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Computer Science > Information Theory

arXiv:1108.0477 (cs)
[Submitted on 2 Aug 2011 (v1), last revised 6 Mar 2013 (this version, v2)]

Title:Asymptotic Analysis of Complex LASSO via Complex Approximate Message Passing (CAMP)

Authors:Arian Maleki, Laura Anitori, Zai Yang, Richard Baraniuk
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Abstract:Recovering a sparse signal from an undersampled set of random linear measurements is the main problem of interest in compressed sensing. In this paper, we consider the case where both the signal and the measurements are complex. We study the popular reconstruction method of $\ell_1$-regularized least squares or LASSO. While several studies have shown that the LASSO algorithm offers desirable solutions under certain conditions, the precise asymptotic performance of this algorithm in the complex setting is not yet known. In this paper, we extend the approximate message passing (AMP) algorithm to the complex signals and measurements and obtain the complex approximate message passing algorithm (CAMP). We then generalize the state evolution framework recently introduced for the analysis of AMP, to the complex setting. Using the state evolution, we derive accurate formulas for the phase transition and noise sensitivity of both LASSO and CAMP.
Subjects: Information Theory (cs.IT)
Cite as: arXiv:1108.0477 [cs.IT]
  (or arXiv:1108.0477v2 [cs.IT] for this version)
  https://doi.org/10.48550/arXiv.1108.0477

Submission history

From: Arian Maleki [view email]
[v1] Tue, 2 Aug 2011 03:23:28 UTC (469 KB)
[v2] Wed, 6 Mar 2013 19:10:19 UTC (1,889 KB)
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Laura Anitori
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Richard G. Baraniuk
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