# Universal Behavior of the Image Resolution for Different Scanning Trajectories
## 3 Results and Discussion
### Image Reconstruction
\begin{table}
\begin{tabular}{c c} \hline Pixel Size & 0.5 \(H_{max}\) of BC mesh \\ \(N_{p}\) Values & 20, 40, 60, 80, 100 \\ Particle Diameter & 30 \(\times\) 10\({}^{-9}\) m \\ Temperature & 310 K \\ Permeability of Air & 4\(\pi\times\) 10\({}^{-7}\) N/A\({}^{2}\) \\ Concentration of Particles & 1.5 mol/m\({}^{3}\) \\ Molar Mass of SPION & 0.231 kg/mol \\ Density of SPION & 5170 kg/m\({}^{3}\) \\ \hline \end{tabular}
\end{table} 
Table 5: Parameters used for reconstruction of image. The NTE for various scanning methods as a function of \(N_{P}\) was calculated and illustrated in Figure 6d. It is important to note that the NTE is expressed as a percentage rather than an intensity unit like the RMSE. For the BC trajectory, it should be noted that this pattern is not as dense, and it has a larger \(H_{max}\) compared to other trajectories. This means that this scanning technique detects less signal than others (refer to Table 2). Figure 6a,b depict the trend of the PSNR and SSIM for all trajectories, demonstrating that the value is highest when \(N_{P}\) is lowest but decreases when \(N_{P}\) increases. This is because the size of the BC mesh is shrinking and becoming more difficult to detect. As can be seen in Figure 6c,d, the RSME and NTE levels start out being low but rise as \(N_{P}\) increases, plateauing at a large \(N_{P}\). In general, the trends of PSNR/SSIM and RMSE/NTE are inverse, which means that when the error is low, PSNR and SSIM must be high, and vice versa. Despite the fact that the mesh was created using the BC method and the FF value is greater than 90% for all conditions, this BC scanning technique shows poor results in terms of reconstruction. The primary cause of this is the formation of the pattern from this trajectory, which is quite sparse and incapable of accurately detecting the objects. Among the methods already described, the TL trajectory has the most consistent and regular pattern. Unfortunately, although having a regular pattern, the image resolution is lower (i.e., \(H_{max}\) value is larger) than the SL and RL trajectories (see Table 2), which results in a lower-quality reconstructed image. Figure 6a,b clearly demonstrate that the PSNR and SSIM values for the SL trajectory are comparable to the TL, and Figure 6c,d show that the values of RMSE and NTE are lower than those of other scanning techniques. This proves that the most appropriate technique for reconstruction of this NU phantom is the SL trajectory. Similar findings are obtained for the SL mesh (see Figure A4 in Appendix A), demonstrating that SL is the best scanning trajectory for generating high signal-to-noise and low error for image reconstruction. Our results confirmed previously reported findings that the SL trajectory is superior to most other trajectories because it produced excellent image quality even at low scanning densities [8,24]. Figure 6: Numerically generated values of reconstructed image using bidirectional Cartesian mesh for (**a**) PSNR, (**b**) SSIM, (**c**) RMSE, and (**d**) NTE over varying \(N_{P}\) for various scanning trajectories. Surprisingly, compared to the other trajectories, the RL produced the greatest RMSE and NTE values while attaining the lowest PSNR and SSIM values, which resulted in the worst reconstruction outcomes (see Figures 5 and 6). According to Table 2 and Figure 3e, RL has the lowest \(H_{max}\). However, it does not scan the corners of the FOV, as seen in Figure 1d. This could result in an increase in the RSME and NTE values at the corners of the image along with a decrease in the PSNR and SSIM. Additionally, the BC, SL, and RL trajectories all have the same repetition time. This means that for a trajectory with a much denser scanning pattern, the time spent continuously resting on the pixel is substantially less, but with a greater frequency. As a result, the short visit of the scan on the pixel may result in a lower signal-to-noise ratio and a higher error.