Support recovery from noisy random measurements via weighted ℓ1 minimization

Jun Zhang, Urbashi Mitra, Kuan Wen Huang, Nicolo Michelusi

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations


Herein, we analyze the sample complexity of general weighted ℓ1 minimization in terms of support recovery from noisy underdetermined measurements. This analysis generalizes prior work for standard ℓ1 minimization by considering the weighting effect. We state explicit relationship between the weights and the sample complexity such that i.i.d random Gaussian measurement matrices used with weighted ℓ1 minimization recovers the support of the underlying signal with high probability as the problem dimension increases. This result provides a measure that is predictive of relative performance of different algorithms. Motivated by the analysis, a new iterative weighted strategy is proposed. In the Reweighted Partial Support (RePS) algorithm, a sequence of weighted ℓ1 minimization problems are solved where partial support recovery is used to prune the optimization; furthermore, the weights used for the next iteration are updated by the current estimate. RePS is compared to other weighted algorithms through the proposed measure and numerical results, which demonstrate its superior performance for a spectrum occupancy estimation problem motivated by cognitive radio.

Original languageEnglish (US)
Title of host publicationProceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages5
ISBN (Electronic)9781509018062
StatePublished - Aug 10 2016
Externally publishedYes
Event2016 IEEE International Symposium on Information Theory, ISIT 2016 - Barcelona, Spain
Duration: Jul 10 2016Jul 15 2016

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
ISSN (Print)2157-8095


Other2016 IEEE International Symposium on Information Theory, ISIT 2016

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Information Systems
  • Modeling and Simulation
  • Applied Mathematics


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