Sharp sufficient condition of block signal recovery via l2/l1-minimisation

This work gains a sharp sufficient condition on the block restricted isometry property for the recovery of sparse signal and corresponding upper bound estimate of error. Under the certain assumption, the signal with block structure can be stably recovered in the presence of noisy case and the block sparse signal can be exactly reconstructed in the noise-free case. Besides, an example is proposed to exhibit the condition is sharp. Numerical simulations are carried out to demonstrate that authors' results are verifiable and l(2)/l(1) minimisation method is robust and stable for the recovery of block sparse signals.