基于向量空间和奇异线性空间的压缩感知矩阵的构造

发布时间：2018-04-19 10:52

本文选题：有限域 + 压缩感知矩阵　；参考：《中国民航大学》2015年硕士论文

【摘要】：随着信息学领域的不断发展和日益完善,压缩感知作为一个全新的理论被人们所认知,它突破了传统的奈奎斯特采样定理对于信号的处理方法,不仅有效地降低了采样的速率、保证信号的准确恢复,而且节省了存储空间、极大地避免了资源浪费,因而在实际应用中获得了广泛的好评与肯定。众所周知压缩感知矩阵的构造是研究压缩感知理论的重要问题之一。本篇论文运用有限域上典型群的几何学作为理论工具结合压缩感知矩阵的相关内容,进行了以下的工作。1.基于有限域上的向量空间构造确定性压缩感知矩阵给定整数是一个二元矩阵,其行用上的维子空间标定;列用上的m维子空间标定,其中的(i,j)元为1当且仅当第i个1m维子空间包含于第j个m维子空间;否则为0。运用向量空间的计数公式求出行数、列数、信号稀疏度k与矩阵的列重,进而通过计算与仿真将其与已有的矩阵进行比较。2.基于有限域上奇异线性空间构造确定性压缩感知矩阵利用奇异线性空间,构造了两种确定性压缩感知矩阵,计算了相应参数,进而通过计算与仿真将其与已有的矩阵进行比较。
[Abstract]:With the continuous development and improvement of informatics, compression perception is recognized as a new theory. It breaks through the traditional Nyquist sampling theorem for signal processing, and not only effectively reduces the rate of sampling.It can ensure the accurate recovery of the signal, save the storage space and avoid the waste of resources greatly, so it has been widely praised and affirmed in the practical application.It is well known that the construction of compressed perception matrix is one of the important problems in the theory of compressed perception.In this paper, the geometry of a typical group over a finite field is used as a theoretical tool to combine the related contents of compressed perception matrix, and the following work is done.Construction of deterministic Compression perception Matrix based on Vector Space on finite Field given integer is a binary matrix, its row is calibrated in dimensional subspace, column is calibrated in m-dimensional subspace,The element is 1 if and only if the first 1m dimensional subspace is contained in the j m-dimensional subspace; otherwise, 0.The number of trip, the number of columns, the signal sparsity k and the column weight of the matrix are calculated by using the counting formula of vector space, and then compared with the existing matrix by calculation and simulation.Construction of deterministic contractive perceptual matrix based on singular linear space over finite fields two deterministic contractive perceptual matrices are constructed using singular linear spaces and corresponding parameters are calculated and compared with existing matrices by calculation and simulation.
【学位授予单位】：中国民航大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O151.21

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