# Integrating Dilated Convolution into DenseLSTM for Audio Source Separation
## 1 Introduction  
In a real environment, humans hear several mixed signals simultaneously. In these situations, we can selectively attend to a signal we want, effectively segregating a target from the perceived mixture. This is the so-called auditory scene analysis or the cocktail effect problem [1], which is the main topic of this paper. In particular, when signals such as unwanted noise are mixed with the target signal, system performance is degraded, and the necessity of this study is emphasized [2, 3]. Audio source separation is used to estimate the target signal, such as speech and music, when the target signal and other signals are mixed. If the target signal to be estimated is speech, it is the speech enhancement task; if the target signal is music, it is the music signal separation task. In the conventional method of audio source separation with linear characteristics, non-negative matrix factorization (NMF) [4] is used not only for speech enhancement but for music source separation tasks [5, 6, 7]. NMF is an algorithm that decomposes a signal into two non-negative matrices that are a basis matrix representing independent characteristics and an activation matrix for each characteristic [4]. Each component of the signal can be separated using the basis matrix learned in the training process. Recently, deep learning, which has non-linear characteristics, showed better results than the traditional NMFmethod in audio source separation [8; 9; 10; 11; 12; 13; 14]. Deep learning has several representative architectures, such as the fully connected neural network (FCNN) [15], convolutional neural network (CNN) [16], and recurrent neural network (RNN) [17]. Often, these architectures are modified or combined to design a new architecture suitable for the task. FCNN architecture, which is the most basic deep learning architecture, is an architecture in which the nodes of each layer are fully connected [15], while the CNN designed for image processing is an architecture that convolves filters as a weight sharing method [16]. In addition, an RNN suitable for processing time series data is characterized by accumulating and using the information of the input data in chronological order within the architecture [17]. Many studies have shown better performance than the FCNN by using bidirectional long short-term memory (BLSTM) and CNN architectures [18; 19; 20; 21; 22; 23; 24; 25]. Long short-term memory (LSTM) has a memory cell involved in inputs and outputs to store longer time series information than vanilla RNN [26]. BLSTM architecture determines the output by combining the forward time series information and the backward time series information of the LSTM [27]. The CNN architecture that shares weights can be used to design deeper layers of networks with the same parameters, which means that CNNs can learn more complex patterns of filters than FCNN architecture. Recently, the convolutional recurrent neural network (CRNN) architecture [28] that uses CNNs suitable for image processing and RNNs suitable for time series data processing in one architecture at the same time shows better performance than other CNN, RNN, and BLSTM architectures [29; 30; 31]. In the CRNN architecture, LSTM or BLSTM architectures of the RNN series, which has better performance than vanilla RNN, is used. The parameters of the CNN are learned to estimate a filter for the target, and also the parameters of the RNN are learned to store the target information using time series information [28]. In the spectrogram of the acoustic signal, the target pattern shows slightly different characteristics depending on the frequency axis but appears at various locations along the time axis. Therefore, it is suitable for the translation-equivariance characteristics of the CNN architecture. In addition, since the time series data is along the time axis, it is suitable for the RNN architecture [29; 30; 31].