Fast Approximate Joint Diagonalization Incorporating Weight Matrices

We propose a new low-complexity approximate joint diagonalization (AJD) algorithm, which incorporates nontrivial block-diagonal weight matrices into a weighted least-squares (WLS) AJD criterion. Often in blind source separation (BSS), when the sources are nearly separated, the optimal weight matrix for WLS-based AJD takes a (nearly) block-diagonal form. Based on this observation, we show how the new algorithm can be utilized in an iteratively reweighted separation scheme, thereby giving rise to fast implementation of asymptotically optimal BSS algorithms in various scenarios. In particular, we consider three specific (yet common) scenarios, involving stationary or block-stationary Gaussian sources, for which the optimal weight matrices can be readily estimated from the sample covariance matrices (which are also the target-matrices for the AJD). Comparative simulation results demonstrate the advantages in both speed and accuracy, as well as compliance with the theoretically predicted asymptotic optimality of the resulting BSS algorithms based on the weighted AJD, both on large scale problems with matrices of the size 100$\,\times\,$100.