关于rip兼容矩阵等价类的存在性

P. Sasmal, C. S. Sastry, P. Jampana
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引用次数: 1

摘要

在压缩感知(CS)中,满足受限等距特性(RIP)的矩阵起着重要的作用。但众所周知,矩阵Φ及其“加权矩阵”GΦ (G为非奇异矩阵)的RIP特性在RIP常数方面变化很大。在本文中,我们考虑相反的问题:给定一个矩阵Φ,我们能否找到一个非奇异矩阵G,使得GΦ符合RIP?我们证明了在某些条件下,存在一类非奇异矩阵(G),使得GΦ具有较好的RIP常数的RIP-柔化。我们还提供了唯一表示性质(URP)和限制等距性质(RIP)之间的关系,以及RIP与线性方程组的最稀疏解之间的直接关系。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On the existence of equivalence class of RIP-compliant matrices
In Compressed Sensing (CS), the matrices that satisfy the Restricted Isometry Property (RIP) play an important role. But it is known that the RIP properties of a matrix Φ and its `weighted matrix' GΦ (G being a non-singular matrix) vary drastically in terms of RIP constant. In this paper, we consider the opposite question: Given a matrix Φ, can we find a non-singular matrix G such that GΦ has compliance with RIP? We show that, under some conditions, a class of non-singular matrices (G) exists such that GΦ has RIP-compliance with better RIP constant. We also provide a relationship between the Unique Representation Property (URP) and Restricted Isometry Property (RIP), and a direct relationship between RIP and sparsest solution of a linear system of equations.
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