## 2 Materials and Methods
### Multi-Input Image DCNN Model  
An overview of the proposed framework is shown in Figure 2. The system received FAM and HEX images simultaneously, and the images were subsequently normalized in the range of \([-1,\,1]\). Both normalized images were then presented to the pre-trained deep network model in parallel. The deep network architecture used in this study was MobileNetV2 [26]. This deep network model is computationally the cheapest and one of the fastest architectures with 53 deep layers and approximately a total of 3.5 M parameters in comparison with other ImageNet deep neural network architectures such as ResNets [27; 28], Inceptions [29], and VGGs [30]. The first version of the MobileNet architecture [31] introduced a depthwise separable convolution layer that required a lower number of network connection weights in comparison to the use of a traditional convolution layer. Figure 1: Representative sample input images for each class. (**a**) Positive-FAM. (**b**) Positive-HEX. (**c**) Negative-FAM. (**d**) Negative-HEX. (**e**) Weak positive-FAM. (**f**) Weak positive-HEX. (**g**) Rerun-FAM. (**h**) Rerun-HEX. Depthwise separable convolution achieves this by performing depthwise and pointwise convolutions separately for image feature filtering. The performance of MobileNet was slightly improved in the second version of the network by adding the idea of expanding (decompression) and shrinking (compression) the number of channels of the input features before and after depthwise convolution, which is also known as a bottleneck block. During expansion, a modified version of the rectified linear unit activation function (ReLU6) was used. In contrast, no activation function is used (i.e., a linear function is used) when shrinking the channel number at the end of the block; therefore, the relevant information extracted from the input data is not lost. In addition, the number of deep layers was increased in the second version of the MobileNet model. Therefore, to prevent the network from the vanishing gradient problem [32], a residual connection (also known as a skip connection) was added to the bottleneck layer to forward a copy of the input features to the end of this layer before the input features passed through the layer. It is important to note that the residual-connection-based bottleneck block is only performed whenever the number of channels of the input and output of the bottleneck block is the same. Training this type of large network from scratch, which relies on high runtime memory and multi-processing tasks on the graphics processing unit (GPU), is a difficult task, particularly on personal computers, which have limited processing power. To overcome this difficulty, the existing knowledge gained from the ImageNet database was transferred to the classification problem of COVID-19 RT-PCR diagnosis, which is also known as transfer learning. During the training of the proposed system, the weights of the MobileNetV2 model were frozen to extract only image features. The feature extraction network, MobileNetV2, and its bottleneck block are shown in Figure 3.  
Figure 3: Architecture of MobileNetV2 and bottleneck residual block. Figure 2: The multi-input image DCNN model where the two MobileNetV2 models are used simultaneously to extract deep features from FAM and HEX images. There were 345,600 deep features for each image yielded by the MobileNetV2 network. Both deep feature vectors were concatenated before they were connected to the fully connected layer. This layer is also known as the classification layer, in which the relationship between the deep features and classes is learned. Only one dense layer with 40 hidden nodes was used in the proposed framework. The output of the hidden nodes was computed using the standard rectified linear unit (ReLU) activation function. The outputs from the dense layer were first normalized (i.e., batch normalization) and then connected to the softmax layer that outputs four possible classes for the final decision.