Precise Performance Analysis of the Box-Elastic Net under Matrix Uncertainties

Ayed Alrashdi, Ismail Ben Atitallah, Tareq Y. Al-Naffouri

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


In this letter, we consider the problem of recovering an unknown sparse signal from noisy linear measurements, using an enhanced version of the popular Elastic-Net (EN) method. We modify the EN by adding a box-constraint, and we call it the Box-Elastic Net (Box-EN). We assume independent identically distributed (iid) real Gaussian measurement matrix with additive Gaussian noise. In many practical situations, the measurement matrix is not perfectly known, and so we only have a noisy estimate of it. In this letter, we precisely characterize the mean squared error and the probability of support recovery of the Box-EN in the high-dimensional asymptotic regime. Numerical simulations validate the theoretical predictions derived in the letter and also show that the boxed variant outperforms the standard EN.
Original languageEnglish (US)
Pages (from-to)655-659
Number of pages5
JournalIEEE Signal Processing Letters
Issue number5
StatePublished - Feb 5 2019

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): OSR-2016-KKI-2899
Acknowledgements: This work was supported by the KAUST’s Office of Sponsored Research under Award OSR-2016-KKI-2899. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. David I. Shuman.


Dive into the research topics of 'Precise Performance Analysis of the Box-Elastic Net under Matrix Uncertainties'. Together they form a unique fingerprint.

Cite this