Recovery analysis for weighted mixed ${\ell }_2/{\ell }_p$ minimization with $0<p\le 1$

Abstract

We study the recovery conditions of weighted mixed ${\ell }_2/{\ell }_p(0<p\le 1)$ minimization for block sparse signal reconstruction from compressed measurements when partial block support information is available. We show that the block $p$-restricted isometry property (RIP) can ensure the robust recovery. Moreover, we present the sufficient and necessary condition for the recovery by using weighted block $p$-null space property. The relationship between the block $p$-RIP and the weighted block $p$-null space property has been established. Finally, we illustrate our results with a series of numerical experiments.