Multidimensional blind source separation using joint block-diagonalization

In multidimensional blind source separation(MBSS)， sources belonging to the same tuples are correlated whereas sources belonging to different tuples are independent. We propose a method of MBSS using approximate joint blockdiagonalization and implement it with the improved Jacobi algorithm. The correlation matrix of sources is block-diagonal. This makes the whitened signal’s time delay correlation matrices containing  joint block-diagonalizable structure. So， separating matrix can be identified by joint block-diagonalization and sources can be recovered. Then， based on the property of joint blockdiagonalization，we improve the Jacobi method in two aspect: one is transforming the parameter selection of rotation matrix to the optimization problem of a trigonometric function polynomial of degree 4，the other is adjusting the sequences of loops. So joint block-diagonalization can be implemented with successive GIVENS rotation. Numerical experiments with analysis demonstrate the effectiveness of the algorithm.