## 4 Conclusions  
A new SALDL method for inverse halftoning was proposed. First, a new residual learning method based on the Gaussian convolution model was introduced for base layer generation. Compared to the additive model, which has been used for image denoising and rain removal, this Gaussian convolution model utilizes a statistical distribution in which the image difference between the blurred original image and blurred halftone image with a Gaussian filter can possess a narrow brightness range. Second, a structure-aware residual deblurring strategy was presented. To remove the Gaussian blurring of the base layer and recover the image structures effectively, an image structure map predictor was designed to estimate the image structures from halftone patterns. This image structure map predictor enabled the entire network to be trained adaptively to local image structures; hence, noisy dot patterns on flat areas were suppressed and local image structures such as lines and text were described precisely. The experimental results confirmed that the proposed method surpassed state-of-the-art inverse halftoning methods based on deep learning, such as U-net, DCNN, DDN, and PRL. In addition, it was verified that the proposed image decomposition model was extremely effective in obtaining high-quality continuous-tone images from input halftone images. This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2020R1A2C1010405). **Institutional Review Board Statement:** Not applicable. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Methods** & **Proposed Method** & \multicolumn{3}{c}{**U-Net [35]**} & \multicolumn{3}{c}{**DCNN [37]**} & \multicolumn{3}{c}{**DDN [39]**} & \multicolumn{3}{c}{**PRL [23; 25]**} \\ \hline Test & \multirow{2}{*}{PSNR} & \multirow{2}{*}{SSIM} & \multirow{2}{*}{PSNR} & \multirow{2}{*}{SSIM} & \multirow{2}{*}{PSNR} & \multirow{2}{*}{SSIM} & \multirow{2}{*}{PSNR} & \multirow{2}{*}{SSIM} & \multirow{2}{*}{PSNR} & \multirow{2}{*}{SSIM} & \multirow{2}{*}{PSNR} & \multirow{2}{*}{SSIM} \\ \hline
1 & 25.943 & 0.835 & 25.563 & 0.815 & 25.181 & 0.808 & 24.747 & 0.783 & 25.639 & 0.818 \\ \hline
2 & 25.916 & 0.913 & 25.590 & 0.904 & 25.395 & 0.900 & 25.139 & 0.894 & 25.632 & 0.905 \\ \hline
3 & 26.013 & 0.878 & 25.247 & 0.857 & 24.810 & 0.846 & 24.308 & 0.826 & 25.379 & 0.859 \\ \hline
4 & 29.951 & 0.901 & 29.262 & 0.873 & 28.608 & 0.854 & 28.997 & 0.864 & 28.843 & 0.866 \\ \hline
5 & 31.974 & 0.981 & 31.901 & 0.979 & 31.818 & 0.979 & 31.064 & 0.978 & 31.488 & 0.979 \\ \hline
6 & 26.373 & 0.909 & 25.820 & 0.899 & 25.370 & 0.890 & 24.974 & 0.88 & 25.814 & 0.896 \\ \hline
7 & 31.601 & 0.981 & 31.248 & 0.979 & 31.084 & 0.979 & 30.522 & 0.977 & 31.069 & 0.979 \\ \hline
8 & 28.659 & 0.969 & 27.992 & 0.966 & 27.275 & 0.959 & 26.698 & 0.953 & 27.823 & 0.963 \\ \hline
9 & 31.145 & 0.953 & 30.539 & 0.948 & 30.237 & 0.949 & 29.517 & 0.933 & 30.449 & 0.942 \\ \hline
10 & 30.281 & 0.939 & 29.601 & 0.930 & 29.214 & 0.928 & 28.721 & 0.914 & 29.581 & 0.929 \\ \hline
11 & 24.853 & 0.859 & 24.098 & 0.832 & 23.738 & 0.828 & 23.388 & 0.805 & 24.258 & 0.839 \\ \hline
12 & 25.654 & 0.816 & 24.718 & 0.751 & 24.441 & 0.739 & 24.274 & 0.741 & 24.904 & 0.771 \\ \hline
13 & 33.381 & 0.966 & 33.302 & 0.964 & 33.282 & 0.964 & 32.426 & 0.959 & 32.777 & 0.961 \\ \hline
14 & 29.901 & 0.846 & 29.631 & 0.840 & 29.753 & 0.832 & 29.253 & 0.822 & 29.645 & 0.833 \\ \hline
15 & 27.119 & 0.904 & 26.878 & 0.897 & 26.755 & 0.894 & 26.422 & 0.89 & 26.841 & 0.898 \\ \hline AVG. & 28.584 & 0.910 & 28.093 & 0.896 & 27.797 & 0.890 & 27.363 & 0.881 & 28.009 & 0.896 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Performance evaluation for the small texture dataset.