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Weighted ℓ_1 minimization for sparse recovery with prior information

Khajehnejad, M. Amin and Xu, Weiyu and Avestimehr, A. Salman and Hassibi, Babak (2009) Weighted ℓ_1 minimization for sparse recovery with prior information. In: 2009 IEEE International Symposium on Information Theory. IEEE , Piscataway, NJ, pp. 483-487. ISBN 978-1-4244-4312-3. https://resolver.caltech.edu/CaltechAUTHORS:20100816-133504795

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Abstract

In this paper we study the compressed sensing problem of recovering a sparse signal from a system of underdetermined linear equations when we have prior information about the probability of each entry of the unknown signal being nonzero. In particular, we focus on a model where the entries of the unknown vector fall into two sets, each with a different probability of being nonzero. We propose a weighted ℓ_1 minimization recovery algorithm and analyze its performance using a Grassman angle approach. We compute explicitly the relationship between the system parameters (the weights, the number of measurements, the size of the two sets, the probabilities of being non-zero) so that an iid random Gaussian measurement matrix along with weighted ℓ_1 minimization recovers almost all such sparse signals with overwhelming probability as the problem dimension increases. This allows us to compute the optimal weights. We also provide simulations to demonstrate the advantages of the method over conventional ℓ_1 optimization.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://doi.org/10.1109/ISIT.2009.5205716 DOIArticle
https://arxiv.org/abs/0901.2912arXivDiscussion Paper
Additional Information:© 2009 IEEE.
Record Number:CaltechAUTHORS:20100816-133504795
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20100816-133504795
Official Citation:M. A. Khajehnejad, W. Xu, A. S. Avestimehr and B. Hassibi, "Weighted ℓ1 minimization for sparse recovery with prior information," 2009 IEEE International Symposium on Information Theory, Seoul, 2009, pp. 483-487. doi: 10.1109/ISIT.2009.5205716
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:19442
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:16 Aug 2010 20:46
Last Modified:03 Oct 2019 01:57

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