Shifting Inequality and Recovery of Sparse Signals
Name
Cai-2010-Shifting Inequality and Recovery of Sparse Signals.pdf
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245.45 KB
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Adobe PDF
Checksum (MD5)
888c744185b98cd3f33b78da0858ec5a
Author(s)
Wang, Lie
Cai, T. Tony
Xu, Guangwu
Date Issued
February 2010
Journal
IEEE Transactions on Signal Processing
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Citation
Cai, T.T., Lie Wang, and Guangwu Xu. “Shifting Inequality and Recovery of Sparse Signals.” IEEE Transactions on Signal Processing 58.3 (2010): 1300–1308. Web. 4 Apr. 2012. © 2010 Institute of Electrical and Electronics Engineers
Version
Final published version
Abstract
In this paper, we present a concise and coherent analysis of the constrained ℓ₁ minimization method for stable recovering of high-dimensional sparse signals both in the noiseless case and noisy case. The analysis is surprisingly simple and elementary, while leads to strong results. In particular, it is shown that the sparse recovery problem can be solved via ℓ₁ minimization under weaker conditions than what is known in the literature. A key technical tool is an elementary inequality, called Shifting Inequality, which, for a given nonnegative decreasing sequence, bounds the ℓ₂ norm of a subsequence in terms of the ℓ₁ norm of another subsequence by shifting the elements to the upper end.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1109/tsp.2009.2034936
