The high order block RIP condition for signal recovery

In this paper, we consider the recovery of block sparse signals, whose nonzero entries appear in blocks (or clusters) rather than spread arbitrarily throughout the signal, from incomplete linear measurement. A high order sufficient condition based on block RIP is obtained to guarantee the stable recovery of all block sparse signals in the presence of noise, and robust recovery when signals are not exactly block sparse via mixed $l_{2}/l_{1}$ minimization. Moreover, a concrete example is established to ensure the condition is sharp. The significance of the results presented in this paper lies in the fact that recovery may be possible under more general conditions by exploiting the block structure of the sparsity pattern instead of the conventional sparsity pattern.