压缩感知中测量矩阵与重建算法的协同构造

doi:10.3969/j.issn.0372-2112.2013.01.006

电子学报 ›› 2013, Vol. 41 ›› Issue (1): 29-34.DOI: 10.3969/j.issn.0372-2112.2013.01.006

压缩感知中测量矩阵与重建算法的协同构造

李佳, 王强, 沈毅, 李波

哈尔滨工业大学控制科学与工程系,黑龙江哈尔滨 150001

收稿日期:2012-03-27 修回日期:2012-08-10 出版日期:2013-01-25
- 作者简介:
- 李佳 男,1986年出生于河北衡水.2010年、2012年获得哈尔滨工业大学理学学士和工学硕士学位,现为哈尔滨工业大学博士研究生.研究方向为压缩感知、图像处理、无线传感器网络等. E-mail:hitsalijia@163.com 王强 男,1975年出生于辽宁沈阳.哈尔滨工业大学控制科学与工程系教授、博士生导师.主要研究方向为多传感器数据融合,图像处理,智能检测技术等. E-mail:wangqiang@hit.edu.cn沈毅男,1965年出生于吉林扶余.哈尔滨工业大学控制科学与工程系教授、博士生导师.主要研究方向为导航、制导与控制,故障诊断和数字超声成像技术.李波男,1985年出生于黑龙江虎林.2008年、2010年获得哈尔滨工业大学工学学士和工学硕士学位,现为哈尔滨工业大学博士研究生.研究方向为目标跟踪,压缩感知理论与应用.
- 基金资助:
- 国家自然科学基金 (No.61174016,No.61171197)

Collaborative Construction of Measurement Matrix and Reconstruction Algorithm in Compressive Sensing

LI Jia, WANG Qiang, SHEN Yi, LI Bo

Department of Control Science and Engineering, Harbin Institute of Technology, Harbin, Heilongjiang 150001, China

Received:2012-03-27 Revised:2012-08-10 Online:2013-01-25 Published:2013-01-25
- Supported by:
- National Natural Science Foundation of China (No.61174016, No.61171197)

摘要/Abstract

摘要： 本文提出基于感知字典的迭代硬阈值(SDIHT)算法,以此协同构造压缩感知中测量矩阵与重建算法.将成对测量矩阵与感知字典分别用于压缩投影和构造重建算法,重建迭代至残差为零,从而精确恢复原始稀疏信号.本文证明了SDIHT算法精确恢复原始稀疏信号的充分条件.SDIHT算法的优点是重建精度高和计算复杂度低.仿真实验表明,当信号稀疏度或测量次数相同时,相比IHT、OMP和BIHT算法,SDIHT算法重建0-1稀疏信号和二维图像效果更好、算法效率更高.

关键词: 压缩感知, 测量矩阵, 重建算法, 感知字典

Abstract: This paper proposes a novel Sensing Dictionary-based Iterative Hard Thresholding (SDIHT) algorithm,which can collaboratively construct the measurement matrix and the reconstruction algorithm in compressive sensing.Pairs of measurement matrix and sensing dictionary are used for compressive projection and designing reconstruction algorithm respectively.The original sparse signal can be recovered exactly until the residual is reduced to zero as iteration proceeds.A sufficient condition for SDIHT algorithm is given and proved.The benefit of SDIHT is its high reconstruction accuracy and low computational complexity.Computer simulation indicates that when the signal sparsity or the measurement number is fixed,SDHIT algorithm can reconstruct 0-1 sparse signal and two dimensional images with better performance and higher efficiency than IHT,OMP and BIHT algorithm can.

Key words: compressive sensing, measurement matrix, reconstruction algorithm, sensing dictionary

中图分类号:

TN911

李佳, 王强, 沈毅, 等. 压缩感知中测量矩阵与重建算法的协同构造[J]. 电子学报, 2013, 41(1): 29-34.

LI Jia, WANG Qiang, SHEN Yi, et al. Collaborative Construction of Measurement Matrix and Reconstruction Algorithm in Compressive Sensing[J]. Acta Electronica Sinica, 2013, 41(1): 29-34.

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压缩感知中测量矩阵与重建算法的协同构造

Collaborative Construction of Measurement Matrix and Reconstruction Algorithm in Compressive Sensing

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