## 3 Methods
### Proposed Model Generator  
The optimization based on depthwise separable convolution in the HDR-GAN generator blocks [16] uses not only the encoder-decoder scheme introduced by U-Net [39], but also a merging block to help with both image alignment and fusion. In order to assess the impact of these modifications, the original configurations of the other components of the HDR-GAN model were maintained, such as the loss function based on [PERSON] et al.'s model [10], the Patch-GAN-based discriminator [40] with the sphere GAN loss function [41], and the pre-processing of the dataset for training.  
Based on the research carried out by [PERSON] et al. [16], where quantitative comparisons were conducted to assess the impact of different depths, the presence or absence of merging blocks and the use or not of the auxiliary upsampling path, three scales of depth, merging block and auxiliary upsampling path are used.  
Thus, as illustrated in Figure 6, the proposed model receives as input three LDR images of different exposures, selects the medium exposure image as the reference, and the reconstruction process occurs through the multi-scale LDR encoder, reference-aligned feature fusion, and deep HDR supervision steps, generating the HDR image. In the multi-scale LDR encoder step, feature extraction is performed at three scales. For each input, the encoder block, represented by the blue blocks, is applied, which is a two-layer residual structure without a pooling layer, using two depthwise separable convolutions and adding them to the block input. Then, downsampling is performed, represented by the red arrows, using a depthwise separable convolution of a 3 \(\times\) 3 kernel with stride 2, to move to the next scale. The reference-aligned feature fusion step merges the features extracted by scale, concatenating the results obtained by each encoder block of the same scale and processing them with the merging block, represented by the red blocks. The merging blocks have a four-layer residual structure, using four depthwise separable convolutions with a dilated factor of 2 and adding the feature corresponding to the average exposure image. Then, the deep HDR supervision step is performed from the merging block, in which the processed data are upsampled, represented by the blue arrows, and then concatenated with the data from the upper layer to serve as input for the decoder blocks, represented by the green blocks, with the same structure as the encoder block. In contrast to previous deep supervision methods [39], deep HDR supervision generates a sub-network, with a smaller number of layers and an auxiliary image output. This auxiliary upsampling path improves the quality of the output image and is used to benefit the training of the main upsampling path, composed of a larger number of layers representing the final HDR output of the network.  
Due to the effect of the discoloration generated by using the HDR image to calculate the supervised loss function of the generating model, as demonstrated by [PERSON] et al. [10], the loss is measured from the images generated by the generating model in the tone-mapping domain, transformed from the \(\mu\)-law function defined by Equation (6).  
\[\mathcal{T}(H)=\frac{\log(1+\mu H)}{\log(1+\mu)}\qquad\mu=5000 \tag{6}\]  
where \(\mathcal{T}(H)\) represents the image in the tone-mapping domain, \(H\) is the image in the HDR domain, and \(\mu\) is the determined compression factor.  
Based on the research of [PERSON] et al. [16], the outputs of the auxiliary upsampling path and main upsampling path of the model are used for measurement. Thus, the loss function defined in Equation (7) is used.  
\[\mathcal{L}_{1}=\min_{G}(||\mathcal{T}(\hat{H}_{1})-\mathcal{T}(H_{gt})||_{1}+ ||\mathcal{T}(\hat{H}_{2})-\mathcal{T}(H_{gt})||_{1}) \tag{7}\]  
where \(\hat{H}_{1}\) represents the HDR image generated by the auxiliary upsampling path, \(\hat{H}_{2}\) corresponds to the HDR image generated by the main upsampling path, and \(H_{gt}\) is the ground truth HDR image.