Precise error analysis of the LASSO

Christos Thrampoulidis; Ashkan Panahi; Daniel Guo; Babak Hassibi

ICASSP 2015accepted0 citations

Precise error analysis of the LASSO

Christos Thrampoulidis, Ashkan Panahi, Daniel Guo, Babak Hassibi

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 x̂ = arg min x ∥y - Ax∥ 2 +λ∥x∥ 1 , which is known as the ℓ 2 -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 σ 2 . 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 ∥x̂ - x 0 ∥ 2 2 /σ 2 . Our numerical illustrations validate our theoretical predictions.

BibTeX

@inproceedings{icassp2015_preciseerroranal,
  title = {Precise error analysis of the LASSO},
  author = {Christos Thrampoulidis and Ashkan Panahi and Daniel Guo and Babak Hassibi},
  booktitle = {ICASSP 2015},
  year = {2015}
}