Recovery analysis for weighted mixed $\ell_2/\ell_p$ minimization with $0<p\leq 1$

TL;DR

This paper investigates the conditions under which weighted mixed / minimization can reliably recover block sparse signals from compressed measurements, emphasizing the role of block p-RIP and null space properties.

Contribution

It introduces new recovery conditions based on block p-RIP and null space properties for weighted mixed / minimization, extending existing theories to partial support information.

Findings

Block p-RIP guarantees robust recovery.

Necessary and sufficient conditions via weighted block p-null space property.

Numerical experiments validate theoretical results.

Abstract

We study the recovery conditions of weighted mixed $\ell_2/\ell_p\,(0<p\leq 1)$ 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.