Recovery analysis for weighted mixed ℓ2∕ℓp minimization with 0<p≤1

Abstract

We study the recovery conditions of weighted mixed ℓ 2 ∕ ℓ p ( 0 < p ≤ 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.