## 3 Materials and Methods
### Deep Learning Models for Detecting COVID-19 Based on CXR Images  
#### 3.3.1 The Deep Learning Models  
To detect COVID-19 based on CXR images, five deep transfer learning models were used: InceptionResNetV2, Xception, SqueezeNet, VGG16, and AlexNet. These models were selected to range in size, i.e., the number of layers and size on disk. In the following, we provide a brief description of each model.  
* InceptionResNetV2 is a type of convolutional neural network that consists of 164 layers deep with image input size 299 \(\times\) 299. The architecture of InceptionResNetV2 is formulated based on a combination of the Inception structure and a residual network (ResNet) connection. The usage of a ResNet connection not only eliminates degradation issues during deep structure but also reduces the training time. The InceptionResNetV2 architecture consists of a stem block that contains three standard convolutional layers and two 3 \(\times\) 3 max-pooling layers. Multiple convolutional and max-pooling layers follow stem blocks with different sizes and different orders using ReLU and SoftMax functions [42]. The InceptionResNetV2 architecture is depicted in Figure 5(a).
* Xception is a convolutional neural network that was adapted from the Inception network, where the Inception modules are replaced with depthwise separable convolutions. The network has an image input size of 299 \(\times\) 299 and is 71 layers deep. Figure 5(b) shows the architecture of Xception, which consists of multiple convolutions with 1 \(\times\) 1 size and depthwise separable convolutions with 3 \(\times\) 3 size using the batch normalization, ReLU, and SoftMax functions [43].
* SqueezeNet is a small convolutional neural network that is 18 layers deep. It was designed to reduce the number of parameters to fit into computer memory or be easily transmitted over computer networks. SqueezeNet begins with a standard convolutional layer followed by eight fire modules, ending with a final convolutional layer and the SoftMax function. It performs max-pooling after the first standard convolutional layer, Fire4, Fire8, and the last standard convolutional layer [44]. Figure 6c shows the architecture of SqueezeNet.
* VGG16: The most straightforward method to improve deep neural networks' performance is by increasing the network's size. For this reason, the visual geometry group (VGG) was created with three fully connected layers, 13 convolutional layers, and smaller size filters (2 \(\times\) 2 and 3 \(\times\) 3) using ReLU and SoftMax functions. It performs max-pooling twice with size 2 \(\times\) 2 [45]. The architecture of VGG16 is depicted in Figure 6d.
* AlexNet is a convolutional neural network eight layers deep. It contains five convolution layers, three max-pooling layers, and three fully-connected layers using ReLU and SoftMax functions. The input image size is 227 \(\times\) 227 [46]. Figure 6e shows the architecture of SqueezeNet.  
Figure 6: Deep transfer learning models used for detection: (**a**) Inception-ResNetV2 architecture; (**b**) Xception architecture; (**c**) SqueezeNet architecture; (**d**) VGG16 architecture; (**e**) AlexNet architecture.  
The five models were trained on the expanded dataset, which contains the real images from the original dataset and the images generated by the proposed CGAN. To enable fair comparison among the different models, all the models were trained with the same parameters' configurations. Table 3 shows the parameter configurations of the training process.