基于m序列的压缩感知测量矩阵构造

doi:10.3969/j.issn.1001-2400.2015.02.031

J4 ›› 2015, Vol. 42 ›› Issue (2): 186-192.doi: 10.3969/j.issn.1001-2400.2015.02.031

基于m序列的压缩感知测量矩阵构造

党骙^1,2;马林华^1,2;田雨¹;张海威³;茹乐¹; 李小蓓⁴

(1. 空军工程大学航空航天工程学院，陕西西安 710038; 2. 西安电子科技大学综合业务网理论及关键技术国家重点实验室，陕西西安 710071; 3. 宇航动力学国家重点实验室，陕西西安 710043; 4. 空军工程大学信息与导航学院，陕西西安 710077)

收稿日期:2013-12-25 修回日期:2014-04-30 出版日期:2015-04-20 发布日期:2015-04-14
通讯作者: 党骙
作者简介:党骙(1990-)，男，空军工程大学硕士研究生，E-mail：dk_npc1990@163.com．
基金资助:
武器装备预研基金资助项目(9140A25031112JB32001)；西安电子科技大学综合业务网理论及关键技术国家重点实验室开放研究课题资助项目(ISN15-13)

Construction of the compressive sensing measurement matrix based on m sequences

DANG Kui^1,2;MA Linhua^1,2;TIAN Yu¹;ZHANG Haiwei³;RU Le¹;LI Xiaobei⁴

(1. School of Aeronautics and Astronautics Engineering, Air Force Engineering Univ., Xi'an 710038, China; 2. State Key Lab. of Integrated Service Networks, Xidian Univ., Xi'an 710071, China; 3. State Key Laboratory of Astronautic Dynamics, Xi'an 710043, China; 4. Information and Navigation College, Air Force Engineering Univ., Xi'an 710077, China)

Received:2013-12-25 Revised:2014-04-30 Online:2015-04-20 Published:2015-04-14
Contact: DANG Kui

摘要/Abstract

摘要： 利用m序列，提出了一种新的确定性测量矩阵构造方法，称为m序列矩阵．在压缩感知理论中，spark定义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m序列的相关特性，推导了所构造测量矩阵spark值的一个下界．仿真实验表明，该方式构造的测量矩阵的重建概率明显高于同条件下的高斯随机测量矩阵；一旦给定m序列，则能确定出所构造矩阵的每一个元素值，避免了随机矩阵的不确定性;所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，具有实用价值．

关键词: 压缩感知, 测量矩阵, m序列, spark

Abstract: Sequence is an important pseudo random sequence with good correlation. A new method for the deterministic constructing compressive sensing measurement matrix is given through m sequences and called the m Sequence Matrix. In Compressive Sensing, the spark, the smallest number of linearly dependent columns in a matrix, is an important parameter to measure the performance of the measurement matrix. A lower bound of the spark of the proposed measurement matrix is given by considering its correlation. Besides, numbers of simulations show that the proposed matrix has much higher reconstruction probability than the corresponding Gaussian random measurement matrix. The elements of the proposed matrix are deterministic once the m sequence is given, which avoids the uncertainty of random matrices. And the proposed matrix with a perfect cyclic structure can make the hardware realization convenient and easy, which illiminates the storage space waste of random measurement matrices, thus having great potentials in practice.

Key words: compressive sensing, measurement matrix, m sequence, spark

党骙;马林华;田雨;张海威;茹乐; 李小蓓. 基于m序列的压缩感知测量矩阵构造[J]. J4, 2015, 42(2): 186-192.

DANG Kui;MA Linhua;TIAN Yu;ZHANG Haiwei;RU Le;LI Xiaobei. Construction of the compressive sensing measurement matrix based on m sequences [J]. J4, 2015, 42(2): 186-192.

参考文献

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基于m序列的压缩感知测量矩阵构造

Construction of the compressive sensing measurement matrix based on m sequences

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