Enhanced Block-Sparse Signal Recovery Performance via Truncated $ℓ_2/ℓ_{1−2}$ Minimization

Abstract

In this paper, we investigate truncated $ℓ_2/ℓ_{1−2}$ minimization and its associated alternating direction method of multipliers (ADMM) algorithm for recovering the block sparse signals. Based on the block restricted isometry property (Block-RIP), a theoretical analysis is presented to guarantee the validity of proposed method. Our theoretical results not only show a less error upper bound, but also promote the former recovery condition of truncated ℓ₁₋₂ method for sparse signal recovery. Besides, the algorithm has been compared with some state-of-the-art algorithms and numerical experiments have shown excellent performances on recovering the block sparse signals.