  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 work, we precisely
characterize the mean squared error and the probability of support recovery of
the Box-Elastic Net in the high-dimensional asymptotic regime. Numerical
simulations validate the theoretical predictions derived in the paper and also
show that the boxed variant outperforms the standard EN.
