Paper Info
Title
Weighted-{$\ell_1$} minimization with multiple weighting sets
Abstract
In this paper, we study the support recovery conditions of weighted $\ell_1$ minimization for signal reconstruction from compressed sensing measurements when multiple support estimate sets with different accuracy are available. We identify a class of signals for which the recovered vector from $\ell_1$ minimization provides an accurate support estimate. We then derive stability and robustness guarantees for the weighted $\ell_1$ minimization problem with more than one support estimate. We show that applying a smaller weight to support estimate that enjoy higher accuracy improves the recovery conditions compared with the case of a single support estimate and the case with standard, i.e., non-weighted, $\ell_1$ minimization. Our theoretical results are supported by numerical simulations on synthetic signals and real audio signals.
Year
Venue
Keywords
2012
CoRR
signal reconstruction,compressed sensing,numerical simulation
Field
DocType
Volume
Minimization problem,Audio signal,Mathematical optimization,Weighting,L1 minimization,Robustness (computer science),Minification,Signal reconstruction,Compressed sensing,Physics
Journal
abs/1205.6845
Citations 
PageRank 
References 
4
0.47
6
Authors
2
Name
Order
Citations
PageRank
Hassan Mansour134934.12
Özgür Yilmaz268551.36