scholarly journals Sparse recovery with coherent tight frames via analysis Dantzig selector and analysis LASSO

2014 ◽  
Vol 37 (1) ◽  
pp. 126-139 ◽  
Author(s):  
Junhong Lin ◽  
Song Li
Keyword(s):  
Sparse Recovery ◽  
Tight Frames ◽  
Dantzig Selector

scholarly journals Weaker Regularity Conditions and Sparse Recovery in High-Dimensional Regression

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Shiqing Wang ◽  
Yan Shi ◽  
Limin Su
Keyword(s):  
Linear Regression ◽  
Regularity Condition ◽  
Sparse Recovery ◽  
High Dimensional ◽  
Regularity Conditions ◽  
Dantzig Selector ◽  
High Dimensional Regression ◽  
Prediction Risk ◽  
Eigenvalue Condition ◽  
Lasso Estimator

Regularity conditions play a pivotal role for sparse recovery in high-dimensional regression. In this paper, we present a weaker regularity condition and further discuss the relationships with other regularity conditions, such as restricted eigenvalue condition. We study the behavior of our new condition for design matrices with independent random columns uniformly drawn on the unit sphere. Moreover, the present paper shows that, under a sparsity scenario, the Lasso estimator and Dantzig selector exhibit similar behavior. Based on both methods, we derive, in parallel, more precise bounds for the estimation loss and the prediction risk in the linear regression model when the number of variables can be much larger than the sample size.

Sparse recovery with general frame via general-dual-based analysis Dantzig selector

2019 ◽  
Vol 12 (07) ◽  
pp. 2050143
Author(s):  
Chol-Guk Choe ◽  
Myong-Gil Rim ◽  
Ji-Song Ryang
Keyword(s):  
Gaussian Noise ◽  
Text Analysis ◽  
Additive Noise ◽  
Sparse Recovery ◽  
Dual Frame ◽  
Measurement Matrix ◽  
Dantzig Selector ◽  
General Frame ◽  
Special Case ◽  
Undersampled Data

This paper considers recovery of signals that are sparse or approximately sparse in terms of a general frame from undersampled data corrupted with additive noise. We show that the properly constrained [Formula: see text]-analysis, called general-dual-based analysis Dantzig selector, stably recovers a signal which is nearly sparse in terms of a general dual frame provided that the measurement matrix satisfies a restricted isometry property adapted to the general frame. As a special case, we consider the Gaussian noise.

SegOMP: Sparse Recovery with Fewer Measurements

2014 ◽  
Vol E97.A (3) ◽  
pp. 862-864 ◽  
Author(s):  
Li ZENG ◽  
Xiongwei ZHANG ◽  
Liang CHEN ◽  
Weiwei YANG
Keyword(s):  
Sparse Recovery

Joint Sparse Recovery for Signals of Spark-level Sparsity via MMV Tail-$\ell_{2,1}$ Minimization

2021 ◽  
pp. 1-1
Author(s):  
Baifu Zheng ◽  
Cao Zeng ◽  
Shidong Li ◽  
Guisheng Liao
Keyword(s):  
Sparse Recovery
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