scholarly journals Generalized Notions of Sparsity and Restricted Isometry Property. Part II: Applications

2021 ◽  
Vol 27 (2) ◽  
Author(s):  
Marius Junge ◽  
Kiryung Lee
Keyword(s):  
Restricted Isometry Property

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

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

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

scholarly journals Generalized notions of sparsity and restricted isometry property. Part I: a unified framework

2019 ◽  
Vol 9 (1) ◽  
pp. 157-193 ◽  
Author(s):  
Marius Junge ◽  
Kiryung Lee
Keyword(s):  
Banach Space ◽  
Inverse Problems ◽  
Compressed Sensing ◽  
Dimensionality Reduction ◽  
Group Actions ◽  
Function Spaces ◽  
Restricted Isometry Property ◽  
Low Rank ◽  
Unified Framework ◽  
Order Tensor

Abstract The restricted isometry property (RIP) is an integral tool in the analysis of various inverse problems with sparsity models. Motivated by the applications of compressed sensing and dimensionality reduction of low-rank tensors, we propose generalized notions of sparsity and provide a unified framework for the corresponding RIP, in particular when combined with isotropic group actions. Our results extend an approach by Rudelson and Vershynin to a much broader context including commutative and non-commutative function spaces. Moreover, our Banach space notion of sparsity applies to affine group actions. The generalized approach in particular applies to high-order tensor products.

scholarly journals The Road to Deterministic Matrices with the Restricted Isometry Property

2013 ◽  
Vol 19 (6) ◽  
pp. 1123-1149 ◽  
Author(s):  
Afonso S. Bandeira ◽  
Matthew Fickus ◽  
Dustin G. Mixon ◽  
Percy Wong
Keyword(s):  
Restricted Isometry Property ◽  
The Road
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