Nakasako N., Ogura H., Nakamura S., Yamamoto D.

Many works on the blind signal separation (BSS) have been reported from various viewpoints, and the authors have also proposed some approaches for BSS problem using the higher order statistics. We developed Independent Component Analysis (ICA) for narrowband complex signals with time-delayed or convoluted mixture by means of complex Hermite moments and unitary transformations (SU(2)) for 2-dimensional (2D) case. In this paper, we expand the previous method to the case when 3 source signals are mixed with time-delay or convolution. More concretely, a practical scheme for 3-dimensional (3D) blind separation is formulated based on the cost function in terms of the complex Hermite moment, combined with the use of the group properties of 3-D unitary group SU(3). The cost function is defined as a square norm of the complex Hermite moments with respect to separated signals and the optimal solution is found by maximizing the cost function. The optimal unitary matrix that transforms 3-D standardized mixed signals into a possible of 3 independent components is searched for by the gradient method, introducing parameterized matrices for SU(3). To confirm the validity and the effectiveness of our method, it is applied to speech data, introducing Principal Component Analysis as a preprocessing method.