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基于三阶统计量的欠定盲源分离方法

邹亮 张鹏 陈勋

邹亮, 张鹏, 陈勋. 基于三阶统计量的欠定盲源分离方法[J]. 电子与信息学报, 2022, 44(11): 3960-3966. doi: 10.11999/JEIT210844
引用本文: 邹亮, 张鹏, 陈勋. 基于三阶统计量的欠定盲源分离方法[J]. 电子与信息学报, 2022, 44(11): 3960-3966. doi: 10.11999/JEIT210844
ZOU Liang, ZHANG Peng, CHEN Xun. Underdetermined Blind Source Separation Based on Third-order Statistics[J]. Journal of Electronics & Information Technology, 2022, 44(11): 3960-3966. doi: 10.11999/JEIT210844
Citation: ZOU Liang, ZHANG Peng, CHEN Xun. Underdetermined Blind Source Separation Based on Third-order Statistics[J]. Journal of Electronics & Information Technology, 2022, 44(11): 3960-3966. doi: 10.11999/JEIT210844

基于三阶统计量的欠定盲源分离方法

doi: 10.11999/JEIT210844
基金项目: 国家自然科学基金(61901003, 61922075),江苏省自然科学基金(BK20190623)
详细信息
    作者简介:

    邹亮:男,副教授,研究方向为统计信号处理与人工智能

    张鹏:男,硕士,研究方向为盲源分离

    陈勋:男,教授,研究方向为医学人工智能和移动健康监护

    通讯作者:

    陈勋 xunchen@ustc.edu.cn

  • 中图分类号: TN911.7; TN958.97

Underdetermined Blind Source Separation Based on Third-order Statistics

Funds: The National Natural Science Foundation of China (61901003, 61922075), The Natural Science Foundation of Jiangsu Province (BK20190623)
  • 摘要: 盲源分离(BSS)在缺失源信号信息及信息混合方式信息的情况下,仅利用观测信号实现源信号恢复,是信号处理中的重要手段。欠定盲源分离(UBSS)中观测信号少于源信号数目,因此,相较于正定/超定情形,其更接近现实情况。然而,观测信号往往受到噪声干扰,传统基于2阶统计量和信号稀疏性的欠定盲源分离结果对噪声较为敏感。鉴于3阶统计量在处理对称分布噪声时的优势,该文利用观测信号的3阶统计信息实现混合矩阵的估计。考虑到源信号的自相关特性,计算多时延下观测信号一系列的3阶统计信息,并堆叠成4阶张量,进而将混合矩阵估计问题转化为4阶张量的典范双峰分解问题。该文进一步利用广义高斯模型和期望最大算法实现源信号的恢复。1000次蒙特卡罗实验表明该文算法能够有效抑制噪声的影响。针对3×4混合模型,当信噪比为15 dB时,该文算法对混合矩阵的平均估计误差达到–20.35 dB,所恢复出的源信号与真实源信号之间的平均绝对相关系数达0.84,与现有方法相比,取得了最好的分离结果。
  • 图  1  4个语音源信号

    图  2  3路观测信号

    图  3  恢复的源信号

    图  4  欠定盲源分离算法混合矩阵估计的归一化均方误差比较

    图  5  源信号和观测信号数目变化时,算法的性能

    表  1  本文算法步骤

     输入:${{M}}$维观测信号${\boldsymbol{X}}$。
     输出:混合矩阵${\boldsymbol{A}}$和恢复的源信号$\hat {\boldsymbol{S}}$。
     步骤1 计算观测信号的3阶统计量。
     步骤2 通过对观测信号进行延时,计算出不同的3阶张量,并将
        这些3阶张量堆叠成4阶张量。
     步骤3 通过张量的CP分解,计算出混合矩阵${{\boldsymbol{A}}^{(1)} },{{\boldsymbol{A}}^{(2)} },{{\boldsymbol{A}}^{(3)} }$。
     步骤4 通过奇异值分解优化混合矩阵的估计$\hat {\boldsymbol{A}}$ 。
     步骤5 通过信号恢复算法对信号进行恢复,获得恢复信号$\hat {\boldsymbol{S}}$。
    下载: 导出CSV

    表  2  各算法恢复出的源信号与真实源信号间的平均绝对皮尔逊相关系数

    信噪比(dB)
    –5051015202530
    文献[13]0.25380.39660.53950.62060.67990.72500.74270.7662
    文献[14]0.23500.38320.53800.66160.73260.79510.83060.8439
    文献[15]0.20800.29330.38030.47520.64720.70650.71350.7441
    文献[16]0.25860.37810.49230.65630.78050.81960.83500.8288
    文献[17]0.25560.42140.59580.71030.78790.81490.81780.8339
    文献[18]0.29250.45950.63300.74650.82100.84750.86960.8691
    本文算法0.30050.48660.65980.77750.84410.86720.88160.8887
    下载: 导出CSV

    表  3  各种算法平均运行1次所需要的时间(s)

    文献[13]文献[14]文献[15]文献[16]文献[17]文献[18]本文算法
    0.19610.236910.97943.18720.00120.00110.0012
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-08-18
  • 修回日期:  2022-01-30
  • 录用日期:  2022-03-10
  • 网络出版日期:  2022-03-20
  • 刊出日期:  2022-11-14

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