# A Novel Guided Box Filter Based on Hybrid Optimization for Medical Image Denoising
## 4 Results and Discussion
### Result Analysis  
In this section, first, a comparison is provided for the ablation study of the designed hybrid approach with other bio-inspired optimization approaches. This analysis emphasizes the behavior of hybrid cuckoo particle swarm optimization with decimation box filters concerning medical images. The learning parameters for each bio-inspired optimization algorithm are listed in Table 1.  
Figure 5 shows the convergence analysis of optimization-based filters with different algorithms, such as PSO, firefly, cuckoo, and the proposed HCPSO model. The number of iterations taken is 100 epochs, and it shows the fitness value vs. the number of iteration curves. The hybrid model fitness value curve shows a better convergence curve. The graph of the designed hybrid approach shows retrieval of the best cost function. Table 2 shows the optimal parameter values for GDBF + HCPSO with different algorithm parameters. The first set of parameters is related to the filter order, which determines the complexity of the filter. The values tested in this case are 20, 25, 30, and 35. The best value is obtained at order 30. The next set of parameters is the population size, such as 5, 10, 15, and 20. The corresponding PSNR values for these population sizes are 35.75, 35.79, 35.72, and 35.63, respectively. In this optimal population size was 10. Finally, the table includes the initial training parameter (Initial Tr) with values of 0.01, 0.02, and 0.03. The associated PSNR values are 35.79, 35.49, and 35.62, respectively. The optimal initial Tr was 0.01. \begin{table}
\begin{tabular}{l l} \hline
**Algorithm** & **Parameter** \\ \hline \multirow{4}{*}{Particle swarm optimization} & Size of particle = 20 \\  & No. of iterations = 100 \\  & Max inertia wt. = 0.95 \\  & Min inertia wt. = 0.4 \\ \hline \multirow{4}{*}{Firefly algorithm} & Size of fireflies = 15 \\  & No. of iterations = 100 \\  & Absorption coefficient = 1 \\  & Light absorption coefficient = 1 \\  & Mutation value = 0.2 \\ \hline \multirow{4}{*}{Cuckoo search} & Size of nests = 15 \\  & No. of iterations = 100 \\  & Mutation probability = 0.1 \\  & Scaling factor = 1.5 \\ \hline \multirow{4}{*}{Hybrid cuckoo particle swarm optimization} & Size of particle = 15 \\  & Size of nests = 10 \\  & Max inertia wt. = 0.9 \\  & Min inertia wt. = 0.4 \\  & No. of iterations = 100 \\  & Mutation probability = 0.1 \\  & Scaling factor = 1.5 \\ \hline \end{tabular}
\end{table} 
Table 1: Parameters for bio-inspired optimization algorithms. Figure 5: Convergence analysis of optimization-based filters. Figure 6 shows the visual representation after denoising. Hereafter, RGB decomposition, LPF, is applied to each component individually. Its outcome with a varying cutoff frequency \(D_{o}\) is represented in Figure 6. Here, \(D_{o}=192\) shows the best outcome. Then, it is decomposed using 2 DWT, and coefficient optimization is performed using HCPSO. After optimization and noise coefficient removal, 2 DWT reconstruction is performed, whose outcome is represented below. Finally, all DWT components are combined to visualize the final image. Below, Figure 6 represents stepwise image reconstruction. Table 3 shows the performance analysis of conventional filters, such as the bilateral filter and FIR filters, with the proposed bio-inspired optimization algorithms, i.e., the HCPSO model. The number of images taken for testing was 25. Table 3 shows the performance analysis by considering PSNR, SSIM, and FSIM. The results analysis was performed on an input medical image of size 192 \(\times\) 192. The input image is corrupted with noise, having variable variance ranging from 0.01 to 0.09. In Table 3, it is observed that the proposed HCPSO has achieved the highest PSNR, SSIM, and FSIM values. Therefore, from this analysis, it is observed that the designed hybrid HCPSO model shows fast and best convergence towards the best solution compared to conventional approaches.