Collaborative Construction of Measurement Matrix and Reconstruction Algorithm in Compressive Sensing

LI Jia; WANG Qiang; SHEN Yi; LI Bo

doi:10.3969/j.issn.0372-2112.2013.01.006

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Collaborative Construction of Measurement Matrix and Reconstruction Algorithm in Compressive Sensing

更新时间：2025-07-16

- Collaborative Construction of Measurement Matrix and Reconstruction Algorithm in Compressive Sensing
- Acta Electronica Sinica Vol. 41, Issue 1, Pages: 29-34(2013)
- 作者机构：
  
  哈尔滨工业大学控制科学与工程系,黑龙江,哈尔滨,150001
- 作者简介：
- 基金信息：
  
  National Natural Science Foundation of China (No.61174016, No.61171197)
- DOI：10.3969/j.issn.0372-2112.2013.01.006
  CLC： TN911
- Published：2013
- 稿件说明：
移动端阅览
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.
DOI：

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. DOI： 10.3969/j.issn.0372-2112.2013.01.006.

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.

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.

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