TY - GEN
T1 - Support recovery from noisy random measurements via weighted ℓ1 minimization
AU - Zhang, Jun
AU - Mitra, Urbashi
AU - Huang, Kuan Wen
AU - Michelusi, Nicolo
N1 - Funding Information:
This research has been funded in part by the following grants and organizations: AFOSR FA9550-12-1-0215, NSF CNS-1213128, NSF CCF-1410009, NSF CPS-1446901, ONR N00014-09-1-0700, and ONR N00014-15-1-2550. J. Zhang is in part supported by NSFC 61403085, NSFC 51275094 and E. Y. D. Proj. of Uni.in GuangDong under grant 2012LYM0057
Publisher Copyright:
© 2016 IEEE.
PY - 2016/8/10
Y1 - 2016/8/10
N2 - 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.
AB - 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.
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U2 - 10.1109/ISIT.2016.7541534
DO - 10.1109/ISIT.2016.7541534
M3 - Conference contribution
AN - SCOPUS:84985911823
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 1426
EP - 1430
BT - Proceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2016 IEEE International Symposium on Information Theory, ISIT 2016
Y2 - 10 July 2016 through 15 July 2016
ER -