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The majority of deep neural network&#x00A0;(DNN) based speech enhancement algorithms rely on the mean-square error&#x00A0;(MSE) criterion of short-time spectral amplitudes&#x00A0;(STSA), which has no apparent link to human perception, e.g., speech intelligibility. Short-time objective intelligibility&#x00A0;(STOI), a popular state-of-the-art speech intelligibility estimator, on the other hand, relies on linear correlation of speech temporal envelopes. This raises the question if a DNN training criterion based on envelope linear correlation&#x00A0;(ELC) can lead to improved speech intelligibility performance of DNN-based speech enhancement algorithms compared to algorithms based on the STSA&#x2013;MSE criterion. In this paper, we derive that, under certain general conditions, the STSA&#x2013;MSE and ELC criteria are practically equivalent, and we provide empirical data to support our theoretical results. Furthermore, our experimental findings suggest that the standard STSA minimum-MSE estimator is near optimal, if the objective is to enhance noisy speech in a manner, which is optimal with respect to the STOI speech intelligibility estimator.

On the Relationship Between Short-Time Objective Intelligibility and Short-Time Spectral-Amplitude Mean-Square Error for Speech Enhancement