基于QR分解的类Jacobi联合对角化算法  

Jacobi-like Joint Diagonalization Algorithm Based on QR Decomposition

作　　者：季策 李烨[1] 李伯群 JI Ce;LI Ye;LI Bo-qun(School of Computer Science&Engineering,Northeastern University,Shenyang 110169,China;Key Laboratory of Intelligent Computing in Medical Image,Ministry of Education,Northeastern University,Shenyang 110169,China;School of Electronic and Information Engineering,University of Science and Technology Liaoning,Anshan 114051,China)

机构地区：[1]东北大学计算机科学与工程学院,辽宁沈阳110169 [2]东北大学医学影像智能计算教育部重点实验室,辽宁沈阳110169 [3]辽宁科技大学电子与信息工程学院,辽宁鞍山114051

出　　处：《东北大学学报（自然科学版）》2024年第3期305-313,共9页Journal of Northeastern University(Natural Science)

摘　　要：为提高实矩阵集的近似联合对角化的盲源分离性能,避免平凡解,提出了一种基于QR分解的类Jacobi联合对角化算法.利用QR分解的数值稳定性,采用Jacobi旋转矩阵,将分离矩阵分解为多个初等三角矩阵和正交矩阵的乘积,利用Jacobi旋转矩阵的结构及矩阵变换后的相关元素求解最优参数,将高维矩阵最小化问题转化为一系列低维矩阵子问题,提升源信号恢复精度.通过求解简化的Frobenius范数目标函数降低算法复杂度.混合心电信号仿真结果表明,与QRJ2D,LUCJD,EGJLUD算法相比,本文算法在分离精度和收敛速度方面均有一定优势.In order to improve the blind separation performance of approximate joint diagonalization of real matrix sets and to avoid trivial solutions,a Jacobi‑like joint diagonalization algorithm based on QR decomposition is proposed.Using the numerical stability of QR decomposition,the Jacobi rotation matrix is used to decompose the separation matrix into the product of several elementary triangular matrices and orthogonal matrices.The structure of Jacobi rotation matrix and the related elements of the target matrix transformation are used to obtain the optimal parameters.The high-dimensional minimization problem is iteratively transformed into a series of low-dimensional sub-problems,which enhances the recovery accuracy of the source signal.The algorithm complexity is reduced by solving the simplified Frobenius-norm objective function.The simulation results of mixed electrocardiogram(ECG)signals show that compared with QRJ2D,LUCJD and EGJLUD,the proposed algorithm has certain advantages in separation accuracy and convergence speed.

关 键 词：盲源分离 非正交联合对角化 QR分解 类Jacobi算法 心电信号模型 

分 类 号：TN911.7[电子电信—通信与信息系统]