# A Novel Guided Box Filter Based on Hybrid Optimization for Medical Image Denoising
## 4 Results and Discussion
### Result Analysis
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Variance** & **Bilateral Filter** & **FIR** & **HCPSO** \\ \hline \multirow{8}{*}{PSNR} & 0.01 & 23.80 & 29.14 & 35.704 \\  & 0.03 & 17.41 & 25.46 & 33.981 \\  & 0.05 & 14.94 & 23.62 & 33.229 \\  & 0.07 & 13.50 & 22.22 & 32.967 \\  & 0.09 & 12.64 & 21.22 & 32.664 \\ \hline \multirow{8}{*}{SSIM} & **Variance** & **Bilateral Filter** & **LPF** & **HCPSO** \\ \cline{2-6}  & 0.01 & 0.26 & 0.56 & 0.916 \\  & 0.03 & 0.09 & 0.47 & 0.872 \\  & 0.05 & 0.06 & 0.41 & 0.843 \\  & 0.07 & 0.05 & 0.38 & 0.822 \\  & 0.09 & 0.04 & 0.35 & 0.798 \\ \hline \multirow{8}{*}{FSIM} & **Variance** & **Bilateral Filter** & **LPF** & **HCPSO** \\ \cline{2-6}  & 0.01 & 0.67 & 0.84 & 0.886 \\ \cline{1-1}  & 0.03 & 0.43 & 0.78 & 0.842 \\ \cline{1-1}  & 0.05 & 0.34 & 0.72 & 0.819 \\ \cline{1-1}  & 0.07 & 0.30 & 0.69 & 0.802 \\ \cline{1-1}  & 0.09 & 0.27 & 0.66 & 0.781 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparative analysis of conventional filters with proposed bio-optimized filter with respect to noise variance. 30 achieved better results, i.e., PSNR = 35.727, SSIM = 0.929, and FSIM = 0.887. Therefore, in this analysis, it was observed that the best filter order was 30, in which the HCPSO algorithm achieved better performance compared to others. Overall, the HCPSO algorithm performed consistently well across all three image quality metrics and all filter orders, making it a promising bio-inspired optimization algorithm for image-filtering applications. In Figure 7, the paper presents a visual comparison of bio-inspired algorithms, i.e., particle swarm optimization (PSO), firefly (FF) algorithm, cuckoo search (CS) optimization, and hybrid cuckoo particle swarm optimization (HCPSO) on all three datasets, as described above. For this, \(\sigma^{2}\) is kept at 0.01. Similarly, in Figure 8, the paper presents a visual comparison with the variable \(\sigma^{2}\). In both diagrams, it is seen that edges are preserved more in the designed HCPSO-based guided decimation box filter. \begin{table}
\begin{tabular}{l l l l l l} \hline \hline  & **Filter Order** & **PSO** & **FF** & **CS** & **HCPSO** \\ \hline \multirow{5}{*}{PSNR} & 20 & 33.509 & 33.094 & 34.342 & 35.162 \\  & 25 & 34.239 & 33.091 & 34.370 & 35.300 \\  & 30 & 33.758 & 33.100 & 34.868 & 35.727 \\  & 35 & 32.730 & 31.777 & 34.394 & 35.167 \\ \hline \hline \multirow{5}{*}{SSIM} & **Filter Order** & **PSO** & **FF** & **CS** & **HCPSO** \\ \cline{2-6}  & 20 & 0.696 & 0.647 & 0.693 & 0.924 \\  & 25 & 0.720 & 0.637 & 0.684 & 0.924 \\  & 30 & 0.639 & 0.655 & 0.678 & 0.929 \\  & 35 & 0.711 & 0.644 & 0.688 & 0.921 \\ \hline \hline \multirow{5}{*}{FSIM} & **Filter Order** & **PSO** & **FF** & **CS** & **HCPSO** \\ \cline{2-6}  & 20 & 0.502 & 0.494 & 0.571 & 0.882 \\ \cline{1-1}  & 25 & 0.531 & 0.487 & 0.583 & 0.882 \\ \cline{1-1}  & 30 & 0.495 & 0.477 & 0.558 & 0.887 \\ \cline{1-1}  & 35 & 0.533 & 0.472 & 0.586 & 0.878 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Performance analysis of bio-inspired optimization algorithms with respect to filter order. Figure 7: Visual comparison of different bio-inspired-optimization-based filters on (**a**) CHSEDB1 dataset, (**b**) MRI dataset, and (**c**) ultrasound dataset. Figure 8: Visual comparison of different bio-inspired optimization-based filters of variable \(\sigma^{2}\) on (**a**) CHSEDB1 dataset, (**b**) MRI dataset, and (**c**) ultrasound dataset. Figure 9 shows the performance of the HCPSO-based GDB filter on varying noise variance with the datasets CHSEDB1, MRI, and ultrasound. The variance varied from \(\sigma^{2}\) = 0.01 to \(\sigma^{2}\) = 0.09. PSNR, SSIM, and FSIM are the maximum for \(\sigma^{2}\) = 0.01, i.e., 35.77, 0.926, and 0.899, respectively, for the CHASEDB1 dataset. PSNR, SSIM, and FSIM are the maximum for \(\sigma^{2}\) = 0.01, i.e., 33.33, 0.925, and 0.915, respectively, for the MRI dataset. PSNR, SSIM, and FSIM are the maximum for \(\sigma^{2}\) = 0.01, i.e., 35.63, 0.928, and 0.904, respectively, for the ultrasound dataset.