# Research on Radionuclide Identification Method Based on GASF and Deep Residual Network
## 3 Establishment of Neural Network Model  
### Modeling  
Early convolutional neural networks primarily relied on simple stacking of convolutional layers, pooling layers, and fully connected layers to increase the network depth. Data were transmitted layer by layer from the input to the output through hierarchical connections. However, as the depth of the network increased, the weights failed to update or updated insignificantly, leading to the vanishing or exploding gradient problem, which hindered effective network training. To address this issue, [PERSON] et al. proposed the deep convolutional neural network ResNet (Residual Network) [17], which mitigates the training degradation problem in deep networks by introducing residual connections. In a traditional convolutional neural network, as shown in Figure 3A, the output H(X) = F(X) is obtained after the input X passes through the convolutional layer and activation function. In contrast, the residual block introduced by ResNet, shown in Figure 3B, adds a shortcut connection before the activation function of the next layer, transforming the input of the next layer from the original output H(X) = F(X) to H(X) = F(X) + X. By incorporating residual blocks and adding the original input X to the output, the network can better preserve and utilize the useful information from the original input, leading to more effective feature representations and improved performance and generalization ability. Furthermore, the subsequent input levels also include the original input X, enabling the network to learn mappings that retain the input information without fully recalculating the output. This allows the network to be easier to train and optimize, facilitating the construction of deeper network architectures.  
Taking into account the task requirements and model complexity, this paper adopts the ResNet18 architecture from the ResNet model family. The overall structure of the ResNet18 network is shown in Figure 4a. Stage 1 can be considered the preprocessing stage, consisting of a \(7\times 7\) convolutional layer for feature extraction from the input data, followed by a max pooling layer to reduce the dimensionality of the feature map. Each stage from Stage 2 to Stage 5 contains two residual blocks: CONV BLOCK and ID BLOCK.  
Figure 2: Two-dimensional representation of the energy spectrum based on segmented GASF: (**a**) segmented GASF conversion for channels 1–192; (**b**) segmented GASF conversion for channels 513–704.  
Each residual block consists of two 3 \(\times\) 3 convolutional layers, with residual connections that allow the model to skip layers during training, facilitating the learning of identity mappings. The structures of the CONV BLOCK and ID BLOCK are shown in Figure 4b,c. The end of the network features a global average pooling layer and a fully connected layer. The global average pooling layer downsamples the feature map output by the last convolutional layer, while the fully connected layer maps the output feature vectors to the final class labels. Nuclide recognition based on neural network models is treated as a multi-class classification task, with a Softmax activation function added after the fully connected layer to convert the output into a probability distribution.