计算机应用 ›› 2013, Vol. 33 ›› Issue (08): 2387-2389.

• 典型应用 • 上一篇    下一篇

稀疏补分析模型下迭代硬阈值正交投影

张宗念1,李金徽2,黄仁泰3,闫敬文3   

  1. 1. 东莞理工学院 电子工程学院，广东 东莞 523808;
    2. 东莞理工学院 网络中心，广东 东莞 523808；
    3. 东莞理工学院 计算机学院，广东 东莞 523808;
  • 收稿日期:2013-02-04 修回日期:2013-04-09 发布日期:2013-09-11 出版日期:2013-08-01
  • 通讯作者: 张宗念
  • 作者简介:张宗念(1963-),男,河北深州人,副教授,博士,主要研究方向:压缩感、图像分析与处理;
    李金徽(1980-),男,辽宁沈阳人,工程师，主要研究方向：分布式计算机网络;
    黄仁泰(1964-),男,广东东莞人,副教授，主要研究方向：嵌入式系统设计;
    闫敬文(1964-),男,吉林磐石人,教授,博士生导师,主要研究方向:图像处理和分析、遥感图像处理。
  • 基金资助:
    国家自然科学基金资助项目;东莞市科技计划项目

Iterative Hard Thresholding Orthogonal Projection under Cosparsity Analysis Model

ZHANG Zongnian1,LI Jinhui2,HUANG Rentai3,YAN Jingwen4   

  1. 1. School of Electronic Engineering, Dongguan University of Technology, Dongguan Guangdong 523808, China
    2. Network Center, Dongguan University of Technology, Dongguan Guangdong 523808, China
    3. School of Computer Science, Dongguan University of Technology, Dongguan Guangdong 523808, China
    4. Department of Electronic Engineering, Shantou University, Shantou Guangdong 515063, China
  • Received:2013-02-04 Revised:2013-04-09 Online:2013-09-11 Published:2013-08-01
  • Contact: ZHANG Zongnian

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摘要： 为了从含噪声的测量矢量中重构信号，研究了稀疏补分析模型理论及其迭代硬阈值正交投影算法。通过采用稀疏补正交投影修改了稀疏补分析模型下迭代硬阈值算法的迭代追踪过程；分析了迭代步长和稀疏补取值大小对算法收敛速度和重构性能的影响，找出了选取最优迭代步长和最佳稀疏补取值方法；提出并实现了稀疏补分析模型下迭代硬阈值正交投影算法，给出了算法收敛的充分条件和重构信号误差范围。仿真实验结果表明，算法的平均运算时间仅仅为AIHT、AL1和GAP算法的19%、11%和10%；算法重构信号的综合平均峰值信噪比(PSNR)比AIHT算法提高了0.89dB，但比AIHT、AL1算法稍逊色。算法在满足给定条件下能够以高概率实现含噪信号重构，重构信号的综合平均PSNR与典型算相比没有明显下降，但运算时间大为缩短，收敛速度更快。

关键词: 稀疏补分析模型, 迭代, 硬阈值, 正交投影, 信号重构, 压缩感知

Abstract: To reconstruct the original signal from a set of linear measurements with noise, the cosparsity analytical model theory was analyzed and the hard thresholding orthogonal projection algorithm under the cosparsity analysis model was proposed. The cosparsity orthogonal projection strategy was used to improve the iterative process for the proposed algorithm, and the methods for selecting iterative step size and the length of cosparsity were given. The sufficient condition of convergence for the algorithm and the reconstructed signal error range between the reconstructed signal and the original one were provided. The experiments show that the CPU running time of the algorithm is only equal to 19%, 11% and 10% of AIHT, AL1 and GAP algorithms, and the average Peak Signal-to-Noise Ratio (PSNR) of reconstructed signal improves 0.89dB than that of AIHT but degrades a little bit than that of AL1 and GAP. It is concluded that the proposed algorithm can reconstruct the signal with Gaussion noise in high probability with very short running time or faster convergence speed than that of the current typical algorithm when some conditions are satisfied.

Key words: cosparsity analysis model, iteration, hard thresholding, orthogonal projection, signal reconstruction, compressed sensing

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