IEEE - Institute of Electrical and Electronics Engineers, Inc. - Weighted one-norm minimization with inaccurate support estimates: Sharp analysis via the null-space property

2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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We study the problem of recovering sparse vectors given possibly erroneous support estimates. First, we provide necessary and sufficient conditions for weighted ℓ₁ minimization to... View More

We study the problem of recovering sparse vectors given possibly erroneous support estimates. First, we provide necessary and sufficient conditions for weighted ℓ₁ minimization to successfully recovery all sparse signals whose support estimate is sufficiently accurate. We relate these conditions to the analogous ones for ℓ₁ minimization, showing that they are equivalent when the support estimate is 50% accurate but that the weighted ℓ₁ conditions are easier to satisfy when the support is more than 50% accurate. Second, to quantify this improvement, we provide bounds on the number of Gaussian measurements that ensure, with high probability, that weighted ℓ₁ minimization succeeds. The resulting number of measurements can be significantly less than what is needed to ensure recovery via ℓ₁ minimization. Finally, we illustrate our results via numerical experiments.

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Author(s):	Hassan Mansour ; Rayan Saab
Publisher:	IEEE - Institute of Electrical and Electronics Engineers, Inc.
Publication Date:	1 April 2015
Conference Location:	South Brisbane, QLD, Australia
Conference Date:	19 April 2015
Page(s):	3,317 - 3,321
ISBN (Electronic):	978-1-4673-6997-8
DOI:	10.1109/ICASSP.2015.7178585