The High Order Block RIP Condition for Signal Recovery (Journal of Computational Mathematics, 2018)
In this paper, we consider the recovery of block sparse signals, whose nonzero entriesappear in blocks (or clusters) rather than spread arbitrarily throughout the signal, fromincomplete linear measurements. A high order sufficient condition based on block RIPis obtained to guarantee the stable recovery of all block sparse signals in the presenceof 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 issharp. The significance of the results presented in this paper lies in the fact that recoverymay be possible under more general conditions by exploiting the block structure of thesparsity pattern instead of the conventional sparsity pattern.