Precise error analysis of the LASSO
Paper i 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.

LASSO

square-root LASSO

Gaussian min-max theorem

normalized squared error

sparse recovery

Författare

C. Thrampoulidis

CalTech

Ashkan Panahi

Chalmers, Data- och informationsteknik, Datavetenskap

D. Guo

CalTech

B. Hassibi

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

Ämneskategorier

Elektroteknik och elektronik

DOI

10.1109/ICASSP.2015.7178615

ISBN

978-1-4673-6997-8