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

TL;DR

This paper investigates the relationship between the traditional spectral amplitude MSE criterion and the STOI-based intelligibility measure in speech enhancement, showing their practical equivalence and near-optimality of MSE for intelligibility.

Contribution

It establishes a theoretical link between STSA-MSE and STOI, demonstrating their equivalence and the near-optimality of MSE for improving speech intelligibility.

Findings

STSA-MSE and ELC criteria are practically equivalent under certain conditions.

Standard STSA minimum-MSE estimator is near optimal for STOI-based intelligibility.

Empirical data supports the theoretical equivalence between MSE and STOI-based measures.

Abstract

The majority of deep neural network (DNN) based speech enhancement algorithms rely on the mean-square error (MSE) criterion of short-time spectral amplitudes (STSA), which has no apparent link to human perception, e.g. speech intelligibility. Short-Time Objective Intelligibility (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 (ELC) can lead to improved speech 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. 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.