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Single microphone speech enhancement systems have typically shown limited performance, while multiple microphone systems based on a least-squares error criterion have shown encouraging results in some contexts. In this paper we formulate a new approach to multiple microphone speech enhancement. Specifically, we formulate a maximum likelihood (ML) problem for estimating the parameters needed for canceling the noise in a two microphone speech enhancement system. This ML problem is solved via the iterative EM (Estimate-Maximize) technique. The resulting algorithm shows encouraging results when applied to the speech enhancement problem.