GEOMETRIC OPTIMIZATION METHODS FOR BLIND SOURCE SEPARATION OF SIGNALS

Kamran Rahbar and James P. Reilly
kamran@reverb.crl.mcmaster.ca, reillyj@mcmaster.ca

In this paper we develop a new blind signal separation (BSS) algorithm using conjugate gradient optimization over the Stiefel manifold. We express the BSS problem mathe- matically as an optimization problem with an orthonormal constraint. This can be expressed as an unconstrained op- timization over the Stiefel manifold [1]. To derive the algo- rithm, we only use second order statistics of the observed signals a criterion which has been shown to be suĂcient for separation providing that sources have linearly independent temporal correlations. The new optimization method dis- plays a quadratic convergence property. Simulation results corresponding to two di erent optimization strategies are presented that verify the performance of the new algorithm and also it's convergence behaviour.