A Minimization Formulation for Source Separation with a Microphone Array

We consider the problem of source separation using a microphone array. We propose a minimization formulation for the problem. In forming the function to be minimized, we propose a penalty function that takes into account the sensitivity of the directional filters especially when a few microphones are used. We propose an algorithm for the minimization problem and provide the conditions of convergence. We discuss the performance of the proposed method based on a synthetic experiment.