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In this paper, we use the block orthogonal matching pursuit (BOMP) algorithm to recover block sparse signals x from measurements y= A x+ v, where v is an ℓ 2-bounded noise vector (ie,‖ v‖ 2≤ ϵ for some constant ϵ). We investigate some sufficient conditions based on the block restricted isometry property (block-RIP) for exact (when v= 0) and stable (when v≠ 0) recovery of block sparse signals x. First, on the one hand, we show that if A satisfies the block-RIP with δ K+ 1< 1/K+ 1, then every block K-sparse signal x can be exactly or stably recovered by BOMP in K iterations. On the other hand, we show that, for any K≥ 1 and 1/K+ 1≤ δ< 1, there exists a matrix A satisfying the block-RIP with δ K+ 1= δ and a block K-sparse signal x such that BOMP may fail to recover x in K iterations. Then, we study some sufficient conditions for recovering block α-strongly-decaying K-sparse signals. We show that if A satisfies the …