A sharp recovery condition for block sparse signals by block orthogonal multi-matching pursuit
A sharp recovery condition for block sparse signals by block orthogonal multi-matching pursuit
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DOI：
10.1007/s11425-016-0448-7
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发表时间：
2016-07
期刊：
影响因子：
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通讯作者：
Wengu Chen;Huanmin Ge
中科院分区：
文献类型：
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作者：
Wengu Chen;Huanmin Ge
我们考虑了块正交多匹配追踪(BOMMP)算法来恢复块稀疏信号。基于块受限等距常数(BLOCK-RIC)，给出了在无噪声的情况下，用BOMMP算法精确重构块K-稀疏信号的精确条件。此外，我们证明了锐化条件和关于非零块K-稀疏信号块的最小ℓ2范数的额外条件足以确保BOMMP算法在每次迭代中至少选择一个真块索引，直到在噪声情况下选择所有真块索引。本文所得到的结果的意义在于，显式地利用块稀疏信号的块稀疏性可以获得比传统意义上忽略问题中的附加结构更好的恢复性能。
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 blockK-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 ℓ2norm of nonzero blocks of blockK-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.