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A simpler approach to weighted ℓ_1 minimization

Krishnaswamy, Anilesh K. and Oymak, Samet and Hassibi, Babak (2012) A simpler approach to weighted ℓ_1 minimization. In: 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE , Piscataway, NJ, pp. 3621-3624. ISBN 978-1-4673-0045-2.

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In this paper, we analyze the performance of weighted ℓ_1 minimization over a non-uniform sparse signal model by extending the “Gaussian width” analysis proposed in [1]. Our results are consistent with those of [7] which are currently the best known ones. However, our methods are less computationally intensive and can be easily extended to signals which have more than two sparsity classes. Finally, we also provide a heuristic for estimating the optimal weights, building on a more general model presented in [11]. Our results reinforce the fact that weighted ℓ_1 minimization is substantially better than regular ℓ_1 minimization and provide an easy way to calculate the optimal weights.

Item Type:Book Section
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Additional Information:© 2012 IEEE.
Subject Keywords:weighted ℓ_1 minimization, compressed sensing, Gaussian measurements, recovery threshold, Gaussian width
Record Number:CaltechAUTHORS:20150224-072919592
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:55131
Deposited By: Shirley Slattery
Deposited On:25 Feb 2015 01:10
Last Modified:03 Oct 2019 08:03

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