Exploiting the Convex-Concave Penalty for Tracking: A Novel Dynamic Reweighted Sparse Bayesian Learning Algorithm

Abstract

We propose a novel dynamic reweighted $\ell_{2}({\rm DR}\ell_{2})$ algorithm in the regime of dynamic compressive sensing. Our analysis shows that aiming to solve a Type II optimization problem, ${\rm DR}\ell_{2}$ is effectively minimizing a ‘convex-concave’ penalty in the coefficients that transitions from a convex region to a concave function using knowledge of past estimations. ${\rm DR}\ell_{2}$ thus provides superior reconstruction performance compared with state-of-the-art dynamic CS algorithms.