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.
Bibliographical noteKAUST 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.