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.
http://resolver.caltech.edu/CaltechAUTHORS:20150203-110637079

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## Abstract

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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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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Record Number: | CaltechAUTHORS:20150203-110637079 | ||||||||||||||||||

Persistent URL: | http://resolver.caltech.edu/CaltechAUTHORS:20150203-110637079 | ||||||||||||||||||

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: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=7028545&isnumber=7028426 | ||||||||||||||||||

Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||||||||

ID Code: | 54326 | ||||||||||||||||||

Collection: | CaltechAUTHORS | ||||||||||||||||||

Deposited By: | Tony Diaz | ||||||||||||||||||

Deposited On: | 04 Feb 2015 01:27 | ||||||||||||||||||

Last Modified: | 04 Feb 2015 01:27 |

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