Joint Approximate Diagonalization Using Bilateral Rank-Reducing Householder Transform with Application in Blind Source Separation

This paper addresses the problem of Jointapproximate diagonalization (JAD) of a set of given matrices andproposes a new efficient iterative algorithm for JAD that based on therank-reducing structure of Householder transform. The proposedalgorithm, named as HJD, completes the simultaneous diagonalization ofthe target matrices by successive Householder transform from the pointof view of matrix power concentration. Generally, the power of theelements below diagonal element was concentrated to the diagonalelement by the rank-reducing Householder transform. Such a particularstructure of Householder transform at each iteration prevents thedivergence of matrix power. The diagonalization matrix was calculatedby the product of all Householder matrices. By applying our algorithmto blind source separation, we demonstrate the efficiency andimprovement of the proposed algorithm in estimating the separationmatrix.