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In this paper, we propose a statistical model for speech enhancement that takes into account the time-correlation between successive speech spectral components. It retains the simplicity associated with the Gaussian statistical model, and enables the extension of existing algorithms to noncausal estimation. The sequence of speech spectral variances is a random process, which is generally correlated with the sequence of speech spectral magnitudes. Causal and noncausal estimators for the a priori SNR are derived in agreement with the model assumptions and the estimation of the speech spectral components. We show that a special case of the causal estimator degenerates to a “decision-directed” estimator with a time-varying frequency-dependent weighting factor. Experimental results demonstrate the improved performance of the proposed algorithms.