A novel approximate joint diagonalization algorithm

Most existing blind source separation algorithms unmix the sources in two stages. First the data are decorrelated. Then, the transformation that relates the independent sources to the decorrelated mixture is found as a pure rotation since these two, the sources and the decorrelated data, are spatially white vectors. This rotation is found by jointly diagonalizing a set of covariance matrices, or alternatively a set of cumulant slices, by a unitary matrix. The fundamental problem is to retain the unitary property of the operators, and this is achieved in this paper via the Cayley transformation. Based on this approach, we present two novel joint unitary diagonalization algorithms. Simulation studies are undertaken to evaluate the proposed schemes.