电子学报 ›› 2016, Vol. 44 ›› Issue (10): 2289-2293.DOI: 10.3969/j.issn.0372-2112.2016.10.001

• 学术论文 • 上一篇    下一篇

基于稀疏补分析模型的近似最优子空间追踪

张宗念1, 李金徽2, 黄仁泰3, 闫敬文4   

  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;
    4. 汕头大学电子工程系, 广东汕头 515063
  • 收稿日期:2013-01-18 修回日期:2016-03-04 出版日期:2016-10-25 发布日期:2016-10-25
  • 作者简介:张宗念,男,1963年6月生于河北深州,副教授.2000年获华南理工大学博士学位.主要研究方向为压缩感知理论与应用、图像处理.E-mail:zzn99@sohu.com;李金徽,男,1980年4月生于辽宁沈阳,工程师.2004年获重庆工商大学学士学位.主要研究方向为分布式计算机网络.E-mail:li@dgut.edu.cn;黄仁泰,男,1964年12月生于广东东莞,副教授.2006年获华中科技大学硕士学位.主要研究方向为分布式计算机网络.E-mail:huangrt@dgut.edu.cn;闫敬文,男,1964年7月生于吉林磐石,博士,教授,博士生导师.1997获中国科学院长春光机所博士学位.主要研究方向为图像处理和分析、遥感图像处理等.E-mail:jwyan@stu.edu.cn
  • 基金资助:

    国家自然科学基金(No.40971206);广东省自然科学基金(No.2015A030313654)

Approximately Optimal Subspace Pursuit Based on Cosparse Analysis Model

ZHANG Zong-nian1, LI Jin-hui2, HUANG Ren-tai3, YAN Jing-wen4   

  1. 1. Department of Electronic Engineering, Dongguan University of Technology, Dongguan, Guangdong 523808, China;
    2. Network Center, Dongguan University of Technology, Dongguan, Guangdong 523808, China;
    3. Department of Computer Science, Dongguan University of Technology, Dongguan, Guangdong 523808, China;
    4. Department of Electronics Engineering, Shantou University, Shantou, Guangdong 515063, China
  • Received:2013-01-18 Revised:2016-03-04 Online:2016-10-25 Published:2016-10-25

摘要:

为了从含噪声的测量矢量中重构原始信号,研究了稀疏补分析模型下近似最优子空间追踪信号重构算法.针对直接采用稀疏综合模型下子空间追踪过程非最速梯度下降和信号重构概率不高的缺点,根据稀疏补分析模型下不同类型分析字典的结构特点来设计近似目标优化函数;改进了迭代追踪过程;优化了稀疏补取值方法;提出并实现了基于稀疏补分析模型的近似最优分析子空间追踪算法.仿真实验证明,当稀疏补运算符分别采用随机紧支框架和二维全变分矩阵时,算法的完全重构信号概率均明显高于ASP、AHTP、AIHT、AL1、GAP算法的完全重构信号概率;对于含高斯噪声的输入信号,算法的重构信号综合平均PSNR比相应的ASP、AHTP、AIHT算法分别提高了0.8dB、1.38dB、3.13 dB,但比GAP和AL1算法降低了0.32 dB和0.6dB.算法的完全重构概率与综合重构性能有了明显提高,收敛充分条件得到进一步简化.

关键词: 稀疏补分析模型, 近似最优, 子空间, 追踪

Abstract:

An approximately optimal subspace pursuit algorithm under cosparse analysis model was studied to reconstruct the original signal from the noisy measurement vectors.To overcome the drawbacks of the non steepest gradient during the pursuit process and the low successful reconstruction probability for sparse synthesis model,an approximately optimal subspace pursuit algorithm based on cosparse analysis model was presented and realized.The approximately optimal optimization object function for the algorithm was designed according to the structure of the different analysis dictionaries,the iterative pursuit process of the algorithm was revised,and the methods of selecting cosparsity was optimized.The simulation experiments show that the complete reconstruction probability of the new algorithm is evidently larger than that of the algorithm for ASP,AHTP,AIHT,AL1 and GAP when the cosparse operator is a random compact frame or a two dimension total variant matrix.The comprehensive average PSNR of the output signal for the new algorithm is larger than that of the algorithm of ASP,AHTP,and AIHT for 0.8dB,1.38dB and 3.13 dB respectively and is less than that of the algorithm of GAP and AL1 for 0.32 dB and 0.6dB when the input signal is with Gaussion noise.The complete reconstruction probability of the new algorithm was greatly improved by adopting the above measures,and the convergence condition for the new algorithm was simplified.

Key words: cosparse analysis model, approximately optimal, subspace, pursuit

中图分类号: