欠定系统
块(置换群论)
连贯性(哲学赌博策略)
匹配追踪
算法
相互连贯
限制等距性
数学
计算机科学
压缩传感
信号恢复
匹配(统计)
稀疏逼近
组合数学
统计
作者
Yonina C. Eldar,Patrick Kuppinger,Helmut Bölcskei
标识
DOI:10.1109/tsp.2010.2044837
摘要
We consider compressed sensing of block-sparse signals, i.e., sparse signals that have nonzero coefficients occurring in clusters. An uncertainty relation for block-sparse signals is derived, based on a block-coherence measure, which we introduce. We then show that a block-version of the orthogonal matching pursuit algorithm recovers block $k$-sparse signals in no more than $k$ steps if the block-coherence is sufficiently small. The same condition on block-coherence is shown to guarantee successful recovery through a mixed $\ell_2/\ell_1$-optimization approach. This complements previous recovery results for the block-sparse case which relied on small block-restricted isometry constants. The significance of the results presented in this paper lies in the fact that making explicit use of block-sparsity can provably yield better reconstruction properties than treating the signal as being sparse in the conventional sense, thereby ignoring the additional structure in the problem.
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