On the Equivalence between Objective Intelligibility and Mean-Squared Error for Deep Neural Network based Speech Enhancement

Abstract

Although speech enhancement algorithms based on deep neural networks (DNNs) have shown impressive results, it is unclear, if they are anywhere near optimal in terms of aspects related to human auditory perception, e.g. speech intelligibility. The reason is that the vast majority of DNN based speech enhancement algorithms rely on the mean squared error (MSE) criterion of short-time spectral amplitudes (STSA). State-of-the-art speech intelligibility estimators, on the other hand, rely on linear correlation of speech temporal envelopes. This raises the question if a DNN training criterion based on envelope linear correlation (ELC) can lead to improved intelligibility performance of DNN based speech enhancement algorithms compared to algorithms based on the STSA-MSE criterion. In this paper we derive that, under certain general conditions, the STSA-MSE and ELC criteria are practically equivalent, and we provide empirical data to support our theoretical results. The important implication of our findings is that the standard STSA minimum-MSE estimator is optimal, if the objective is to perform optimally with respect to a state-of-the-art speech intelligibility estimator.