# Hybrid Dilated and Recursive Recurrent Convolution Network for Time-Domain Speech Enhancement
###### Abstract  
In this paper, we propose a fully convolutional neural network based on recursive recurrent convolution for monaural speech enhancement in the time domain. The proposed network is an encoder-decoder structure using a series of hybrid dilated modules (HDM). The encoder creates low-dimensional features of a noisy input frame. In the HDM, the dilated convolution is used to expand the receptive field of the network model. In contrast, the standard convolution is used to make up for the under-utilized local information of the dilated convolution. The decoder is used to reconstruct enhanced frames. The recursive recurrent convolutional network uses GRU to solve the problem of multiple training parameters and complex structures. State-of-the-art results are achieved on two commonly used speech datasets.  
speech enhancement; time domain; hybrid dilated convolution; recurrent convolution +
Footnote †: journal:  
One-dimensional dilated convolution can improve the receptive field of the network model. However, when one-dimensional dilated convolution is used for time-domain speech enhancement tasks, there is a problem as local information cannot be fully utilized. The reason is that when the dilation rate is greater than one during the convolution, holes in dilated convolutions lead to local information loss. Therefore, a hybrid dilated convolution module is proposed to combine dilated convolution with conventional convolution.  
The end-to-end speech enhancement algorithm directly processes the original waveform of the speech, avoiding the low calculation efficiency and \"phase inconsistency\" problems based on the time-frequency domain-speech enhancement algorithm and also achieves a better enhancement effect. However, whether based on end-to-end or non-end-to-end speech enhancement algorithms, these models have a large number of trainable parameters. Recently, recursive learning mechanisms have been applied to a variety of tasks, such as single-image de-rain [17] and image super-resolution [18]. The principle of recursive learning is to train the network recursively using the same network parameters, similar to a mathematical iterative process in which the entire process of mapping the network model is handled in several stages. Thus, through recursive learning, the network parameters can be reused at each stage, and we can explore the network at a deeper level without using additional parameters. Inspired by recursive learning, this paper proposes a speech enhancement algorithm based on combining a hybrid dilated convolution module and recursive learning. The contributions of this article can be summarized as:  
1. Proposed hybrid dilated convolution module (HDM), which consists of dilated convolution and conventional convolution;
2. Proposed recursive recurrent speech enhancement network (RRSENet), which uses a GRU module to solve the problem of multiple training parameters and complex structures;
3. Extensive experiments are performed on dataset synthesized by TIMIT corpus and NOISEX92, and the proposed model achieves excellent results.  
The remainder of this paper is structured as follows. Section 2 describes the related work on speech enhancement, RNN, and dilated convolution. Section 3 formulates the problem and proposes the architecture. Section 4.3 presents the experiment settings, results, and analysis. Some conclusions are drawn in Section 5.