Recovery analysis for ℓ2/ℓ1−2 minimization via prior support information

Abstract

This paper discusses the block sparse signal recovery when the partial prior support information is available. A high order block RIP condition for our proposed weighted ℓ2/ℓ1−2 minimization is established, which in absence of support information is proved to improve the previous one. We demonstrate that the obtained recovery condition is weaker than the analogous one for ℓ2/ℓ1−2 minimization if at least 50% of the estimated block support information is accurate, and the corresponding recovery error estimate is also better. In addition, a series of numerical experiments are carried out to show the excellent recovery performance of the weighted ℓ2/ℓ1−2 minimization.