Precise error analysis of the LASSO
Paper in proceedings, 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

Gaussian min-max theorem

normalized squared error

sparse recovery


C. Thrampoulidis

California Institute of Technology (Caltech)

Ashkan Panahi

Chalmers, Computer Science and Engineering (Chalmers), Computing Science (Chalmers)

D. Guo

California Institute of Technology (Caltech)

B. Hassibi

California Institute of Technology (Caltech)

40th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2015; Brisbane Convention and Exhibition CentreBrisbane; Australia; 19 April 2014 through 24 April 2014

1520-6149 (ISSN)

Vol. 2015-August 3467-3471

Subject Categories

Electrical Engineering, Electronic Engineering, Information Engineering





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