Generalized Restricted Isometry Property for alpha-stable random projections
Generalized Restricted Isometry Property for alpha-stable random projections
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DOI：
10.1109/icassp.2011.5947148
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发表时间：
2011-05
期刊：
影响因子：
--
通讯作者：
D. Otero;G. Arce
中科院分区：
文献类型：
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作者：
D. Otero;G. Arce
限制等距性（RIP）是压缩感知中的一个重要概念。众所周知，只要随机矩阵的元素具有有限的二阶矩，许多随机矩阵就以很高的概率满足RIP。最近在压缩感知方面的工作表明，使用柯西随机投影进行降维和信号重构是可能的。这表明，当一组数据点从高维空间投影到具有不具有有限方差的随机矩阵的低维空间时，l1距离保持不变。本文推广了这一概念，证明了保持lα距离的α-稳定投影也满足广义RIP性质，从而从α-稳定投影重建是可行的。
The Restricted Isometry Property (RIP) is an important concept in compressed sensing. It is well known that many random matrices satisfy the RIP with high probability, whenever the entries of the random matrix have finite second order moment. Recent work in compressed sensing has shown that it is possible to do dimensionality reduction and signal reconstruction using Cauchy random projections. This suggests that the l1 distance is preserved when one projects a set of data points from a high-dimensional space, to one of lower dimension with a random matrix which does not have finite variance. This paper generalizes this concept where it is shown that α-stable projections, which preserve the lα distance, also satisfy a generalized RIP property and consequently reconstruction from α-stable projections is feasible.