TY - GEN

T1 - Precise performance analysis of the LASSO under matrix uncertainties

AU - Alrashdi, Ayed

AU - Ben Atitallah, Ismail

AU - Al-Naffouri, Tareq Y.

AU - Alouini, Mohamed-Slim

N1 - KAUST Repository Item: Exported on 2020-10-01

PY - 2018/3/12

Y1 - 2018/3/12

N2 - In this paper, we consider the problem of recovering an unknown sparse signal x ∈ R from noisy linear measurements {equation presented}. A popular approach is to solve the ℓ-norm regularized least squares problem which is known as the LASSO. In many practical situations, the measurement matrix H is not perfectely known and we only have a noisy version of it. We assume that the entries of the measurement matrix H and of the noise vector z are iid Gaussian with zero mean and variances 1 /n and σ . In this work, an imperfect measurement matrix is considered under which we precisely characterize the limilting behavior of the mean squared error and the probability of support recovery of the LASSO. The analysis is performed when the problem dimensions grow simultaneously to infinity at fixed rates. Numerical simulations validate the theoretical predictions derived in this paper.

AB - In this paper, we consider the problem of recovering an unknown sparse signal x ∈ R from noisy linear measurements {equation presented}. A popular approach is to solve the ℓ-norm regularized least squares problem which is known as the LASSO. In many practical situations, the measurement matrix H is not perfectely known and we only have a noisy version of it. We assume that the entries of the measurement matrix H and of the noise vector z are iid Gaussian with zero mean and variances 1 /n and σ . In this work, an imperfect measurement matrix is considered under which we precisely characterize the limilting behavior of the mean squared error and the probability of support recovery of the LASSO. The analysis is performed when the problem dimensions grow simultaneously to infinity at fixed rates. Numerical simulations validate the theoretical predictions derived in this paper.

UR - http://hdl.handle.net/10754/628305

UR - https://ieeexplore.ieee.org/document/8309169/

UR - http://www.scopus.com/inward/record.url?scp=85048097677&partnerID=8YFLogxK

U2 - 10.1109/GlobalSIP.2017.8309169

DO - 10.1109/GlobalSIP.2017.8309169

M3 - Conference contribution

SN - 9781509059904

SP - 1290

EP - 1294

BT - 2017 IEEE Global Conference on Signal and Information Processing (GlobalSIP)

PB - Institute of Electrical and Electronics Engineers (IEEE)

ER -