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In this paper, we propose a two-stage speech enhancement technique. In the training stage, a Gaussian Mixture Model (GMM) of the melfrequency cepstral coefficients (MFCCs) of a user's clean speech is computed wherein the component densities of the GMM serve to model the user's "acoustic classes." In the enhancement stage, MFCCs from a noisy speech signal are computed and the underlying clean acoustic class is identified via a maximum a posteriori (MAP) decision and a novel mapping matrix. The associated GMM parameters are then used to estimate the MFCCs of the clean speech from the MFCCs of the noisy speech. Finally, the estimated MFCCs are transformed back to a time-domain waveform. Our results show that we can improve PESQ in environments as low as -10 dB SNR.