一种利用结构特点实现复数域联合对角化解盲源分离新算法研究及应用

Research on a New Structural Traits Based Complex-Valued Space Joint Diagonalization Algorithm for Blind Source Separation and Its Applications

联合对角化方法是求解盲源分离问题的有力工具.但是现存的联合对角化算法大都只能求解实数域盲源分离问题,且对目标矩阵有诸多限制.为了求解更具一般性的复数域盲源分离问题,提出了一种基于结构特点的联合对角化(Structural Traits Based Joint Diagonalization,STBJD)算法,既取消了预白化操作解除了对目标矩阵的正定性限制,又允许目标矩阵组为复值,具有极广的适用性.首先,引入矩阵变换,将待联合对角化的复数域目标矩阵组转化为新的具有鲜明结构特点的实对称目标矩阵组.随后,构建联合对角化最小二乘代价函数,引入交替最小二乘迭代算法求解代价函数,并在优化过程中充分挖掘所涉参量的结构特点加以利用.最终,求得混迭矩阵的估计并据此恢复源信号.仿真实验证明与现存的有代表性的对目标矩阵无特殊限制的复数域联合对角化算法FAJD算法及CVFFDIAG算法相比,STBJD算法具有更高的收敛精度,能有效地解决盲源分离问题.

Joint diagonalization（ JD） is an efficient tool for blind source separation（ BSS） problems. However,most existing JD algorithms could only be used for real-valued space BSS problems and set many constraints on target matrices.In order to solve the general complex-valued space BSS problems,a structural traits based joint diagonalization（ STBJD） algorithm is proposed. The algorithm discards pre-whitening procedure,relaxes the positive-definiteness assumption on target matrices and can be used in complex-valued space,thus has more general utilizations. Matrix transformation was adapted to transform the complex-valued space target matrices being jointly diagonalized to real-valued space ones with distinct structural traits. Furthermore,the Least Square cost function for JD was established and solved by alternate least squares（ ALS） iterative algorithm. The structural traits of concerned variables were fully exploited and technical utilized in the optimizing process. Finally,the mixing matrix could be estimated and the sources could be retrieved. Numerical simulations illustrated the better convergence performance of STBJD than that of the state-of-the-art algorithms such as FAJD and CVFFDIAG.Thus it could be applied to solve the BSS problems efficiently.