Precise Performance Analysis of the Box-Elastic Net under Matrix Uncertainties
Type
ArticleKAUST Department
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) DivisionElectrical Engineering Program
KAUST Grant Number
OSR-2016-KKI-2899Date
2019-02-05Online Publication Date
2019-02-05Print Publication Date
2019-05Permanent link to this record
http://hdl.handle.net/10754/631833
Metadata
Show full item recordAbstract
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.Citation
Alrashdi AM, Ben Atitallah I, Alnaffouri T (2019) Precise Performance Analysis of the Box-Elastic Net under Matrix Uncertainties. IEEE Signal Processing Letters: 1–1. Available: http://dx.doi.org/10.1109/LSP.2019.2897215.Sponsors
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.Journal
IEEE Signal Processing LettersarXiv
1901.04469Additional Links
https://ieeexplore.ieee.org/document/8633429ae974a485f413a2113503eed53cd6c53
10.1109/LSP.2019.2897215