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Minimum mean-square error (MMSE) approaches to speech enhancement are widely used in the literature. The quality of enhanced speech produced by an MMSE approach is directly impacted by the accuracy of the employed a priori signal-to-noise ratio (SNR) estimator. In this paper, the a priori SNR estimate spectral distortion (SD) level that results in a just-noticeable difference (JND) in the perceived quality of MMSE approach enhanced speech is found. The JND SD level is indicative of the accuracy that an a priori SNR estimator must exceed