# Hybrid Dilated and Recursive Recurrent Convolution Network for Time-Domain Speech Enhancement
## 2 Related Work  
### Speech Enhancement  
Spectral subtraction, Wiener filtering, and subspace algorithm are the three most classic traditional monaural speech enhancement methods. Spectral subtraction methods [19; 20; 21; 22; 1] firstly obtains the noise spectrum to be processed by estimating and updating the noise spectrum operation in the non-speech segment. After that, the enhanced speech spectrum will be estimated through the subtraction operation. Finally, the speech spectrum is converted into a speech waveform. Although the spectral subtraction method is relatively simple, there will be problems such as voice distortion and music noise, and this type of method is suitable for the case of stable noise. The effect of suppressing non-stationary noise is relatively poor.  
The Wiener filtering algorithms [23; 24; 25; 26; 2] originated during the Second World War. It was proposed by the mathematician [PERSON] to solve the military air shooting control problem. It is mainly used to extract the required clean signal from the noisy observation signal. The Wiener filtering algorithm has a history of nearly 80 years, and its ideas have undergone many variations after decades of development. The essence of the Wiener filtering algorithm is to extract the signal from the noise and use the minimum mean square value of the error between the estimated result and the true value of the signal as the best criterion. Therefore, the Wiener filter is the optimal filter in the statistical sense or the optimal linear estimator of the waveform. However, the Wiener filter method has a general ability to handle non-stationary noise, which will cause voice distortion.  
The principle of the subspace algorithms is to decompose the vector space of the observed signal into a signal subspace, a noise subspace, and estimate the clean speech by eliminating the noise subspace and retaining the signal subspace. The process of subspace decomposition is to perform KLT transformation on the noisy speech signal, then set the KLT coefficient of the noise to 0, and finally obtain the enhanced speech through the inverse KLT transformation. The subspace method generally does not cause the problem of voice distortion and can maintain the quality of the enhanced voice. Its disadvantage is that it removes less noise and the enhancement effect is also not very good.  
Compared with traditional speech enhancement algorithms, the algorithms [27; 28; 29; 30; 31] based on deep learning have obtained a relatively obvious improvement in performance and effect. With the development of deep neural network (DNN), which has promoted the rapid development of related research in the field of speech enhancement, researchers have proposed many DNN models to solve the problem of speech enhancement [28]. Computational inefficiencies and phase inconsistencies exist in non-end-to-end algorithms, so the researchers performed speech enhancement directly in the time domain. Most of the end-to-end algorithms use one-dimensional dilated convolution to improve the network's extraction of contextual information from the original speech waveform, and to a certain extent, the enhancement effect of the network model is improved.