Precise Performance Analysis of the Box-Elastic Net under Matrix Uncertainties
This work addresses sparse signal recovery for applications like compressed sensing or imaging, but it is incremental as it modifies an existing method (Elastic-Net) with a constraint and analyzes it under matrix uncertainties.
The paper tackles the problem of sparse signal recovery from noisy linear measurements with an imperfectly known measurement matrix by proposing the Box-Elastic Net, an enhanced version of Elastic-Net with a box constraint. It precisely characterizes the mean squared error and support recovery probability in high-dimensional asymptotics, showing through simulations that the boxed variant outperforms standard Elastic-Net.
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.