# Image Resolution Enhancement of Highly Compressively Sensed CT/PET Signals
## 8 Discussion  
In this paper, the algorithm for improving CT/PET hybrid scanner's image resolution keeping acquisition time at as low a level as possible is presented. The obtained results show an improved spatial resolution and quality, see Figures 3-9. The procedure applied to lesions that are considered to be potentially malignant or pre-malignant unveil a higher ability to detect them due to the improved resolution and readability. Designing and developing of CT/PET scanners is still an open issue and has been recognised as the grand challenge of the next few years. In this work, it has been proven that the proposed super-resolution algorithm based on modifications made to a well-known Iterative Back Projection scheme produces highly accurate results. The extensive studies confirmed that the algorithm might be applied even if very challenging medical modalities are the subject of interest. This paper also \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Compressed Sensing Quality \({}^{*}\) [\%]** & **PSNR [dB]** & **MAE** & **N** & **M** & **SD** & **t(99)** & \(p\) \\ \hline
20 & 19.40 & 21.03 & 100 & 19.40 & 0.03 & \(-1.502\) & 0.131 \\ \hline
40 & 22.89 & 19.44 & 100 & 22.89 & 0.02 & \(-1.016\) & 0.323 \\ \hline
50 & 34.59 & 13.37 & 100 & 34.59 & 0.03 & \(-1.284\) & 0.102 \\ \hline
80 & 36.21 & 15.58 & 100 & 36.21 & 0.03 & \(-1.415\) & 0.123 \\ \hline
100 & 37.63 & 13.21 & 100 & 37.63 & 0.03 & \(-1.420\) & 0.103 \\ \hline \hline \end{tabular} \({}^{*}\) Compressed Sensing quality ratio refers to the remaining number of the input samples in comparison with fully sampled scans, i.e., 60 means that 40% of the fully sampled scan samples was removed.  
\end{table} 
Table 10: The performance of the presented algorithm for the data from Figure 9 at different Compressed Sensing quality ratios. \begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Registration Algorithm** & \multicolumn{3}{c}{**TRE [Voxels ]**} \\ \cline{2-5}
**Mean** & **Std** & _p-Value_ \\ \hline No registration applied & 4.8 & 2.7 & \textless{}0.002 \\ \hline Entropy images based SSD & 2.5 & 0.7 & \textless{}0.002 \\ \hline Non-rigid multi modal medical & & & \\ image registration by combining & 2.2 & 0.3 & \textless{}0.002 \\ L-BFGS-B with cat swarm optimisation & & & \\ \hline Modality independent neighborhood descriptor & 1.8 & 0.1 & \textless{}0.002 \\ \hline Globally optimal deformable registration & 1.6 & 0.1 & \textless{}0.002 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: The stats of several motion estimation procedures have been compared with the applied one. \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline
**Reconstruction Algorithm** &
\begin{tabular}{c} **PSNR** \\ **[dB]** \\ \end{tabular} & **MAE** & **N** & **M** & **SD** & **t(99)** & \(p\) \\ \hline LR input & 21.11 & 20.33 & 100 & 21.11 & 0.03 & \(-1.282\) & 0.193 \\ \hline B-spline Cubic interpolation & 24.26 & 18.41 & 100 & 24.26 & 0.03 & \(-1.451\) & 0.142 \\ \hline Non-Rigid Multi-Modal 3D Medical Image Registration Based & & & & & & & \\ on Foveated Modality Independent Neighborhood Descriptor & 33.22 & 16.83 & 100 & 33.22 & 0.03 & \(-1.373\) & 0.173 \\ \hline Enhanced deep residual networks for single image & 31.03 & 15.71 & 100 & 30.33 & 0.03 & \(-1.281\) & 0.214 \\ super-resolution & & & & & & & \\ \hline Image super-resolution using very deep residual chanel & & & & & & & \\ attention networks & & & & & & & \\ \hline Residual dense network for image super-resolution & 32.44 & 14.60 & 100 & 32.44 & 0.03 & \(-1.311\) & 0.213 \\ \hline The presented algorithm & 34.59 & 13.37 & 100 & 34.59 & 0.03 & \(-1.284\) & 0.102 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Statistical parameters of the model performance metrics for Figure 9.  
shows the successful application of a super-resolution algorithm to enhance the resolution of CT as well as PET images.