The restricted isometry property for time–frequency structured random matrices
The restricted isometry property for time–frequency structured random matrices
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DOI：
10.1007/s00440-012-0441-4
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发表时间：
2010-10
影响因子：
2
通讯作者：
H. Rauhut;J. Romberg;J. Tropp
中科院分区：
文献类型：
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作者：
H. Rauhut;J. Romberg;J. Tropp
本文建立了n维随机窗函数的n ~ 2个时频位移产生的Gabor系统的约束等距性。当n × n2 Gabor综合矩阵的第s阶限制等距常数≤cn2/3/log 2n时，它是很小的。这一界限提供了一个定性的改进，以前的估计，实现只有二次缩放的sparsityswith吨。证明依赖于二阶混沌的期望上确界的估计。
This paper establishes the restricted isometry property for a Gabor system generated byn2time–frequency shifts of a random window function inndimensions. Thesth order restricted isometry constant of the associatedn×n2Gabor synthesis matrix is small provided thats≤cn2/3/ log2n. This bound provides a qualitative improvement over previous estimates, which achieve only quadratic scaling of the sparsityswith respect ton. The proof depends on an estimate for the expected supremum of a second-order chaos.