# Serial Decoders-Based Auto-Encoders for Image Reconstruction
## 4 Experiments
### Experimental Results
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Algorithms**} & \multicolumn{8}{c}{**SSIM**} \\ \multicolumn{2}{c}{**ASSIM**} & \multicolumn{8}{c}{**SSIM**} \\ \cline{2-11}  & **Breast** & **Chest** & **Derma** & **Oct** & **Axial** & **C Coronal** & **Sagittal** & **Pathology** & **Pneumonia** & **Retina** \\ \hline AE & 0.88868 & 0.98363 & 0.97103 & 0.98851 & 0.81806 & 0.82470 & 0.79883 & 0.89644 & 0.94760 & 0.97366 \\  & 0.00000 & 0.00000 & 0.00000 & 0.00000 & 0.00000 & 0.00000 & 0.00000 & 0.00000 & 0.00000 & 0.00000 \\ \hline GCDAE & 0.89228 & 0.98836 & 0.97103 & 0.98856 & 0.92817 & 0.83320 & 0.84211 & 0.89720 & 0.95782 & 0.97751 \\  & 0.00360 & 0.00473 & 0.00000 & 0.00005 & 0.11011 & 0.00850 & 0.04328 & 0.00076 & 0.01022 & 0.00385 \\ \hline RCDAE & **0.90574** & **0.98857** & **0.97396** & **0.98927** & 0.90092 & 0.83467 & 0.84180 & 0.89724 & **0.96115** & 0.98233 \\  & **0.01706** & **0.00494** & **0.00295** & **0.00076** & 0.08286 & 0.00997 & 0.04297 & 0.00080 & **0.01355** & 0.00867 \\ \hline ACDAE & 0.87883 & 0.98682 & 0.96834 & 0.98780 & 0.93012 & 0.83450 & **0.84302** & 0.89548 & 0.95469 & 0.97892 \\  & \(-\)0.00985 & 0.00319 & \(-\)0.00269 & \(-\)0.00071 & 0.11206 & 0.00980 & **0.04419** & \(-\)0.00096 & 0.00709 & 0.00526 \\ \hline RACDAE & 0.89908 & 0.98543 & 0.97028 & 0.98832 & 0.89931 & **0.83494** & 0.84155 & 0.89594 & 0.95784 & 0.98067 \\  & 0.01040 & 0.00180 & \(-\)0.00075 & \(-\)0.00019 & 0.08125 & **0.01024** & 0.04272 & \(-\)0.00050 & 0.01008 & 0.00701 \\ \hline AAE & 0.88527 & 0.97240 & 0.97052 & 0.98858 & 0.81498 & 0.83347 & 0.84202 & 0.89603 & 0.95356 & 0.97646 \\  & \(-\)0.00341 & \(-\)0.01230 & \(-\)0.00051 & 0.00007 & \(-\)0.00308 & 0.00877 & 0.04319 & \(-\)0.00041 & 0.00596 & 0.00280 \\ \hline GCDAAE & 0.89139 & 0.98847 & 0.97054 & 0.98867 & **0.93736** & 0.83347 & 0.84261 & 0.89714 & 0.95811 & 0.97839 \\  & 0.00271 & 0.00484 & \(-\)0.00053 & 0.00016 & **0.11930** & 0.01000 & 0.04378 & 0.00070 & 0.01051 & 0.00473 \\ \hline RCDAAE & 0.89772 & 0.98852 & 0.97262 & 0.98920 & 0.89873 & 0.83321 & 0.84179 & **0.89747** & 0.96076 & **0.98261** \\  & 0.00094 & 0.00489 & 0.00159 & 0.00069 & 0.08607 & 0.00851 & 0.04296 & **0.00103** & 0.01316 & **0.00895** \\ \hline ACDAAE & 0.88895 & 0.98673 & 0.96987 & 0.98769 & 0.93286 & 0.83421 & 0.84129 & 0.89695 & 0.95389 & 0.97942 \\  & 0.00027 & 0.00310 & \(-\)0.00116 & \(-\)0.00082 & 0.11480 & 0.00951 & 0.04246 & 0.00051 & 0.00629 & 0.00576 \\ \hline RACDAE & 0.90113 & 0.98831 & 0.97062 & 0.98865 & 0.90580 & 0.83380 & 0.83975 & 0.89728 & 0.95720 & 0.98117 \\  & 0.01245 & 0.00468 & \(-\)0.00041 & 0.00014 & 0.08702 & \(-\)0.00090 & 0.04092 & 0.00084 & 0.00510 & 0.00751 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Experimental results on the MMNIST data set. Since the proposed RCDAE algorithm owns the best performance, it is taken as an example. Figure 15: Experimental results of different algorithms on the four data sets. Figure 16: Reconstruction images on the MNIST data set. For each subfigure, the top row shows the original images, the middle row shows the recovery images of AE, and the bottom row shows the recovery images of RCDAE. The recovery images on the MNIST data set are shown in Figure 16. For each subfigure in Figure 16, the top row shows the original images, the middle row shows the recovery images of AE, and the bottom row shows the recovery images of RCDAE. It is not easy to find the SSIM differences between AE and RCDAE in Figure 16. Therefore, the marked re-establishment images on the MNIST data set are illustrated in Figure 17. The left column shows the original images, the middle column shows the re-establishment images of AE, and the right column shows the re-establishment images of RCDAE. It is easy to notice the SSIM differences between AE and RCDAE in the red marked squares in Figure 17.  
Figure 17: Marked reconstruction images on the MNIST data set. Figure 18: Reconstruction image on the EMNIST data set (**big letters**).