基于四階累積量張量聯(lián)合對角化的多數(shù)據(jù)集聯(lián)合盲源分離

龔曉峰; 毛蕾; 林秋華; 徐友根; 劉志文

doi:10.11999/JEIT180414

基于四階累積量張量聯(lián)合對角化的多數(shù)據(jù)集聯(lián)合盲源分離

doi: 10.11999/JEIT180414

1.
大連理工大學信息與通信工程學院 ??大連 ??116024
2.
北京理工大學信息與電子學院 ??北京 ??100081

基金項目: 國家自然科學基金面上項目(61671106, 61871067)，國家自然科學基金重點項目(61331019)

詳細信息

作者簡介:
龔曉峰：男，1981年生，副教授，研究方向為盲信號處理、陣列信號處理

毛蕾：女，1991年生，碩士生，研究方向為盲信號處理

林秋華：女，1970年生，教授，研究方向為盲信號處理及其應用

徐友根：男，1975年生，教授，研究方向為陣列信號處理及其應用

劉志文：男，1962年生，教授，研究方向為數(shù)字信號與圖像處理及應用，嵌入式系統(tǒng)開發(fā)及應用，生物醫(yī)學信息獲取與處理

通訊作者:
龔曉峰　xfgong@dlut.edu.cn

中圖分類號: TN911.7
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- 文章訪問數(shù): 2816
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- 被引次數(shù): 0
出版歷程
- 收稿日期: 2018-05-03
- 修回日期: 2018-10-11
- 網(wǎng)絡出版日期: 2018-10-31
- 刊出日期: 2019-03-01

Joint Blind Source Separation Based on Joint Diagonalization of Fourth-order Cumulant Tensors

1.
School of Information and Communication Engineering, Dalian University of Technology, Dalian 116024, China
2.
School of Information and Electronics, Beijing Institute of Technology, Beijing 100081, China

Funds: The National Natural Science Foundation of China (61671106, 61871067, 61331019)

摘要

摘要:
該文提出一種基于四階累積量張量聯(lián)合對角化的聯(lián)合盲源分離(J-BSS)算法。首先通過計算4階互累積量將多數(shù)據(jù)集信號的J-BSS問題轉(zhuǎn)化為4階張量聯(lián)合對角化問題。接下來，基于雅可比連續(xù)旋轉(zhuǎn)將張量聯(lián)合對角化這類非線性優(yōu)化問題，轉(zhuǎn)化為一系列可獲取閉式解的簡單子優(yōu)化問題，并通過交替迭代對多數(shù)據(jù)集混合矩陣進行更新，進而實現(xiàn)J-BSS。實驗結(jié)果表明，所提算法具有良好的收斂性能，較之現(xiàn)有的同類型BSS及J-BSS算法具有更高的精度。此外，該算法在分離實際胎兒心電信號方面也表現(xiàn)出良好的性能。
- 聯(lián)合盲源分離 /
- 聯(lián)合張量對角化 /
- 4階累積量
Abstract:
A new Joint Blind Source Separation (J-BSS) algorithm is proposed based on joint diagonalization of fourth-order cumulant tensors. This algorithm constructs first a set of fourth-order tensors by computing the fourth-order cross cumulant of the multiset signals. Then, based on the Jacobian successive rotation strategy, the highly nonlinear optimization problem of joint tensor diagonalization is transformed into a series of simple sub-optimization problems, each admitting a closed form solution. The multiset mixing matrices are hence updated via alternating iterations, which diagonalize jointly the data tensors. Simulation results show that the proposed algorithm has nice convergence pattern and higher accuracy than existing BSS and J-BSS algorithms of a similar type. In addition, the algorithm works well in a real-world application to fetal ECG separation.
- Joint Blind Source Separation (J-BSS) /
- Joint Tensor Diagonalization (JTD) /
- Fourth-order cumulant

HTML全文

圖 1 無噪聲下JTD和GOJD的A-PI值隨掃描次數(shù)的變化曲線

下載: 全尺寸圖片幻燈片

圖 2 本文算法和同類型算法在分離計算機合成信號時的性能對比

下載: 全尺寸圖片幻燈片

圖 3 實際FECG信號分離實驗結(jié)果

下載: 全尺寸圖片幻燈片

表 1 基于雅克比旋轉(zhuǎn)的四階張量聯(lián)合對角化算法

輸入：　K個滿足式(5)的張量 ${\mathcal{T}_1},{\mathcal{T}_{\rm{2}}},·\!·\!·,{\mathcal{T}_K} \in {\mathbb{C}^{R \times R \times R \times R}}$ 。
對因子矩陣進行初始化，進行如下步驟，直至收斂。
令i從1至 $R - 1$ 變化， j從i +1至R變化，對固定索引(i, j)：　　　(1)根據(jù)式(16)，計算矩陣 ${\tilde{ G}}_{i,j}^{(m)},m = 1,2,3,4$ ；
(2)根據(jù)式(10)，更新矩陣 ${{\tilde{ U}}^{(m)}}$ 及 ${T_1},{T_2},·\!·\!·,{T_K}$ 。
輸出：　4個因子矩陣估計值 ${{\tilde{ U}}^{(1)}},{{\tilde{ U}}^{(2)}},{{\tilde{ U}}^{(3)}},{{\tilde{ U}}^{(4)}}$ 。

下載: 導出CSV

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