Optimization of JADE using a novel optimally weighted joint diagonalization approach

The JADE algorithm (Cardoso and Souloumiac, 1993) is a popular batch-type algorithm for Blind Source Separation (BSS), which employs approximate joint diagonalization (AJD) of fourth-order cumulant matrices, following a whitening stage. In this paper we propose a computationally attractive optimization of JADE for noiseless mixtures, in the form of a post-processing tool. First, we cast the AJD of 4th- and 2nd- order estimated matrices as a weighted least-squares (WLS) problem. We then show (under some commonly met conditions), that in the vicinity of a non-mixing condition (such as at the output of traditional JADE), the asymptotically optimal WLS criterion can be easily formulated and conveniently optimized via a novel algorithm, which uses non-unitary AJD of transformed subsets of the estimated matrices. Optimality with respect to general mixing is maintained, as we show, thanks to the equivariance of the optimal WLS solution. The performance of the new algorithm is analyzed and compared to JADE, identifying the conditions for most pronounced improvement, as demonstrated by simulation.