## 2 Methodologies
### Denoising the Deep Neural Network  
To improve the estimation performance in (14), \(\hat{x}_{m}^{k}(t)\) is processed before the subtraction for each iteration by the DNN [33]. The DNN contains four hidden layers without any dropout regularization and is pre-trained in an unsupervised manner, with each layer possessing 2048, 4096, 2048, and 512 hidden neural units. In the training stage, the adaptive gradient descent method is adopted as the optimization process, in which the learning rate decreases from 0.08 to 0.001 as the epoch increases, and the mean square error (MSE) is selected as the loss function to measure the error between the prediction of DNN and the training target. The sigmoid function is adopted as the activation function in each hidden layer. Moreover, to make full use of the feature information contained in the speech, four parameters are extracted from the pending signal: MFCC, AMS, GFPS, and RASTA-PLP [35; 36]. To obtain the MFCC involving the envelope and detail of the frequency spectrum, each piece of raw data is divided into frames of 20 ms, with a 10 ms overlap. The Hamming window is applied to each frame, and the short-time Fourier transform (STFT) is utilized to obtain the power spectrum, which can be converted to 31-dimensional (31-D) MFCC by a log operation and discrete cosine transform (DCT) in the mel scale. To obtain AMS, the full-wave rectification and the decreased sample by a factor of 4 are applied to the speech signal, which is divided into frames of 32 ms, with a 10 ms frame shift. The Hamming window and a 256-point fast Fourier transform (FFT) are applied to each frame to obtain the power spectrum, which is converted to a 15-dimensional (15-D) feature by utilizing 15 triangular windows uniformly centered from 15.6 400 Hz. To obtain GFPS, a 64-channel gammatone filter bank is applied to the speech signal to obtain sub-band signals, and the energy spectrum is derived from the energy function to sub-band signals. It is noted that the RASTA-PLP is the spectral feature of the sound signals. Generally, it is a modified linear prediction cepstral coefficient to make the extracted power spectrum more suitable for the processing characteristics of the human ear [39]. To obtain RASTA-PLP, RASTA filtering is applied to PLP, which can minimize the differences among the dominant dormant structures of different speakers. After converting the power spectrum of the signal to the bark scale, the log application and RASTA filter were then applied to the resulting spectrum. Finally, by expanding the filtered log spectrum with an exponential function and performing a linear prediction analysis, the 13-D RASTA-PLP can be derived. The characteristics of the pending signal were obtained from these four parameters using their sequential derivatives. Although the speech signal is usually regarded as a non-stationary signal, it has been reported that within a diminutive duration range, the speech signal can be regarded as a stationary signal owing to the motion inertia of the vocal organ [40]. In addition, to preserve the time-domain characteristics of the speech signal spectrum, in speech signal analysis, researchers usually adopt a 20-30 ms frame length during processing [35; 41]. As a result, the original irregular signal could exhibit periodic properties without losing too much edge information. The Free Surfing-Tech Chinese Mandarin Corpus dataset, which was recorded in a silent indoor environment by a cell phone, was adopted in the learning and training stage of DNNs. The dataset contained 855 different speakers with 120 short utterances for each speaker. A dataset of 700 speakers was randomly selected as the training set, while the remaining data were the testing set. A suitable training target significantly affects the performance of the network training.