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

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

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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

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