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In this paper, we propose a class of complex non-orthogonal joint diagonalization (NOJD) algorithms with successive rotations. The proposed methods consider LU or LQ decompositions of the mixing matrices, and propose to solve the NOJD problem via two successive stages: L-stage and U (or Q)-stage. Moreover, as the manifolds of target matrices in these stages could be appropriately parameterized by a sequence of simple elementary triangular or unitary matrices, which depend on only one or two parameters, the high-dimensional minimization problems could be replaced by a sequence of lower-dimensional ones. As such, the proposed algorithms are of simple closed-form in each iteration, and do not require the target matrices to be Hermitian nor positive definite. Simulations are provided to compare the proposed methods to other complex NOJD methods.

This paper considers separation of convolutive speech mixtures in frequency-domain within a tensorial framework. By assuming that components associated with neighboring frequency bins of the same source are still correlated, a set of cross-frequency covariance tensors with trilinear structure are established, and an algorithm consisting of consecutive parallel factor (PARAFAC) decompositions is developed. Each PARAFAC decompositon used in the proposed method can simultaneously estimate two neighboring frequency responses, one of which is a common factor with the subsequent crossfrequency covariance tensor, and thus could be used to align the permutations of the estimates in all the PARAFAC decompositions. In addition, the issue of identifiability is addressed, and simulations with synthetic speech signals are provided to verify the efficacy of the proposed method.

Complex independent component analysis (ICA) has found utility in separation of complex-valued signals such as communications, functional magnetic resonance imaging, and frequency-domain speeches. However, permutation ambiguity is a main problem of complex ICA for order-sensitive applications, e.g., frequency-domain speech separation. This paper proposes a semi-blind complex ICA algorithm based on negentropy maximization. The magnitude correlation of a source signal is utilized to constrain the separation process. As a result, the complex-valued signals are separated without permutation. Experiments with synthetic complex-valued signals, synthetic speech signals, and recorded speech signals are performed. The results demonstrate that the proposed algorithm can not only solve the permutation problem, but also achieve slightly improved separation compared to the standard blind algorithm.