# Disentangled Feature Learning for Noise-Invariant Speech Enhancement
## 1 Introduction  
Speech enhancement techniques aim to improve the quality and intelligibility of a given speech degraded by certain additive noise in the background. In a variety of applications, speech enhancement is considered as an essential pre-processing step. This technique can be directly employed to improve the quality of mobile communications [1] in noisy environments or to enhance speech signals for hearing aid devices [2, 3] before amplification. Speech enhancement has also been widely used as a pre-processing technique in automatic speech recognition (ASR) [4, 5] and speaker recognition systems [6] for more robust performances. Over the past several decades, myriads of approaches have been developed in the speech research community for better speech enhancement. Spectral subtraction method [7] suppresses stationary noise from the input noisy speech by subtracting the spectral noise bias computed during the non-speech activity periods. The minimum mean-square error (MMSE)-based spectral amplitude estimator [8, 9] showed promising results in terms of reducing residual noise as compared to the spectral subtraction method or Wiener filtering-based algorithm [10]. The least mean square adaptive filtering (LMSAF) based speech enhancement approaches have the best filtering performances of Wiener filter. Meanwhile, they do not need a priori knowledge, and can be adapted to the external environment by self-learning. But these approaches have some disadvantages including low constituency, strong sensitivity to non-stationary noise and a contradiction between constituency and stability [11, 12]. The minima controlled recursive averaging (MCRA) noise estimation was also introduced in [13] of which the performance is known to be reasonably competitive under the environments with relatively high signal-to-noise ratios (SNR). However, since these statistical models are constructed based on a stationarity assumption, their performances generally tend to deteriorate in low SNR or highly non-stationary noise conditions. Non-negative matrix factorization (NMF) is one of the most common template-based approaches to speech enhancement [14, 15, 16], which models noisy observations as a weighted sum of non-negative source bases. NMF-based speech enhancement methods are more robust to non-stationary noise conditions as compared to the statistical model-based methods. These approaches, however, often result in signal distortion in the enhanced speech since they are based on an unrealistic assumption that speech spectrograms are linear combinations of the basis spectra. Due to the complex nature of the noise corruption process, non-linear models such as deep neural networks (DNNs) have been suggested as an alternative choice for modeling the relationship between the noisy and the corresponding clean speech utterances. DNNs have been successful in solving the speech enhancement tasks under various noise environments since its introduction. Early literature using DNNs as a nonlinear mapping function for estimating clean speech had reported better enhancement results [17, 18, 19, 20] compared to the NMF-based algorithms. Various neural network structures have been employed for speech enhancement, such as multi-context stacking networks for ensemble learning [21], recurrent neural networks (RNNs) [22, 23, 24], and convolutional neural networks (CNNs) [25, 26]. More recently, generative adversarial network (GAN) [27] has become popular in the area of deep learning, and it has been also applied to speech enhancement. [PERSON] et al. proposed end-to-end speech enhancement GAN (SEGAN) in which the generator learns to model the mapping from the noisy speech samples to their clean counterparts, while the discriminator learns to distinguish between the enhanced and the target clean samples within the context of a mini-max game [28].