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基于二進(jìn)制序列族的壓縮感知測量矩陣構(gòu)造

蘆存博 肖嵩 權(quán)磊

蘆存博, 肖嵩, 權(quán)磊. 基于二進(jìn)制序列族的壓縮感知測量矩陣構(gòu)造[J]. 電子與信息學(xué)報, 2016, 38(7): 1682-1688. doi: 10.11999/JEIT151076
引用本文: 蘆存博, 肖嵩, 權(quán)磊. 基于二進(jìn)制序列族的壓縮感知測量矩陣構(gòu)造[J]. 電子與信息學(xué)報, 2016, 38(7): 1682-1688. doi: 10.11999/JEIT151076
LU Cunbo, XIAO Song, QUAN Lei. Construction of Compressed Sensing Measurement Matrix Based on Binary Sequence Family[J]. Journal of Electronics & Information Technology, 2016, 38(7): 1682-1688. doi: 10.11999/JEIT151076
Citation: LU Cunbo, XIAO Song, QUAN Lei. Construction of Compressed Sensing Measurement Matrix Based on Binary Sequence Family[J]. Journal of Electronics & Information Technology, 2016, 38(7): 1682-1688. doi: 10.11999/JEIT151076

基于二進(jìn)制序列族的壓縮感知測量矩陣構(gòu)造

doi: 10.11999/JEIT151076
基金項(xiàng)目: 

國家自然科學(xué)基金(61372069),高等學(xué)校學(xué)科創(chuàng)新引智計劃(111計劃)(B08038)

Construction of Compressed Sensing Measurement Matrix Based on Binary Sequence Family

Funds: 

The National Natural Science Foundation of China (61372069), The Programme of Introducing Talents of Discipline to Universities (111 Project) (B08038)

  • 摘要: 構(gòu)造確定性測量矩陣對壓縮感知理論的推廣與應(yīng)用具有重要的意義。該文源于代數(shù)編碼理論,提出一種基于二進(jìn)制序列族的確定性測量矩陣構(gòu)造算法。相關(guān)性是描述矩陣性質(zhì)的重要準(zhǔn)則,減小相關(guān)性可使重建性能提高。該文推導(dǎo)出所構(gòu)造測量矩陣的相關(guān)性小于同條件下的高斯隨機(jī)矩陣和伯努利隨機(jī)矩陣。理論分析和仿真實(shí)驗(yàn)表明,該方式構(gòu)造的測量矩陣的重建性能優(yōu)于同條件下的高斯隨機(jī)矩陣和伯努利隨機(jī)矩陣;所構(gòu)造矩陣可由線性反饋移位寄存器結(jié)構(gòu)實(shí)現(xiàn),易于硬件實(shí)現(xiàn),有利于壓縮感知理論的實(shí)用化。
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出版歷程
  • 收稿日期:  2015-09-21
  • 修回日期:  2016-01-20
  • 刊出日期:  2016-07-19

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