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基于自适应LASSO先验的稀疏贝叶斯学习算法

白宗龙 师黎明 孙金玮

白宗龙, 师黎明, 孙金玮. 基于自适应LASSO先验的稀疏贝叶斯学习算法. 自动化学报, 2021, 45(x): 1−16 doi: 10.16383/j.aas.c210022
引用本文: 白宗龙, 师黎明, 孙金玮. 基于自适应LASSO先验的稀疏贝叶斯学习算法. 自动化学报, 2021, 45(x): 1−16 doi: 10.16383/j.aas.c210022
Bai Zong-Long, Shi Li-Ming, Sun Jin-Wei. Sparse bayesian learning using adaptive LASSO priors. Acta Automatica Sinica, 2021, 45(x): 1−16 doi: 10.16383/j.aas.c210022
Citation: Bai Zong-Long, Shi Li-Ming, Sun Jin-Wei. Sparse bayesian learning using adaptive LASSO priors. Acta Automatica Sinica, 2021, 45(x): 1−16 doi: 10.16383/j.aas.c210022

基于自适应LASSO先验的稀疏贝叶斯学习算法

doi: 10.16383/j.aas.c210022
详细信息
    作者简介:

    白宗龙:哈尔滨工业大学仪器科学与工程学院博士研究生, 主要研究方向包括稀疏信号恢复, 麦克风阵列信号处理. Email: baizongyao@163.com

    师黎明:奥尔堡大学建筑设计与媒体艺术系博士后. 主要研究方向为稀疏信号处理, 语音信号处理. Email: ls@create.aau.dk

    孙金玮:哈尔滨工业大学仪器科学与工程学院教授. 主要研究方向包括生物信号处理, 主动噪声控制. 本文通讯作者. Emial: jwsun@hit.edu.cn

Sparse Bayesian Learning Using Adaptive LASSO priors

More Information
    Author Bio:

    BAI Zong-Long Ph.D student at the school of instrument science and engineering, Harbin Institute of Technology. His research interest covers sparse signal recovery technology and microphone array signal processing

    SHI Li-Ming postdoctoral scholar at the CREATE, Aalborg University. His research interest covers sparse signal recovery technology and speech signal processing

    SUN Jin-Wei Professor at the school of instrument science and engineering, Harbin Institute of Technology. His research interest covers biomedical signal processing and active noise control

  • 摘要: 为了提高稀疏信号恢复的准确性, 本文开展了基于自适应套索算子(Least absolute shrinkage and selection operator, LASSO)先验的稀疏贝叶斯学习(Sparse bayesian learning, SBL)算法研究. 第一, 在稀疏贝叶斯模型构建阶段, 构造了一种新的多层贝叶斯框架, 赋予信号中元素独立的LASSO先验. 该先验比现有稀疏先验更有效的鼓励稀疏并且该模型中所有参数更新存在闭合解. 然后在该多层贝叶斯框架的基础上提出了一种基于自适应LASSO先验的SBL算法. 第二, 为降低提出的算法的计算复杂度, 在贝叶斯推断阶段利用空间轮换变元方法对提出的算法进行改进, 避免了矩阵求逆运算, 使参数更新快速高效, 从而提出了一种基于自适应LASSO先验的快速SBL算法. 本文提出的算法的稀疏恢复性能通过实验进行了验证, 分别针对不同大小测量矩阵的稀疏信号恢复以及单快拍波达方向(Direction of arrival, DOA)估计开展了实验. 实验结果表明: 本文提出基于自适应LASSO先验的SBL算法比现有算法具有更高的稀疏恢复准确度; 本文提出的快速算法的准确度略低于提出的基于自适应LASSO先验的SBL算法, 但计算复杂度明显降低.
  • 图  1  基于自适应LASSO先验的SBL框架的因子图

    Fig.  1  The factor graph of the proposed SBL framework using adaptive LASSO priors.

    图  2  四种算法的稀疏先验代价函数二维等高线图

    Fig.  2  Two dimensional contour plots of cost functions of different sparse priors.

    图  3  本算法在不同参数下稀疏先验代价函数二维等高线图

    Fig.  3  Two dimensional contour plots of cost functions of the proposed sparse priors versus hyperparameters.

    图  4  一维信号稀疏恢复图

    Fig.  4  Results for one-dimensional signal recovery.

    图  5  实值模型下各算法稀疏恢复准确度与测量数的关系.

    Fig.  5  RMSE of different algorithms with the real-value signal model versus length of measurements.

    图  6  复值模型下各算法稀疏恢复准确度与测量数的关系.

    Fig.  6  RMSE of different algorithms with the complex-value signal model versus length of measurements.

    图  7  高维实值信号模型下各算法稀疏恢复准确度与测量数的关系.

    Fig.  7  RMSE of different algorithms with the high-dimensional real-value signal model versus length of measurements.

    图  8  高维复值信号模型下各算法稀疏恢复准确度与测量数的关系.

    Fig.  8  RMSE of different algorithms with the high-dimensional complex-value signal model versus length of measurements.

    图  9  实值模型下各算法稀疏恢复准确度与稀疏度的关系.

    Fig.  9  RMSE of different algorithms with the real-value signal model versus number of non-zero elements.

    图  10  复值模型下各算法稀疏恢复准确度与稀疏度的关系.

    Fig.  10  RMSE of different algorithms with the complex-value signal model versus number of non-zero elements.

    图  11  高维实值信号模型下各算法稀疏恢复准确度与稀疏度的关系.

    Fig.  11  RMSE of different algorithms with the high-dimensional real-value signal model versus number of non-zero elements.

    图  12  高维复值信号模型下各算法稀疏恢复准确度与稀疏度的关系.

    Fig.  12  RMSE of different algorithms with the high-dimensional complex-value signal model versus number of non-zero elements.

    图  13  实值模型下各算法稀疏恢复准确度与信噪比的关系.

    Fig.  13  RMSE of different algorithms versus SNR with the real-value signal model.

    图  14  复值模型下各算法稀疏恢复准确度与信噪比的关系.

    Fig.  14  RMSE of different algorithms versus SNR with the complex-value signal model.

    图  15  高维实值信号模型下各算法稀疏恢复准确度与信噪比的关系.

    Fig.  15  RMSE of different algorithms versus SNR with the high-dimensional real-value signal model.

    图  16  高维复值信号模型下各算法稀疏恢复准确度与信噪比的关系.

    Fig.  16  RMSE of different algorithms versus SNR with the high-dimensional complex-value signal model.

    图  17  DOA估计的准确度与测量数的关系.

    Fig.  17  RMSE of DOA estimation using different algorithms versus number of measurements.

    图  18  DOA估计准确度与信噪比的关系.

    Fig.  18  RMSE of DOA estimation using different algorithms versus SNRs

    表  1  各算法单次运行时间

    Table  1  Time comsuptions of different algoritms.

    实值信号模型 复值信号模型
    算法 用时/s 算法 用时/s
    FastLaplace 0.11 FastSBL 1.54
    aLASSO 1.94 GAMP-SBL 0.51
    FastSBL 0.40 MFOCUSS 0.21
    GAMP-SBL 0.07 HSL-SBL 3.16
    FaLASSO-SBL 0.26 FaLASSO-SBL 0.74
    aLASSO-SBL 0.98 aLASSO-SBL 2.33
    下载: 导出CSV

    表  2  恢复高维信号时各算法单次运行时间

    Table  2  Time comsuptions of different algoritms when the dimension of signal is high.

    实值信号模型 复值信号模型
    算法 用时/s 算法 用时/s
    FastLaplace 0.83 FastSBL 6.95
    aLASSO 5.71 GAMP-SBL 2.17
    FastSBL 3.40 MFOCUSS 2.86
    GAMP-SBL 0.69 HSL-SBL 15.73
    FaLASSO-SBL 1.06 FaLASSO-SBL 4.61
    aLASSO-SBL 8.38 aLASSO-SBL 17.41
    下载: 导出CSV

    表  3  单快拍DOA估计实验各算法单次运行时间

    Table  3  Time comsuptions of different algoritms for single snapshot DOA estimation.

    算法 用时/s 算法 用时/s
    SS-ESPRIT 0.37 HSL-SBL 0.85
    SURE-IR 1.64 FaLASSO-SBL 0.47
    L1-SR 0.91 aLASSO-SBL 0.83
    OGSBL 0.69
    下载: 导出CSV
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  • 收稿日期:  2021-01-12
  • 录用日期:  2021-04-29
  • 网络出版日期:  2021-06-16

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