###### Abstract  
This study proposes a novel robust speech feature extraction technique to improve speech recognition performance in noisy environments. This novel method exploits the information provided by the original acoustic model in the automatic speech recognition (ASR) system to learn a deep neural network that converts the original speech features. This deep neural network is trained to maximize the posterior accuracy of the state sequences of acoustic models with respect to the speech feature sequences. Compared with the robustness methods that retrain or adapt acoustic models, the new method has the advantages of less computation load and faster training. In the experiments conducted on the medium-vocabulary TIMIT database and task, the presented method provides lower word error rates than the unprocessed baseline and speech-enhancement-based techniques. These results indicate that the presented method is promising and worth further developing. speech recognition; noise-robust acoustic features; deep learning +
Footnote †: journal: Applied system  
However, when it comes to the performance evaluation of a speech enhancement algorithm, some objective metrics, such as the perceptual evaluation of speech quality (PESQ) [13] and short-time objective intelligibility (STOI) [14], are often used. These metrics are not necessarily related to the mean squared distance between the enhanced and original clean speech. Therefore, in some recently developed deep-learning-based SE algorithms [15; 16], PESQ and STOI are employed directly to be the objective functions for the training of DNN models. PESQ is a standard objective metric to measure speech quality, recommended by ITU-T. It is developed to predict the mean opinion scores (MOS) in subjective listening tests, and according to [17], PESQ shows a high correlation (\(r\approx 0.9\)) with MOS. PESQ is widely used to evaluate speech separation and enhancement algorithms. It mainly quantizes speech quality by computing the disturbance between the clean and separated/enhanced speech using cognitive modeling. PESQ ranges within [\(-0.5\), \(4.5\)], with high values indicating better quality [13; 18]. Here, we provide a little more discussion about the issue that using mean squared error (MSE) as the loss function in most deep-learning-based SE algorithms [10; 19; 20; 21] does not necessarily give rise to higher PESQ/STOI scores in the processed utterances. According to [18; 21], two fundamental assumptions of the MSE loss in these SE methods somewhat contradict human auditory perception, which are as follows:  
* **Every estimated element is equally important [18]:** The MSE loss function treats each single data point equally. Regardless of the locations of the processed data, the same difference between the elements of each processed output and the desired output corresponds to the equal MSE loss value. The underlying reason is that the MSE loss is derived from each sample point of the utterance separately and independently instead of the whole utterance trajectory. However, we evaluate the quality and intelligibility of an utterance in a different manner. For example, the speech-dominant portion is treated more crucially than the silence portion in the STOI metric. In contrast, the PESQ metric pays more attention to isolated samples because they are more involved with speech quality. In addition, when considered in the frequency domain, the MSE loss is usually defined at the linear frequency scale. At the same time, the speech quality/intelligibility metrics are measured at human auditory frequency scales (such as the mel scale and Bark scale). To sum up, minimizing the MSE loss is not necessary to optimize the PESQ or STOI scores for noisy utterances.