Paper Info
Title
Proof of Convergence and Performance Analysis for Sparse Recovery via Zero-Point Attracting Projection
Abstract
recursive algorithm named zero-point attracting projection (ZAP) is proposed recently for sparse signal reconstruction. Compared with the reference algorithms, ZAP demonstrates rather good performance in recovery precision and robustness. However, any theoretical analysis about the mentioned algorithm, even a proof on its convergence, is not available. In this work, a strict proof on the convergence of ZAP is provided and the condition of convergence is put forward. Based on the theoretical analysis, it is further proved that ZAP is nonbiased and can approach the sparse solution to any extent, with the proper choice of step-size. Furthermore, the case of inaccurate measurements in noisy scenario is also discussed. It is proved that disturbance power linearly reduces the recovery precision, which is predictable but not preventable. The reconstruction deviation of $p$-compressible signal is also provided. Finally, numerical simulations are performed to verify the theoretical analysis.
Year
DOI
Venue
2012
10.1109/TSP.2012.2195660
IEEE Transactions on Signal Processing
Keywords
DocType
Volume
compressive sensing (cs),p-compressible signal,perturbation analysis,sparse signal reconstruction,convergence analysis,ℓ 1 norm,zero-point attracting projection (zap),convex optimization,noise measurement,signal processing,matching pursuit,signal reconstruction,compressed sensing,numerical simulation,convex programming,convex function,recursive algorithm
Journal
60
Issue
ISSN
Citations 
8
IEEE Transactions on Signal Processing, 60(8): 4081-4093, 2012
6
PageRank 
References 
Authors
0.52
20
3
Name
Order
Citations
PageRank
Xiaohan Wang116213.81
Yuantao Gu275273.88
Laming Chen36010.43