Deterministic Construction of Compressed Sensing Matrices via Vector Spaces Over Finite Fields
Deterministic Construction of Compressed Sensing Matrices via Vector Spaces Over Finite Fields
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有限域上向量空间压缩感知矩阵的确定性构造
DOI：
10.1109/access.2020.3034912
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发表时间：
2020-01-01
期刊：
影响因子：
3.9
通讯作者：
Jia, Lihua
中科院分区：
文献类型：
--
作者：
Liu, Xuemei;Jia, Lihua
压缩感知（CS）是在信号稀疏或可压缩的情况下提出的一种新的信号处理理论。压缩感知的核心问题之一是感知矩阵的构造。本文利用有限域上的向量空间给出了一种新的确定性构造，在一定条件下，它比Devore利用有限域上的多项式构造的方法优越上级.此外，我们使用该算法进行数值模拟实验的传感矩阵。仿真结果还表明，信号恢复性能更好地使用构造的矩阵相比，几个国家的最先进的传感矩阵，如德沃尔矩阵和随机高斯矩阵。
Compressed Sensing (CS) is a new signal processing theory under the condition that the signal is sparse or compressible. One of the central problems in compressed sensing is the construction of sensing matrices. In this paper, we provide a new deterministic construction via vector spaces over finite fields, which is superior to Devore's construction using polynomials over finite fields under some conditions. Moreover, we use the algorithm to perform numerical simulation experiments on sensing matrices. Simulation results also demonstrate that signal recovery performance performs better using the constructed matrices as compared with several state-of-the-art sensing matrices, such as DeVore's matrix and random Gaussian matrix.