# On-the-Fly Machine Learning for Improving Image Resolution in Tomography
## 4 Results
### Simulations
In the pixel-limited dataset, the low-resolution input suffers from partial volume effects, where some voxels contain more than one material. In this case, the foam and void contributions to a voxel are averaged, which leads to jagged edges. The high-resolution data are significantly sharper, but still has some non-smooth texture in the foam and voids. The output of method A with nine input slices makes the edges as sharp as in the high-resolution image, and removes \begin{table}
\begin{tabular}{l l l l} \hline \hline  & **Foam** & **Foam** & **Oatmeal** \\ \cline{2-4}  & **Pixel-Limited** & **Optics-Limited** & \\ \hline Detector & & & \\ Shape & \(1000\times 1000\) & \(1000\times 1000\) & \(1536\times 1944\) \\ Pixel size & \(0.0012\) & \(0.0012\) & \(75\)\(\mu\)m \\ Number of angles & \(1500\) & \(1500\) & \(2000\) \\ \hline Full object & & & \\ Grid shape & \(1064\times 1064\times 1064\) & \(1064\times 1064\times 1064\) & \(1647\times 2084\times 2084\) \\ Voxel size & \(0.0012\) & \(0.0012\) & \(68.26\)\(\mu\)m \\ \hline Central ROI & & & \\ Grid shape & \(888\times 664\times 664\) & \(888\times 664\times 664\) & \(1364\times 1304\times 1304\) \\ Voxel size & \(0.0003\) & \(0.0003\) & \(17.07\)\(\mu\)m \\ \hline Top ROI & & & \\ Grid shape & \(880\times 664\times 664\) & \(880\times 664\times 664\) & \(1364\times 1304\times 1304\) \\ Voxel size & \(0.0003\) & \(0.0003\) & \(17.07\)\(\mu\)m \\ \hline Training epochs & & & \\ Method A 9 slices & \(230\) & \(230\) & \(30\) \\ Method A 1 slice & \(260\) & \(250\) & \(40\) \\ Method B 1 slice & \(1000\) & \(1000\) & \(950\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: A summary of the pixel and voxel grids used for the reconstructions of the full object and regions of interest (ROIs). For each dataset, the network was trained by up-sampling the input (method A) with a slab of nine slices and one slice as input, and by down-sampling the target (method B) with a slab of one slice as input. \begin{table}
\begin{tabular}{l l l l l l l l} \hline \hline \multirow{2}{*}{**Dataset**} & \multicolumn{2}{c}{**Method A**} & \multicolumn{2}{c}{**Method A**} & \multicolumn{2}{c}{**Method B**} & \multicolumn{2}{c}{**Cubic up-Sampling**} \\  & **Slab:** \(\boldsymbol{\hat{9}}\) **Slices** & **Slab:** \(\boldsymbol{\hat{1}}\) **Slice** & **Slab:** \(\boldsymbol{\hat{1}}\) **Slice** & & \\ \hline  & MSE & SSIM & MSE & SSIM & MSE & SSIM & MSE & SSIM \\ \hline Pixel-limited & **0.0044** & **0.9578** & 0.0089 & 0.9281 & 0.0111 & 0.8065 & 0.0125 & 0.6893 \\ Optics-limited & **0.0143** & **0.8275** & 0.0154 & 0.8220 & 0.0178 & 0.8135 & 0.0463 & 0.6038 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Foam ball phantom: comparison of the MSE and SSIM between the output of the three approaches described in this section and cubic up-sampling. For each dataset and metric, the best results are shown in bold. the non-smooth texture in the foam and voids. Moreover, it does not introduce any voids where there are none in the target data. Method A with one input slice performs similarly, but has some difficulty with features that are rapidly introduced in the vertical direction. This is apparent in the magnified image in Figure 7, where the top or bottom of one void in the input data are not correctly removed. As discussed before, method B performs worse than method A when the high-resolution features cannot be represented on the coarse grid. In the optics-limited dataset, both low- and high-resolution slices are less sharp than in the pixel-limited case. Due to the additional blur on the projection data, some of the smaller features in the low-resolution image cannot easily be distinguished. Nonetheless, the output of both methods A has significantly improved resolution and is visually similar to the target slice. With few exceptions, all voids in the output are round, and, without exception, all voids in the output are also present in the target.