基于Rademacher序列的压缩感知测量矩阵构造及其spark估计  

Construction of Compressed Sensing Matrixs Based on Rademacher Sequences and the Estimation of Spark

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作  者:宋儒瑛[1] 程瑞芳 SONG Ru-ying, CHENG Rui-fang(Department of Mathematics, Taiyuan Normal University, Shanxi 030619, Chin)

机构地区:[1]太原师范学院数学系,山西晋中030619

出  处:《中央民族大学学报(自然科学版)》2018年第1期15-20,共6页Journal of Minzu University of China(Natural Sciences Edition)

基  金:山西省高等学校科技项目(No.20121109)

摘  要:构造确定性测量矩阵对压缩感知理论的推广与应用具有重要的意义,本文尝试利用Rademacher序列构造测量矩阵.在压缩感知理论中,spark为测量矩阵的最小线性相关列数,是一个重要的性能参数,利用Rademacher序列的相关特性,推导出Rademacher序列构造测量矩阵spark的一个下界.从理论分析和仿真实验表明,相同条件spark界下,Rademacher序列构造的测量矩阵重构性能优于基于m序列构造的测量矩阵;并且Rademacher序列构造矩阵具有循环特性,易于硬件实现,克服了随机矩阵浪费存储资源的缺陷,有利于压缩感知理论的实用化.To construct deterministic measurement matrix has important significance to the popularization and application of compressed sensing theory( cs). Based on the structural characteristics of structure measurement matrix Rademacher sequence. In CS,the minimum number of columns for the spark definition of linear correlation measurement matrix is one of the most important performance parameters. By using the relevant characteristics of the Rademacher sequence,the lower bound of the measurement matrix spark value is conducted. Theoretical analysis and simulation results show that the way to construct the measurement matrix under the same condition is better than the measurement matrix of the m sequence reconstruction performance; the constructed matrix has cycle characteristics,overcomes the defects of random matrix to waste storage resources,it is easy for hardware implementation and has practical value.

关 键 词:压缩感知 测量矩阵 Rademacher序列 SPARK 

分 类 号:O174[理学—数学]

 

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