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

作　　者：CHEN WenGu GE HuanMin 

机构地区：[1]Institute of Applied Physics and Computational Mathematics, Beijing 100088, China [2]Graduate School, China Academy of Engineering Physics, Beijing 100088, China

出　　处：《Science China Mathematics》2017年第7期1325-1340,共16页中国科学：数学（英文版）

基　　金：National Natural Science Foundation of China(Grant Nos. 11271050 and 11371183)

摘　　要：We consider the block orthogonal multi-matching pursuit(BOMMP) algorithm for the recovery of block sparse signals.A sharp condition is obtained for the exact reconstruction of block K-sparse signals via the BOMMP algorithm in the noiseless case,based on the block restricted isometry constant(block-RIC).Moreover,we show that the sharp condition combining with an extra condition on the minimum l_2 norm of nonzero blocks of block K-sparse signals is sufficient to ensure the BOMMP algorithm selects at least one true block index at each iteration until all true block indices are selected in the noisy case.The significance of the results we obtain in this paper lies in the fact that making explicit use of block sparsity of block sparse signals can achieve better recovery performance than ignoring the additional structure in the problem as being in the conventional sense.We consider the block orthogonal multi-matching pursuit（BOMMP） algorithm for the recovery of block sparse signals.A sharp condition is obtained for the exact reconstruction of block K-sparse signals via the BOMMP algorithm in the noiseless case,based on the block restricted isometry constant（block-RIC）.Moreover,we show that the sharp condition combining with an extra condition on the minimum l2 norm of nonzero blocks of block K-sparse signals is sufficient to ensure the BOMMP algorithm selects at least one true block index at each iteration until all true block indices are selected in the noisy case.The significance of the results we obtain in this paper lies in the fact that making explicit use of block sparsity of block sparse signals can achieve better recovery performance than ignoring the additional structure in the problem as being in the conventional sense.

关 键 词：compressed sensing block sparse signal block restricted isometry property block orthogonal multimatching pursuit 

分 类 号：TN911.7[电子电信—通信与信息系统]