For Matrix Recovery, Rank Restricted Isometry Property and Robust Uniform Boundedness Property Imply Rank Robust Null Space Property

2020 ◽  
Author(s):  
Shashank Ranjan ◽  
Mathukumalli Vidyasagar
Keyword(s):  
Null Space ◽  
Uniform Boundedness ◽  
Restricted Isometry Property ◽  
Boundedness Property ◽  
Matrix Recovery ◽  
Null Space Property ◽  
Space Property

scholarly journals A rice method proof of the null-space property over the Grassmannian

2017 ◽  
Vol 53 (4) ◽  
pp. 1821-1838 ◽  
Author(s):  
Jean-Marc Azaïs ◽  
Stéphane Mourareau ◽  
Yohann De Castro
Keyword(s):  
Null Space ◽  
Null Space Property ◽  
Space Property

scholarly journals On the Null Space Property oflq-Minimization for0

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Yi Gao ◽  
Jigen Peng ◽  
Shigang Yue ◽  
Yuan Zhao
Keyword(s):  
Compressed Sensing ◽  
Null Space ◽  
Equivalent Form ◽  
Sparse Signals ◽  
Null Space Property ◽  
The Relationship ◽  
Space Property

The paper discusses the relationship between the null space property (NSP) and thelq-minimization in compressed sensing. Several versions of the null space property, that is, thelqstable NSP, thelqrobust NSP, and thelq,probust NSP for0<p≤q<1based on the standardlqNSP, are proposed, and their equivalent forms are derived. Consequently, reconstruction results for thelq-minimization can be derived easily under the NSP condition and its equivalent form. Finally, thelqNSP is extended to thelq-synthesis modeling and the mixedl2/lq-minimization, which deals with the dictionary-based sparse signals and the block sparse signals, respectively.

The Null Space Property of the Truncated $\ell _{1-2}$ -Minimization

2018 ◽  
Vol 25 (8) ◽  
pp. 1261-1265 ◽  
Author(s):  
Huanmin Ge ◽  
Jinming Wen ◽  
Wengu Chen
Keyword(s):  
Null Space ◽  
Null Space Property ◽  
Space Property

Stability of lq-analysis based dual frame with Weibull matrices for 0 < q ≤ 1

2017 ◽  
Vol 15 (01) ◽  
pp. 1750001 ◽  
Author(s):  
Yi Gao ◽  
Shigang Yue ◽  
Yongdong Huang
Keyword(s):  
Text Analysis ◽  
High Probability ◽  
Orthonormal Basis ◽  
Null Space ◽  
Stability Estimate ◽  
Dual Frame ◽  
General Frame ◽  
Null Space Property ◽  
The Stability ◽  
Space Property

In practical examples, there are numerous signals that are sparse in a redundant frame rather than an orthonormal basis. This paper mainly focuses on such sparse recovery via [Formula: see text]-analysis-based dual frame with Weibull matrices under the assumption that signals are sparse or compressible in a general frame. First, we give the [Formula: see text] robust null space property and show that it is weaker than the [Formula: see text]-RIP when [Formula: see text] is a general frame. Second, we show that Weibull random matrices with a general dual frame satisfy the [Formula: see text] robust null space property with high probability. Finally, we investigate the stability estimate of [Formula: see text]-analysis based dual frame with Weibull matrices. The result shows that it remains stable and can guarantee accurate recovery of signals with high probability.

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