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

Abstract

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.

arXiv admin note: text overlap with arXiv:1808.04309

References in corpus (3)

• A Joint Indoor WLAN Localization and Outlier Detection Scheme Using LASSO and Elastic-Net Optimization Techniques
• Symbol Error Rate Performance of Box-relaxation Decoders in Massive MIMO
• Precise Performance Analysis of the Box-Elastic Net under Matrix Uncertainties

Cited by in corpus (6)

• Precise Performance Analysis of the Box-Elastic Net under Matrix Uncertainties
• Precise Error Analysis of the LASSO under Correlated Designs
• Optimum GSSK Transmission in Massive MIMO Systems Using the Box-LASSO Decoder
• Asymptotic Characterisation of Regularised Zero-Forcing Receiver for Imperfect and Correlated Massive MIMO Systems with Optimal Power Allocation
• Large System Analysis of Box-Relaxation in Correlated Massive MIMO Systems Under Imperfect CSI (Extended Version)
• Asymptotic Performance of Box-RLS Decoders under Imperfect CSI with Optimized Resource Allocation