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Speech enhancement algorithms are used to remove background noise in a speech signal. In Bayesian short-time spectral amplitude (STSA) estimation for single-channel speech enhancement, the spectral components are traditionally assumed uncorrelated. However, this assumption is inexact since some correlation is present in practice. In this paper, we investigate a multidimensional Bayesian STSA estimator that assumes correlated spectral components. Since the closed-form solution of this optimum estimator is not readily available, we alternatively derive closed-form expressions for an upper and a lower bound on the desired estimator. Using these bounds, we propose a new family of speech enhancement estimators that are characterized by a scalar parameter 0 ≤ γ ≤ 1, with γ = 0 corresponding to the lower bound and γ = 1 to the upper bound. An appropriate estimator for the correlation matrix of the clean speech is further derived. Evaluation results from both objective and subjective speech quality measures show that at moderate to high SNR values, where spectral correlation of speech is most noticeable, the proposed estimators can achieve significant improvements over the traditional STSA and Wiener filter estimators.