Determined and overdetermined convolutive blind source extractions by approximate joint diagonalization

Blind extraction of convolutive speech mixtures can be achieved by the approximate joint diagonalization (AJD) approach. In this paper, we present a least-squares AJD (LS-AJD) algorithm, called fast diagonalization, implemented by minimizing the direct and indirect LS criteria (FDMDI) algorithm. The proposed approach is based on an alternate minimization of the indirect and direct least-squares criteria to the diagonal matrices in the first phase and to the mixing matrix in the second phase, respectively. In our proposed approach, the constrained LS-AJD estimation problem is solved by the method of Lagrange multipliers; moreover, the mixing matrix is estimated by a noniterative method without a nested loop in the second phase. The simulation result demonstrates that overdetermined FDMDI blind source extraction (BSE) provides more effective extracted signals than determined FDMDI BSE in an actual acoustic environment.