Precise Error Analysis of the ℓ_2-LASSO
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.
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.Attached Files
Submitted - Precise_Error_Analysis_of_the_$_ell_2$-LASSO.pdf
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Additional details
- Eprint ID
- 55386
- Resolver ID
- CaltechAUTHORS:20150302-080245100
- NSF
- CNS-0932428
- NSF
- CCF-1018927
- NSF
- CCF-1423663
- NSF
- CCF-1409204
- Office of naval Research (ONR)
- N00014-08–0747
- JPL
- IA100076
- Qualcomm Inc.
- King Abdulaziz University
- Created
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2015-03-03Created from EPrint's datestamp field
- Updated
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2023-06-02Created from EPrint's last_modified field