# Image Resolution Enhancement of Highly Compressively Sensed CT/PET Signals
## 7 Results
The first with all the channels active (as the reference) and one with eight equidistant detectors shut down (subsampled, 12% of the channels have been removed from the datasets). The subsampled sinogram has been divided into two unique segments, each with sparse representation in their orthogonal domains. An iterative procedure was then used to reconstruct the PS sinogram using a hybrid algorithm utilising the conjugate gradient method solving the set of equations and blocked relaxations. In addition, the TV (total variation) is minimised for the first component to turn it into a more advantageous piecewise smooth model. Finally, the two parts were included to accomplish the sinogram, which was utilised to facet the native PS sinogram. This methodology can conceivably be utilised to create PET scans with precise quantitation while decreasing the number of readout channels. The examination has been directed for two unique kinds of information. The objective of the preliminaries was to assess the performance of the compressively sensed SR image reconstruction algorithm in direct battle against the native and naive algorithms. The further goal was to assess MR sampling scheme worthiness. In this experiment in vivo, as well as phantom, inputs have been analysed. Figures 3-9 expose obtained simulation results. The highest PSNR and the lowest MAE (Mean Absolute Error) values have confirmed the robustness of the presented algorithm, see Tables 1-4, 6, 7 and 9. In turn, Tables 5, 8 and 10 have shown that, using only 50 percent of the samples, pretty high PSNR values have been achieved. For all the registration algorithms listed in Table 11, the statistical analysis was evaluated using the mean and the standard deviation (std). The Target to Registration Errors (TRE) values and the \(p\)-values for the \(t\)-test with the significance level = 0.05 have been calculated, see Table 11. It has been shown that all the \(p\)-values are less than 0.002, which means that there is a significant difference between the globally optimal deformable registration method and its competitors. Figure 4: The Zubal phantom images based experiment results for the cases exposed in Table 2 rows numbers: 1, 2, 3. The bottom row refers to: Table 2 rows numbers: 4, 5, 6. Figure 3: The Shepp–Logan phantom images based experiment results for the cases exposed in Table 1 rows numbers: 1, 2, 3. The bottom row refers to: Table 1 rows numbers: 4, 5, 6. Figure 5: The XCAT phantom images based experiment results. The upper row: two CT scans with simulated motion artefacts. The bottom row shows the super-resolution CT scan. Figure 6: CT low-resolution vs. Super-Resolution Images. (**A**) LR input; (**B**) B-spline Cubic interpolation; (**C**) Non-Rigid Multi-Modal 3D Medical Image Registration Based on Foveated Modality Independent Neighbourhood Descriptor [25]; (**D**) Enhanced deep residual networks for single Image Super-Resolution [13]; (**E**) Image SR using very deep residual channel attention networks [14]; (**F**) Residual dense network for image SR [15]; (**G**,**H**) the presented algorithm (the right one exposes details). (The tests were performed using 4096 Projection lines/Coefficients and the ATA reconstruction algorithm.) Figure 8: The performance of various super image reconstruction algorithms CT-in vivo trials input images. From left to right: (**A**) LR input; (**B**) B-spline Cubic interpolation; (**C**) Non-Rigid Multi-Modal 3D Medical Image Registration Based on Foveated Modality Independent Neighbourhood Descriptor [25]; (**D**) Enhanced deep residual networks for single Image Super-Resolution [13]; (**E**) Image super-resolution using very deep residual channel attention networks [14]]; (**F**) Residual dense network for Image Super-Resolution [15]; (**G**) the presented algorithm. Figure 7: The performance of the presented algorithm for the data from Table 6. All the \(y\)-axes of the bee swarm plots represent PSNR values [dB]. Figure 9: An example of CT and FDG-PET data sets.