Performance Analysis for Block ℓ1 − Αℓ2 Minimization Problem Based on Coherence

Compressed sensing shows that a sparse signal can be stably recovered from incomplete linear measurements. But, in practical applications, some signals have additional structure, where the nonzero elements arise in some blocks. We call such signals as block-sparse signals. In this paper, the [Formula: see text] minimization method for the stable recovery of block-sparse signals is investigated. Sufficient conditions based on block mutual coherence property and associating upper bound estimations of error are established to ensure that block-sparse signals can be stably recovered in the presence of noise via the [Formula: see text] minimization method. To the best of our knowledge, it is the first block mutual coherence property condition of stably reconstructing block-sparse signals by the [Formula: see text] minimization method. To solve the model, we propose an efficient algorithm based on the alternating direction method of multipliers and evidence that the obtained algorithm is globally convergence under moderate assumptions. Additionally, the numerical experiments implemented verify the performance of the [Formula: see text] minimization.