## 2 Materials and Methods
### Network Architecture  
The proposed out-painting network architecture was derived from the foundational design of the DCGAN [18]. Typically, the DCGAN generator employs a series of transposed convolutional layers for progressively up-sampling an input image, and each layer includes batch normalization and activation functions to enhance training stability and convergence speed. In this work, the generator of the proposed out-painting network was designed with an encoder-decoder architecture for predicting missing data in s-IGDT projections, as shown in Figure 3.  
Unlike the simple decoder architecture, which is generally used as the DCGAN generator, the encoder-decoder architecture allows for more controlled generation and makes it easier to produce plausible output images because the complex and latent features of input images can be selectively extracted by the encoder structure [19; 20]. Moreover, the dimensionality reduction achieved by using the encoder structure is able to improve the training efficiency. By focusing on selective features for image generation, the encoder-decoder architecture can mitigate the mode collapse issue, which is common in the DCGAN, having a simple decoder architecture-based generator [21]. The encoder of the generator in the proposed out-painting network comprised 5 convolution layers with 4 \(\times\) 4-5 \(\times\) 5 kernel sizes and rectified linear unit (ReLU) activation function. The decoder of the generator consisted of 4 convolution layers with a ReLU activation function, 2 deconvolution layers with a ReLU activation function, and 1 convolution layer with a sigmoid activation function. We added the dilated convolution block, which comprised 4 dilated convolution layers with different dilation rates, for connecting the encoder to the decoder. The out-painting  
Figure 3: Architecture of the generator in the proposed out-painting network. Figure 2: Coronal view of the digital phantom, which was used for preparing test data. The yellow box is the region scanned by the simulated s-IGDT system. task suffers from a lack of learnable data because the image pixels adjacent to missing image regions are fewer than those used for the in-painting task. This fundamental issue can be resolved by providing the learnable data from dilated receptive fields. Compared to the standard convolution layer, features can be extracted from a large image area in the dilated convolution layer because the dilated convolution expands a receptive field. This characteristic of the dilated convolution allows the provision of sufficient information for the out-painting task. The dilated convolution enables a network to aggregate the contextual information of input features during training by using diverse receptive fields. Additionally, the zero-padding in convolution kernels used for dilating receptive fields can prevent the degradation of image resolution [22]. These benefits are able to generate precise output images, and valuable image features for the out-painting can be delivered by dilated receptive fields. Note that dilation rates were empirically determined to ensure acceptable image quality. The configuration of the generator is detailed in Table 2.  
The discriminator of the DCGAN plays a key role in determining whether a generated image is real or fake [18]. In the s-IGDT image, non-truncated regions should maintain the features of input images, and the generated image for truncated regions should harmonize with surrounding regions through the discrimination procedure. But, the single discriminator used in conventional GAN-based networks makes it hard to distinguish the artificiality of each region in a generated image because the training of the single discriminator is implemented by using all areas of the generated image.