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一种变步长稀疏度自适应子空间追踪算法

田金鹏 刘小娟 郑国莘

田金鹏, 刘小娟, 郑国莘. 一种变步长稀疏度自适应子空间追踪算法. 自动化学报, 2016, 42(10): 1512-1519. doi: 10.16383/j.aas.2016.c150801
引用本文: 田金鹏, 刘小娟, 郑国莘. 一种变步长稀疏度自适应子空间追踪算法. 自动化学报, 2016, 42(10): 1512-1519. doi: 10.16383/j.aas.2016.c150801
TIAN Jin-Peng, LIU Xiao-Juan, ZHENG Guo-Xin. A Variable Step Size Sparsity Adaptive Subspace Pursuit Algorithm. ACTA AUTOMATICA SINICA, 2016, 42(10): 1512-1519. doi: 10.16383/j.aas.2016.c150801
Citation: TIAN Jin-Peng, LIU Xiao-Juan, ZHENG Guo-Xin. A Variable Step Size Sparsity Adaptive Subspace Pursuit Algorithm. ACTA AUTOMATICA SINICA, 2016, 42(10): 1512-1519. doi: 10.16383/j.aas.2016.c150801

一种变步长稀疏度自适应子空间追踪算法

doi: 10.16383/j.aas.2016.c150801
基金项目: 

国家自然科学基金 61571282

上海大学创新基金 sdcx2012041

国家自然科学基金 61132003

详细信息
    作者简介:

    刘小娟  上海大学通信与信息工程学院硕士研究生.主要研究方向为图像处理, 压缩感知.E-mail:xjliumail@163.com

    郑国莘  上海大学通信与信息工程学院教授.主要研究方向为信号处理, 限定空间无线电通信.E-mail: gxzheng@staff.shu.edu.cn

    通讯作者:

    田金鹏  博士, 上海大学通信与信息工程学院讲师.主要研究方向为信号处理, 模式识别.本文通信作者.E-mail:adaline@163.com

A Variable Step Size Sparsity Adaptive Subspace Pursuit Algorithm

Funds: 

National Natural Science Foundation of China 61571282

Innovation Foundation of Shanghai University sdcx2012041

National Natural Science Foundation of China 61132003

More Information
    Author Bio:

     Master student at the School of Communication and Information Engineering, Shanghai University. Her research interest covers image processing and compressed sensing. E-mail:

     Professor at the School of Communication and Information Engineering, Shanghai University. His research interest covers signal processing and confined space radio communications.E-mail:

    Corresponding author: TIAN Jin-Peng  Ph. D., lecturer at the School of Communication and Information Engineering, Shanghai University. His research interest covers signal processing and pattern recognition. Corresponding author of this paper. E-mail:adaline@163.com
  • 摘要: 针对压缩感知(Compressive sensing,CS)中未知稀疏度信号的重建问题,本文提出一种变步长稀疏度自适应子空间追踪算法.首先,采用一种匹配测试的方法确定固定步长,然后以该固定步长与变步长方式相结合,通过不同支撑集原子个数下的重建残差变化确定信号稀疏度,算法采用子空间追踪方法确定相应支撑集原子,并完成原始信号准确重建.实验结果表明,与同类算法相比,该算法可以更准确重建原始信号,且信号稀疏度值较高时,运算量低于同类算法.
  • 图  1  支撑集原子个数与残差对应关系示意图

    Fig.  1  The relationship of residual error and the number of support set atom

    图  2  不同信噪比下稀疏度K估计误差

    Fig.  2  Estimating error of signal sparsity under different noise level

    图  3  不同算法信号准确重建率

    Fig.  3  Exact recovery ratio of recovery algorithms by different reconstruction algorithms

    图  4  噪声环境下的重建精度(M=80, N=256, K=20)

    Fig.  4  Reconstruction accuracy in noise environment (M=80, N=256, K=20)

    图  5  算法运行时间对比(M=1 024, N=2 048)

    Fig.  5  Running time by different reconstruction algorithms (M=1 024, N=2 048)

    图  6  样率0.5时, Lena原图像及各算法重建图像

    Fig.  6  Original image and reconstructed image of different algorithms for Lena when sampling rate is 0.5

    表  1  各算法的重建质量及运行时间对比

    Table  1  Comparison of the qualities of images reconstructed and running time by different algorithms

    重建算法 M=0.3 × N M=0.4 × N M=0.5 × N
    PSNR(dB) 运算时间 PSNR(dB) 运算时间 PSNR(dB) 运算时间
    OMP 23.07 0.69 27.48 1.06 30.96 1.24
    ROMP 24.72 0.32 27.89 0.68 31.52 1.05
    SP 23.15 0.76 26.51 0.96 30.84 1.32
    SAMP1 24.80 11.57 27.79 18.25 30.96 26.96
    SAMP5 24.14 2.71 27.49 4.55 30.85 7.46
    SAMP10 23.65 1.55 27.42 2.84 30.72 3.91
    VssSASP 25.26 3.21 28.13 4.92 31.63 7.63
    下载: 导出CSV
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出版历程
  • 收稿日期:  2015-11-26
  • 录用日期:  2016-04-18
  • 刊出日期:  2016-10-20

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