Stability and Instance Optimality in Compressed Sensing

2012 ◽  
Vol 10 (8) ◽  
pp. 1902-1910
Author(s):  
Sheng Zhang ◽  
Peixin Ye
Keyword(s):  
Compressed Sensing ◽  
Instance Optimality

REMARKS ABOUT ORTHOGONAL MATCHING PURSUIT ALGORITHMS

2012 ◽  
Vol 04 (04) ◽  
pp. 1250026 ◽  
Author(s):  
ZHIQIANG XU
Keyword(s):  
Compressed Sensing ◽  
Large Class ◽  
Matching Pursuit ◽  
Orthogonal Matching Pursuit ◽  
Sparse Signal ◽  
Instance Optimality

The orthogonal matching pursuit (OMP) is a popular decoder to recover sparse signal in compressed sensing. Our aim is to investigate the theoretical properties of OMP. In particular, we show that the OMP decoder can give (p, q) instance optimality for a large class of encoders with 1 ≤ p ≤ q ≤ 2 and (p, q) ≠ (2, 2).

A Note on Stability and Instance Optimality in Compressed Sensing

2011 ◽  
Vol 130-134 ◽  
pp. 4194-4197
Author(s):  
Sheng Zhang ◽  
Pei Xin Ye
Keyword(s):  
Compressed Sensing ◽  
Noisy Data ◽  
Sparse Signal ◽  
Measurement Matrix ◽  
Random Measurement ◽  
Restricted Isometry Constant ◽  
Instance Optimality ◽  
Measurement Vector ◽  
The Stability ◽  
Signal Vector

In this note, it is proved that every -sparse signal vector can be recovered stably from the measurement vector via minimization as soon as the restricted isometry constant of the measurement matrix is smaller than . Note that our results contain the case of noisy data, therefore previous known results in the literature are extent and improved. Also we obtain the results on the stability and instance optimality for some random measurement matrices.

Sign in / Sign up

Export Citation Format

Share Document