非酉矩阵联合对角化的唯一性分析
Uniqueness Analysis of Non-Unitary Matrix Joint Diagonalization
摘要：
矩阵联合对角化（MJD）是解决盲声源分离（BSS）问题的一种有效方法。它依赖于由未知的分离矩阵对角化的矩阵的构造。他们的联合对角化作为一个正确的估计，这个去混合矩阵，只有当它是唯一确定的。因此，一个关键问题是在什么条件下联合对角化子是唯一的。在目前的工作中，我们完全回答这个问题的可识别性MJD基于BSS方法，并提供了一个一般性的结果矩阵联合对角化的唯一性条件。它统一了所有现有的结果，利用非圆，非平稳，非白度，非高斯的概念。作为一个推论，我们提出了一个解决方案，复杂的BSS，它可以制定在一个封闭的形式在两个矩阵的特征值和奇异值分解。
英文摘要：
Matrix Joint Diagonalization (MJD) is a powerful approach for solving the Blind Source Separation (BSS) problem. It relies on the construction of matrices which are diagonalized by the unknown demixing matrix. Their joint diagonalizer serves as a correct estimate of this demixing matrix only if it is uniquely determined. Thus, a critical question is under what conditions a joint diagonalizer is unique. In the present work we fully answer this question about the identifiability of MJD based BSS approaches and provide a general result on uniqueness conditions of matrix joint diagonalization. It unifies all existing results which exploit the concepts of non-circularity, non-stationarity, non-whiteness, and non-Gaussianity. As a corollary, we propose a solution for complex BSS, which can be formulated in a closed form in terms of an eigenvalue and a singular value decomposition of two matrices.
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