Precise Performance Analysis of the Box-Elastic Net under Matrix Uncertainties
KAUST DepartmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Electrical Engineering Program
KAUST Grant NumberOSR-2016-KKI-2899
Online Publication Date2019-02-05
Print Publication Date2019-05
Permanent link to this recordhttp://hdl.handle.net/10754/631833
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AbstractIn 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.
CitationAlrashdi 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.
SponsorsThis 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.
JournalIEEE Signal Processing Letters