## 4 Results  
In the experiments, the proposed approach was implemented on a PC with a 64-bit Windows operating system and an Intel Core i7-9700 @ 3.00 GHz CPU with 16 G memory (Intel Corporation, Santa Clara, CA, USA). The used graphics card was an NVIDIA GeForce RTX 2070 SUPER (NVIDIA Corporation, Santa Clara, CA, USA). Our approach was also run on a computer with a 64-bit Ubuntu 18.04.6 LTS operating system and an AMD Ryzen 7 5800X CPU with 16 G memory (AMD, Santa Clara, CA, USA). We used an NVIDIA GeForce RTX 3090 graphics card (NVIDIA Corporation, Santa Clara, CA, USA). The proposed algorithm was mainly written in Python (version 3.10.0.) programming language. We used the HDR-Real dataset as the training data [11] and the HDR-EFE dataset as the testing data [23]. The image resolution was 512 \(\times\) 512. There were 9786 training image pairs and 46 testing image pairs in the original dataset. We established a subset by removing extreme images with a large proportion of overexposed and underexposed areas to improve learning performance. More specifically, if the number of pixels with intensity values greater than 249 or less than 6 exceeded 25% of the total pixels, the image was removed from the subset. After selection, there were 5673 image pairs in the HDR-Real training subset. For stage 1, we used the entire set of the HDR-Real dataset to extract histogram information for histogram learning because we only expanded an input 8-bit LDR image to a 12-bit HDR image. For stage 2, we converted a 12-bit HDR image to a 16-bit HDR image. We used a subset of the HDR-Real dataset for training to improve the performance of reinforcement learning. First, the experiments were conducted in two stages. In the first stage, image histograms were extracted from the complete dataset for training. After predicting the histogram of the HDR image, we performed histogram matching on the EDR image to obtain a 12-bit HDR image. In the second stage, the pixel values of the resulting 12-bit HDR image were multiplied by \(2^{4}\) and then adjusted pixel-by-pixel using a reinforcement learning \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Action** & **Filter Size** & **Parameter** \\ \hline
1 & box filter & \(5\times 5\) & - \\
2 & bilateral filter & \(5\times 5\) & \(\sigma_{c}=1.0,\sigma_{S}=5.0\) \\
3 & bilateral filter & \(5\times 5\) & \(\sigma_{c}=0.1,\sigma_{S}=5.0\) \\
4 & median filter & \(5\times 5\) & \\
5 & Gaussian filter & \(5\times 5\) & \(\sigma=1.5\) \\
6 & Gaussian filter & \(5\times 5\) & \(\sigma=0.5\) \\
7 & pixel intensity + = 1 & - & \\
8 & pixel intensity \(-\) = 1 & - & \\
9 & pixel intensity + = 10 & - & \\
10 & pixel intensity \(-\) = 10 & - & \\
11 & pixel intensity + = 100 & - & \\
12 & pixel intensity \(-\) = & - & \\
13 & do nothing & - & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The action set used by the agents for training and testing. framework to obtain a 16-bit HDR image. Figure 6 shows the resulting images of the proposed approach. In Figure 6, the left column shows LDR images, the second column shows the resulting 12-bit HDR images of stage 1, the third column shows the resulting 16-bit HDR images of stage 2, and the right column illustrates the ground-truth HDR images. Note that the second, third, and right columns of Figure 6 were tone-mapped representations. From the results, the proposed approach can reconstruct the desirable HDR images with high quality. For the resulting HDR images, we used the mean-opinion-score of quality (\(Q_{\text{MOS}}\)) score from HDR-VDP-2 [24] for evaluation. The range of \(Q_{\text{MOS}}\) was 0 to 100. The higher the value, the better the image quality. Using 16-bit ground-truth HDR images as the reference images, the \(Q_{\text{MOS}}\) scores on the two stages of test datasets were 61.29 \(\pm\) 2.71 and 61.54 \(\pm\) 2.55, respectively. This represented a 0.25 improvement in the \(Q_{\text{MOS}}\) score given by the adjustment in the second stage.