## 3 Methods and Data
### Construction of the WaveNet Network Model
#### 3.2.1 Residual Block  
The residual block structure in WaveNet is illustrated in Figure 6. The size of the input feature map is C/2 \(\times\) H \(\times\) W, where C represents the number of channels in the feature map, and H and W represent the height and width of the feature map, respectively. Between every two convolutional layers, there is a batch normalization layer and a rectified linear unit (ReLU) activation function [23]. The use of batch normalization ensures that the input distribution of each neuron remains consistent, which can accelerate the convergence speed of the network and avoid the issues of gradient vanishing and exploding, thereby improving the generalization performance of the model. ReLU is a commonly used activation function in deep learning. ReLU is defined as follows:  
\[f(x)=max(0,x) \tag{2}\]  
In short, for input \(x\), if \(x\) is greater than zero, then output \(x\), otherwise output zero. The advantage of the ReLU activation function is its simplicity and non-linearity. Compared with traditional activation functions (such as sigmoid or tanh), ReLU is more stable for the back propagation of gradients and helps alleviate the vanishing gradient problem. In addition, ReLU introduces non-linearity, allowing the neural network to learn more complex functions. In the architecture of the residual block within WaveNet, the initial convolutional layer plays a pivotal role. Its primary function is to double the number of channels in the feature map while halving its spatial size. This process is crucial for maintaining consistent feature map sizes during the initial addition operation. To achieve this, we employ a \(1\times 1\) convolutional layer that processes the input data, augmenting dimensionality along the channel axis and aligning it with the dimensions of other components within the residual block [24]. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Unit: Images**} & \multirow{2}{*}{\begin{tabular}{c} **Original Data** \\ **Volume** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Dataset Size for** \\ **Traditional Data** \\ **Augmentation** \\ \end{tabular} } & \multicolumn{2}{c}{
\begin{tabular}{c} **Dataset Size** \\ **Generated by** \\ **the Modified** \\ **DCGAN** \\ \end{tabular} } & \multicolumn{2}{c}{**Training Set 1**} & \multicolumn{2}{c}{**Training Set 2**} & \multicolumn{1}{c}{**Test Set**} \\ \hline Cloud & 700 & 1300 & 1300 & 2000 & 2000 & 400 \\ Land & 700 & 1300 & 1300 & 2000 & 2000 & 400 \\ Ocean & 700 & 1300 & 1300 & 2000 & 2000 & 400 \\ Oceanic internal waves & 700 & 1300 & 1300 & 2000 & 2000 & 400 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Number of training and testing sets. Following this dimension alignment, a 3 \(\times\) 3 convolutional layer is utilized for feature extraction. Importantly, the resulting feature map maintains the same spatial dimensions as the input feature map. Subsequently, the output feature map from the initial convolutional layer undergoes further feature extraction via another 3 \(\times\) 3 convolutional layer. An element-wise addition operation is then applied to the output feature map of the second convolutional layer, effectively creating a residual connection. This connection enables the network to learn the difference between the input and output, which enhances network optimization and training. After the residual connection, we apply a ReLU activation function to the feature map, effectively setting all negative values to zero. This introduces non-linear features and amplifies the network's representational capacity. Through this sequence of operations, the residual block efficiently extracts and propagates essential feature information, thereby enhancing the network's overall performance and its ability to learn complex patterns within remote sensing images.