Conference proceeding
Breaking through the thresholds: an analysis for iterative reweighted ℓ1 minimization via the Grassmann angle framework
2010 IEEE International Conference on Acoustics, Speech and Signal Processing, pp.5498-5501
03/2010
DOI: 10.1109/ICASSP.2010.5495210
Abstract
It is now well understood that the ℓ 1 minimization algorithm is able to recover sparse signals from incomplete measurements and sharp recoverable sparsity thresholds have also been obtained for the ℓ 1 minimization algorithm. However, even though iterative reweighted ℓ 1 minimization algorithms or related algorithms have been empirically observed to boost the recoverable sparsity thresholds for certain types of signals, no rigorous theoretical results have been established to prove this fact. In this paper, we try to provide a theoretical foundation for analyzing the iterative reweighted ℓ 1 algorithms. In particular, we show that for a nontrivial class of signals, the iterative reweighted ℓ 1 minimization can indeed deliver recoverable sparsity thresholds larger than that given in. Our results are based on a high-dimensional geometrical analysis (Grassmann angle analysis) of the null-space characterization for ℓ 1 minimization and weighted ℓ 1 minimization algorithms.
Details
- Title: Subtitle
- Breaking through the thresholds: an analysis for iterative reweighted ℓ1 minimization via the Grassmann angle framework
- Creators
- Weiyu Xu - California Institute of TechnologyM Amin Khajehnejad - California Institute of TechnologyA Salman Avestimehr - California Institute of TechnologyBabak Hassibi - California Institute of Technology
- Resource Type
- Conference proceeding
- Publication Details
- 2010 IEEE International Conference on Acoustics, Speech and Signal Processing, pp.5498-5501
- Publisher
- IEEE
- DOI
- 10.1109/ICASSP.2010.5495210
- ISSN
- 1520-6149
- eISSN
- 2379-190X
- Language
- English
- Date published
- 03/2010
- Academic Unit
- Electrical and Computer Engineering
- Record Identifier
- 9984197442702771
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