Precise error analysis of the LASSO
Paper in proceeding, 2015

A classical problem that arises in numerous signal processing applications asks for the reconstruction of an unknown, k-sparse signal x0 ∈ n from underdetermined, noisy, linear measurements y = Ax0 + z ∈ m. One standard approach is to solve the following convex program x = arg minx y -Ax2+λx1, 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 -x0 2 2/σ2. Our numerical illustrations validate our theoretical predictions.

square-root LASSO

sparse recovery

Gaussian min-max theorem

normalized squared error

LASSO

Author

C. Thrampoulidis

California Institute of Technology (Caltech)

Ashkan Panahi

Chalmers, Signals and Systems, Signal Processing and Biomedical Engineering

D. Guo

California Institute of Technology (Caltech)

B. Hassibi

California Institute of Technology (Caltech)

ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings

15206149 (ISSN)

Vol. 2015-August 3467-3471
978-1-4673-6997-8 (ISBN)

Subject Categories

Electrical Engineering, Electronic Engineering, Information Engineering

DOI

10.1109/ICASSP.2015.7178615

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8/8/2023 6