# A Supervised Speech Enhancement Approach with Residual Noise Control for Voice Communication
###### Abstract  
For voice communication, it is important to extract the speech from its noisy version without introducing unnaturally artificial noise. By studying the subband mean-squared error (MSE) of the speech for unsupervised speech enhancement approaches and revealing its relationship with the existing loss function for supervised approaches, this paper derives a generalized loss function that takes residual noise control into account with a supervised approach. Our generalized loss function contains the well-known MSE loss function and many other often-used loss functions as special cases. Compared with traditional loss functions, our generalized loss function is more flexible to make a good trade-off between speech distortion and noise reduction. This is because a group of well-studied noise shaping schemes can be introduced to control residual noise for practical applications. Objective and subjective test  
over-smoothing estimation which omits some important detailed information. To solve these problems, many new criteria, that consider speech perception, have been proposed in recent years [12; 13; 14; 15]. The first one is to use perceptually weighted MSE functions, which are proposed to weight the loss in different T-F regions [13; 16]. Despite the weighted coefficients mitigate the over-smoothing issue of MSE to some extent, most of them are based on the heuristic principles and cannot solve the inherent over-smoothing problem of MSE completely. The second one is to use objective metrics as loss functions. For examples, perceptual evaluation speech quality (PESQ) [17], short-time objective intelligibility (STOI) [18] and scale-invariant speech distortion ratio (SI-SDR) [19] have been adopted as loss functions. Although the metric-based methods facilitate the better optimization of the specific objective metric, other metrics are often non-optimized. Moreover, the calculation of some metrics is often too complicated and non-continuous [20]. In [21], speech distortion and residual noise are considered separately in the loss function, known as the components loss (CL), which obtains relatively better metric scores than MSE when suitable loss-weighted coefficients are selected.  
Note that all the above mentioned loss functions aim at suppressing noise as much as possible at noise-only segments. In other words, at noise-only segments, the amount of noise reduction is expected to be a positive infinite value. However, this aim could not be achieved in most cases for many reasons. First, the noise is often stochastic, and thus it is inevitable that the estimation accuracy is often constrained by a limited number of available observations [22; 23]. Second, there are a great variety of noise signals, so that a DNN model cannot be expected to distinguish all of them correctly from the speech in each T-F unit. Therefore, when the noise cannot be suppressed totally as expected, some unnatural residual noise may severely degrade speech quality [24], which needs to be considered carefully. In this paper, we derive a generalized loss function by introducing multiple manual parameters to flexibly make a balance between speech distortion and noise attenuation. More specifically, we use the residual noise control introduced for voice communication [25; 26]. By theoretical derivations, MSE and some other often-used loss functions can be included in the proposed generalized loss function.  
The remainder of the paper is structured as follows. Section 2 formulates the problem. Section 3 derives the generalized loss in detail and introduces used network architecture. Section 4 is the experimental settings. Results and analysis are given in Section 5. Section 6 presents some conclusions.