# Research on Seismic Signal Denoising Model Based on DnCNN Network
## 2 Design of Seismic Signal Denoising Model Based on DnCNN
### Seismic Signal Denoising Model Structure Based on DtCNN Network  
The seismic signal denoising model, which leverages the DnCNN network, adopts the principle of residual learning and employs residual mapping for processing [16]. Rather than attempting to model pristine seismic signals directly, this approach focuses on capturing the characteristics of noise, which are more tractable for the neural network. Throughout both the training and testing phases, the model takes in seismic signals laden with noise and produces an estimation of the noise present. The clean seismic signal is then derived by subtracting the predicted noise from the original noisy signal. A schematic representation of the DnCNN-based seismic signal denoising model is presented in Figure 2, illustrating its architecture and workflow.  
The DnCNN-based seismic signal denoising model integrates several key components, including convolutional layers, batch normalization, ReLU activation functions, and residual learning. This model steers clear of the pooling layer, which is known to  
Figure 1: Residual learning unit.  
discard important features necessary for effective noise reduction, often leading to inferior signal recovery. Also, given that fully connected layers involve a multitude of parameters and are typically reserved for classification tasks, they are deemed inappropriate for seismic signal denoising, hence their exclusion from the DnCNN architecture. Instead, the model concludes with a convolutional layer to directly generate an output that matches the dimensions of the estimated signal, enhancing the model's efficiency.  
The initial layer of this model combines a convolutional layer with an activation function, which is tasked with extracting features from the input signal. It utilizes a \(3\times 1\) kernel and 64 kernels for this purpose. Unlike DnCNN's two-dimensional kernels designed for image data, the seismic signal denoising model employs one-dimensional kernels to process one-dimensional seismic signals. From the second to the sixteenth layer, the model replicates modules consisting of convolutional layers, batch normalization, and ReLU activations, each equipped with a \(3\times 1\) kernel and 64 kernels. The final layer, which is responsible for noise prediction, uses a \(3\times 1\) kernel and a single kernel. The DnCNN model comprises 17 layers in total, a configuration that has been optimized for image denoising and is similarly effective for seismic signal denoising. The denoised seismic signal is derived by subtracting the predicted noise from the noisy signal, capitalizing on the residual learning approach.  
In this paper, the network structure of the DnCNN is used to construct a CNN model for seismic signal denoising. The model uses the residual learning method to predict the noise in the seismic signal. The final output of the model is the noise \(R(X)\approx V\). The estimation of the original seismic signal can be obtained by subtracting the noise \(R(X)\) from the noisy seismic signal, i.e., \(y_{0}=x-R(X)\). The loss function is used to calculate the error between the estimated value and the expected value. The loss function used in this paper is the MSE (Mean Square Error) loss, as shown in Formula (4).  
\[\psi(\rho)=\frac{1}{2M}\sum_{i=1}^{M}\ ||\ R(x_{i};\rho)-(x_{i}-y_{i})\ ||_{F}^{2} \tag{4}\]  
In Formula (4), \(x_{i}\) (\(i=1,2,\ldots,M\)) are \(M\) training samples of seismic signals with noise, \(y_{i}\) (\(i=1,2,\ldots,M\)) are \(M\) original seismic signal training samples without noise, \(\|\cdot\|\) denotes the Frobenius norm, and \(\rho\) is the parameter of the model, which is obtained through the training process.