
Benjamin Recht ◽  
Mahdi Soltanolkotabi
Keyword(s):  
Dimensionality Reduction ◽  
Random Matrices ◽  
Linear Time ◽  
Restricted Isometry Property ◽  
High Dimensions ◽  
Log Linear ◽  
Matrix Vector

Abstract In this paper we show that for the purposes of dimensionality reduction certain class of structured random matrices behave similarly to random Gaussian matrices. This class includes several matrices for which matrix-vector multiply can be computed in log-linear time, providing efficient dimensionality reduction of general sets. In particular, we show that using such matrices any set from high dimensions can be embedded into lower dimensions with near optimal distortion. We obtain our results by connecting dimensionality reduction of any set to dimensionality reduction of sparse vectors via a chaining argument.

Improved Analysis for SOMP Algorithm in Terms of Restricted Isometry Property

2020 ◽  
Vol E103.A (2) ◽  
pp. 533-537
Author(s):  
Xiaobo ZHANG ◽  
Wenbo XU ◽  
Yan TIAN ◽  
Jiaru LIN ◽  
Wenjun XU
Keyword(s):  
Restricted Isometry Property
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