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Estimating structured signals in sparse noise: A precise noise sensitivity analysis

Thrampoulidis, Christos and Hassibi, Babak (2014) Estimating structured signals in sparse noise: A precise noise sensitivity analysis. In: 52nd Annual Allerton Conference on Communication, Control, and Computing. IEEE , Piscataway, NJ, pp. 866-873. ISBN 978-1-4799-8009-3.

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We consider the problem of estimating a structured signal x_0 from linear, underdetermined and noisy measurements y = Ax_0 + z, in the presence of sparse noise z. A natural approach to recovering x_0, that takes advantage of both the structure of xo and the sparsity of z is solving: x = arg min_x ||y − Ax||1 subject to f(x) ≤ f(x_0) (constrained LAD estimator). Here, f is a convex function aiming to promote the structure of x_0, say ℓ_1-norm to promote sparsity or nuclear norm to promote low-rankness. We assume that the entries of A and the non-zero entries of z are i.i.d normal with variances 1 and σ^2, respectively. Our analysis precisely characterizes the asymptotic noise sensitivity ||x – x_0||^2_2/σ^2 in the limit σ^2 → 0. We show analytically that the LAD method outperforms the more popular LASSO method when the noise is sparse. At the same time its performance is no more than π/2 times worse in the presence of non-sparse noise. Our simulation results verify the validity of our theoretical predictions.

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Thrampoulidis, Christos0000-0001-9053-9365
Additional Information:© 2014 IEEE. The work of B. Hassibi was supported in part by the National Science Foundation under grants CNS-0932428, CCF-1018927, CCF-1423663 and CCF-1409204, by the Office of Naval Research under the MURI grant N00014-08–0747, by the Jet Propulsion Lab under grant IA100076, by a grant from Qualcomm Inc., and by King Abdulaziz University.
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Office of Naval Research (ONR)N00014-08-0747
King Abdulaziz UniversityUNSPECIFIED
Record Number:CaltechAUTHORS:20150203-110637079
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Official Citation:Thrampoulidis, Christos; Hassibi, Babak, "Estimating structured signals in sparse noise: A precise noise sensitivity analysis," Communication, Control, and Computing (Allerton), 2014 52nd Annual Allerton Conference on , vol., no., pp.866,873, Sept. 30 2014-Oct. 3 2014 doi: 10.1109/ALLERTON.2014.7028545 URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:54326
Deposited By: Tony Diaz
Deposited On:04 Feb 2015 01:27
Last Modified:10 Nov 2021 20:32

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