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We consider the block orthogonal multi-matching pursuit (BOMMP) algorithm forthe recovery of block sparse signals. A sharp bound is obtained for the exactreconstruction of block $K$-sparse signals via the BOMMP algorithm in thenoiseless case, based on the block restricted isometry constant (block-RIC).Moreover, we show that the sharp bound combining with an extra condition on theminimum $\ell_2$ norm of nonzero blocks of block $K-$sparse signals issufficient to recover the true support of block $K$-sparse signals by the BOMMPin the noise case. The significance of the results we obtain in this paper liesin the fact that making explicit use of block sparsity of block sparse signalscan achieve better recovery performance than ignoring the additional structurein the problem as being in the conventional sense.

A sharp recovery condition for block sparse signals by block orthogonal multi-matching pursuit