# Signal Separation Based on Knowledge Representation
## 3 Methodology
### Network Architecture  
The architecture of the knowledge-guided autoencoder is illustrated in Figure 3. The observed data size is represented as \(C\times H\times W\), where \(C\) denotes the number of samples, \(H\) represents the height of the observed signals, and \(W\) represents the width. The input data \(\mathbf{X}\in\mathbb{R}^{C\times H\times W}\) undergo the knowledge representation framework, generating knowledge representations of the target source signals, \(\mathbf{K}_{i}\in\mathbb{R}^{C\times H\times W}\). The number of network branches and knowledge representations is determined by the number of separation targets. The knowledge representations guide the branch autoencoder networks, influencing each  
Figure 3: The workflow of signal separation based on knowledge representation framework. Integrating the main steps of knowledge extraction, knowledge representation, and knowledge application with the autoencoder network.  
network branch. This forms the knowledge-guided loss function and the reconstruction loss function. Both loss functions are combined for backpropagation, adjusting neural network parameters to achieve signal separation.  
Since the observed signal consists of multiple source signals, the autoencoder is designed as a multi-branch U-Net network. The encoding and decoding processes in the U-Net network reconstruct the output signal based on input features while effectively leveraging knowledge representations. The U-Net network comprises several key components, summarized in Table 1, each serving a specific purpose.  
The specific parameters of the network architecture can be adjusted based on task requirements. For upgoing and downgoing wave separation and handwritten digit separation, the U-Net network has a depth of 2, with convolutional output channels set to {1, 32, 64}. For P-wave and S-wave separation, the network depth increases to 4, with output channels configured as {1, 32, 64, 128, 256}. The overall structure of the U-Net network is shown in Figure 4.  
Figure 4: Architecture of the U-Net. Multiple U-Net network modules constitute a branch autoencoder. The structure of the network comprises an encoder–decoder architecture. The encoding phase involves normalizing the input data and extracting features through convolutional pooling operations. Subsequently, the decoder phase generates the target data by utilizing convolutions, upsampling, and denormalization operations based on the encoded features.  
\begin{table}
\begin{tabular}{c l} \hline \hline
**Component** & **Description** \\ \hline Convolutional Layers & Extract spatial and feature information from input data \\ \hline Normalization Layers & Standardize input data to stabilize and accelerate training \\ \hline Activation Layers & Introduce nonlinearity to capture complex relationships \\ \hline Pooling Layers & Downsample feature maps, reducing complexity while preserving key features \\ \hline Upsampling Layers & Restore spatial dimensions of feature maps for reconstruction \\ \hline Denormalization Layers & Reverse normalization to recover the original signal scale \\ \hline \hline \end{tabular}
\end{table}
Table 1: Key components of the U-Net network.  
Given the diverse value ranges of different data types, such as seismic wavefield recordings and image signals, which include both positive and negative values, a more generalized basic network unit is provided. The intermediate activation function is LeakReLu, while the hyperbolic tangent function tanh is used as the activation function in the final output. The normalization layer ensures that input observation data are distributed within the range of \([-1,1]\), thereby mitigating adverse effects caused by outlier data and aiding network convergence. The size of the network's input and output remains same as \(C\times H\times W\).