## 2 Adaptive PCNN Combined with GWO and BEMD
### The Proposed BEMD-GWO-PCNN Algorithm
Consequently, the decomposed BIMFs and the corresponding residues can be presented. The original images have salt and pepper noise superimposed on them with density \(\delta\)2 = 0.05, i.e., the percentage of the image area that contains the noise value. Based on observation of the polluted image, the original outlines and the details of these images cannot be distinguished clearly because of the noise interference. BIMFs 1 and 2 contain numerous noise points, such as the irregular black and white clouds of points. The residue contains a relatively small number of noise points, while also containing plentif original details of both the image and the main frame. Therefore, each component should be purified using the PCNN filter. Before PCNN filtering, the optimal parameters must be determined using the GWO. After the relevant calculation processes for the encircling, hunting and attacking operators, the values of \(\alpha_{T}\), \(\beta_{T}\), and \(v_{T}\) that correspond to each component are presented (Table 2). Obviously, the parameters are different for each image component. However, there are no significant data rules between these parameters. Using the calculated parameters above, optimized PCNN filtering is applied to the noise-polluted Lena and Pepper images for denoising. The noise suppression results for BIMFs 1 to 2 and the residue

Figure 5: Results of decomposition by bidimensional empirical mode decomposition (BEMD) for the raw Lena image: (**a**) the original image, (**b**) the noise polluted image, (**c**) the decomposed bidimensional intrinsic mode function (BIMF) 1, (**d**) the decomposed BIMF 2, (**e**) the residue. Figure 6: Results of decomposition by BEMD for the raw Pepper image: (**a**) the original image, (**b**) the noise polluted image, (**c**) the decomposed BIMF 1, (**d**) the decomposed BIMF 2, (**e**) the residue. (Figures 7d-i and 8d-i) show that the heavy salt and pepper noise is eliminated. The valid image details are extracted effectively, and the image outlines and edges are recovered well. Finally, the reconstructed images (Figures 7d and 8d) with the decomposed components enable detailed comparison of the noise suppression effects of the different denoising methods, including the median filter, the particle swarm optimization method (PSO-PCNN), the conventional random PCNN (COR-PCNN) method, the genetic ant colony algorithm (GACA-PCNN) and the non-linear complex diffusion process technique (NLCDP) in the tBEMD domains (tBEMD-NLCDP). Observations indicate that our proposed BEMD-GWO-PCNN approach more than matches the other methods. When compared with the original images, the experimentally reconstructed images show a good performance in terms of the recovery of image details. However, the other methods appear to have processing blur or certain amounts of residual noise. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Mode**} & \multicolumn{3}{c}{**Lena**} & \multicolumn{3}{c}{**Pepper**} \\ \cline{2-7}  & \(\mathbf{\alpha_{T1}}\) & \(\mathbf{\beta_{T1}}\) & \(\mathbf{V_{T1}}\) & \(\mathbf{\alpha_{T2}}\) & \(\mathbf{\beta_{T2}}\) & \(\mathbf{V_{T2}}\) \\ \hline BIMF1 & 0.107 & 0.260 & 273.858 & 0.0318 & 0.0344 & 229.263 \\ BIMF2 & 0.0594 & 0.423 & 119.719 & 0.338 & 0.730 & 256.035 \\ Residue & 0.125 & 0.784 & 222.941 & 0.229 & 0.497 & 100.000 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The experimentally obtained optimal parameters data for each decomposed component corresponding to the Lena and Pepper image. Figure 7: Lena image: (**a–c**) the noise-suppression BIMF 1 to 2 and the residue, (**d**) The proposed BEMD-GWO-pulse-coupled neural network (PCNN) reconstruction image, (**e**) median filter, (**f**) PSO-PCNN method, (**g**) GACA-PCNN, (**h**) conventional random parameters (COR)-PCNN, (**i**) tBEMD-non-linear complex diffusion process (NLCDP).