Deterministic Sensing Matrices Arising from Near Orthogonal Systems
Deterministic Sensing Matrices Arising from Near Orthogonal Systems
复制标题
近正交系统产生的确定性传感矩阵
DOI：
10.1109/tit.2014.2303973
复制
发表时间：
2014-04-01
影响因子：
2.5
通讯作者：
Ge, Gennian
中科院分区：
文献类型：
--
作者：
Li, Shuxing;Ge, Gennian
压缩感知是一种新颖的采样理论，它为数据采集提供了一种全新的方法。它声称，稀疏或可压缩的信号可以重建从更少的测量比传统的方法。压缩感知中的一个核心问题是感知矩阵的构造。虽然随机感知矩阵已经被深入研究，但只有少数确定性结构是已知的。其中，大多数构造是基于相干性的，这实质上生成了低相干性的矩阵。在本文中，我们引入了近正交系的概念来描述低相干矩阵，这是许多不同应用的核心。这些近正交系统的构造导致传感矩阵的确定性构造。我们得到了一系列m × n的二元感知矩阵，其稀疏度k = Theta（m（1/2））或k = O（（m/log m）（（1/2）））.特别是，我们的一些构造是基于连贯性的最佳可能的确定性构造。我们进行了大量的数值实验表明，我们的矩阵产生的近正交系统优于几个典型的已知的传感矩阵。
Compressed sensing is a novel sampling theory, which provides a fundamentally new approach to data acquisition. It asserts that a sparse or compressible signal can be reconstructed from much fewer measurements than traditional methods. A central problem in compressed sensing is the construction of the sensing matrix. While random sensing matrices have been studied intensively, only a few deterministic constructions are known. Among them, most constructions are based on coherence, which essentially generates matrices with low coherence. In this paper, we introduce the concept of near orthogonal systems to characterize the matrices with low coherence, which lie in the heart of many different applications. The constructions of these near orthogonal systems lead to deterministic constructions of sensing matrices. We obtain a series of m x n binary sensing matrices with sparsity level k = Theta(m((1/2))) or k = O((m/log m)((1/2))). In particular, some of our constructions are the best possible deterministic ones based on coherence. We conduct a lot of numerical experiments to show that our matrices arising from near orthogonal systems outperform several typical known sensing matrices.