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Precise Error Analysis of the ℓ_2-LASSO

Thrampoulidis, Christos and Panahi, Ashkan and Guo, Daniel and Hassibi, Babak (2015) Precise Error Analysis of the ℓ_2-LASSO. . (Unpublished) http://resolver.caltech.edu/CaltechAUTHORS:20150302-080245100

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Abstract

A classical problem that arises in numerous signal processing applications asks for the reconstruction of an unknown, k-sparse signal x_0∈R^n from underdetermined, noisy, linear measurements y=Ax_0 + z ∈ R^m. One standard approach is to solve the following convex program x^=arg min_x ∥y−Ax∥_2 + λ∥x∥_1, which is known as the ℓ2-LASSO. We assume that the entries of the sensing matrix A and of the noise vector z are i.i.d Gaussian with variances 1/m and σ2. In the large system limit when the problem dimensions grow to infinity, but in constant rates, we precisely characterize the limiting behavior of the normalized squared-error ∥x^−x_0∥^2_2/σ^2. Our numerical illustrations validate our theoretical predictions.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/1502.04977arXivDiscussion Paper
Additional Information: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.
Funders:
Funding AgencyGrant Number
NSFCNS-0932428
NSFCCF-1018927
NSFCCF-1423663
NSFCCF-1409204
Office of naval Research (ONR)N00014-08–0747
JPLIA100076
Qualcomm Inc.UNSPECIFIED
King Abdulaziz UniversityUNSPECIFIED
Subject Keywords:LASSO, square-root LASSO, normalized squared error, sparse recovery, Gaussian min-max theorem
Record Number:CaltechAUTHORS:20150302-080245100
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20150302-080245100
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:55386
Collection:CaltechAUTHORS
Deposited By: Shirley Slattery
Deposited On:03 Mar 2015 02:23
Last Modified:03 Mar 2015 02:23

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