基于有限域上向量空间的压缩感知矩阵的构造

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英文篇名：New construction of deterministic compressed sensing matrices based on vector space over finite fields 作者：刘雪梅 ; 范倩瑜 ; 盛受琼 英文作者：LIU Xuemei;FAN Qianyu;SHENG Shouqiong;College of Science, Civil Aviation University of China; 关键词：压缩感知矩阵 ; 有限域 ; 向量空间 ; 相关性 ; 稀疏度 英文关键词：compressed sensing matrix;;finite fields;;vector space;;coherence;;sparsity 中文刊名：HLDZ 英文刊名：Journal of Natural Science of Heilongjiang University 机构：中国民航大学理学院; 出版日期：2019-06-25 出版单位：黑龙江大学自然科学学报 年：2019 期：v.36 基金：国家自然科学基金青年基金资助项目(11701558) 语种：中文; 页：HLDZ201903003 页数：5 CN：03 ISSN：23-1181/N 分类号：18-22

摘要

基于有限域上的向量空间,构造新的压缩感知矩阵,计算其相关参数,将其与DeVore构造的基于有限域上多项式的压缩感知矩阵进行对比,证明当满足一定条件时,基于有限域上向量空间构造的压缩感知矩阵的信号恢复性能优于DeVore所构造的矩阵。数值仿真说明,构造的矩阵在恢复信号能力方面优于高斯随机矩阵和DeVore构造的矩阵。
        A compressed sensing matrix based on vector spaces over finite fields is constructed, and the coherence of the matrix is computed. A comparison is made with the matrix constructed by DeVore based on polynomials over finite fields. The character of compressing and recovering signals is better than that of the matrix constructed by DeVore when the matrix is satisfied some conditions. The favorable performance of the matrix is demonstrated by numerical simulations.

引文

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