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Uniqueness Analysis of Non-Unitary Matrix Joint Diagonalization

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2 Author(s)
Kleinsteuber, M. ; Dept. of Electr. Eng. & Inf. Technol., Tech. Univ. Munchen, München, Germany ; Hao Shen

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 is a joint diagonalizer 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 closed form in terms of an eigen and a singular value decomposition of two matrices.

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Signal Processing, IEEE Transactions on  (Volume:61 ,  Issue: 7 )