## 2 Adaptive PCNN Combined with GWO and BEMD
### The Proposed BEMD-GWO-PCNN Algorithm
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Iterations**} & \multicolumn{2}{c}{**PSO**} & \multicolumn{2}{c}{**GACA**} & \multicolumn{2}{c}{**GWO**} \\ \cline{2-7}  & **BFV** & \(\mathbf{T}\) & **BFV** & \(\mathbf{T}\) & **BFV** & \(\mathbf{T}\) \\ \hline
20 & 1146.1940 & 0.02028 & 955.8790 & 0.1327 & 1381.7552 & 0.01928 \\
50 & 22.2860 & 0.03127 & 5.7107 & 0.2156 & 88.7404 & 0.02600 \\
80 & 6.6016 & 0.06410 & 1.8234 & 0.3124 & 13.8223 & 0.04532 \\
120 & 2.8934 & 0.07290 & 1.2502 & 0.4133 & 2.2733 & 0.03903 \\
200 & 0.1724 & 0.07631 & 0.4912 & 0.6303 & 1.7210 & 0.05433 \\
250 & 0.06687 & 0.1040 & 0.2456 & 1.3923 & 1.2444 & 0.1011 \\
300 & 0.009223 & 0.1586 & 0.0003280 & 1.8772 & 0.5071 & 0.1251 \\
400 & 0.003017 & 0.2583 & 0.002050 & 2.3940 & 1.3801 & 0.1436 \\
500 & \(1.5440\times 10^{-5}\) & 0.3397 & 0.02507 & 3.4915 & 0.5012 & 0.1881 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The calculated function fitness values through different iterations and required run time for optimization by the PSO, GACA, and GWO. Figure 3: The flowchart of the proposed noise suppression method. ```

**BEMD decomposition**:

**Input raw image**\(df\)

**Generate** decomposed **BIMF**\(u_{k}\) and residue \(r_{k}\). **Boundary treatment**:

Generate edge-symmetric extension, make the original image \((m,n)\) change into \((m+6,n+6)\);

**Initialize the PCNN parameters**:

**Initialize**\(\alpha_{T}\), \(\beta_{T}\), \(\
u_{T}\) and \(W_{ijkl}\) the number of pass \(N\), step length \(\Delta_{i}\);

**GWO algorithm implement**:

Keep each pixel in an unignited condition;

Obtained optimized \(\alpha_{T}\), \(\beta_{T}\) and \(\
u_{T}\)

**Contaminated points detection and treatment in PCNN**:

**Calculate** every neuron \(L_{ij}[n]\) values in \(3\times 3\) neighboring region using Equation (7) adjust the threshold using Equation (10); calculate the neuron internal modulation signal \(E_{ij}[n]\) using Equation (9);

_if_ a neuron \((i,j)\) is ignited in \(3\times 3\) neighbor region and more than 4 adjacent neurons are unignited, the \((i,j)\) pixels brightness will decline an \(\Delta_{i}\)_end;_

_if_ a neuron \((i,j)\) is unignited in \(3\times 3\) neighbor region and more than 4 adjacent neurons are ignited, the \((i,j)\) pixels brightness will increase a \(\Delta_{i}\)_end;_

_Otherwise_ the pixels brightness values of the \((i,j)\) won't change _end;_

**Compare**\(u_{ij}[n]\) values and \(E_{ij}[n]\) values, record the neuron output, ignited or unignited;

\(N=N-1\), if \(N\
eq 0\), return to contaminated points detection and treatment

**Filtering processing**:

For further noise reduction, apply median filter to the treated image

_end;_

**Otherwise, end. **

**Reconstruct** each component \(u_{k}\) and \(r_{k}\), and obtain the final denoising image

**Algorithm 3** The Adaptive PCNN Optimized by the GWO and BEMD Algorithm

## 3 Experimental Results and Analysis

The effectiveness of the proposed PCNN-BEMD when combined with the GWO method can be verified experimentally. The best parameters for the PCNN can be obtained from GWO, from which noise separation can be obtained and a pre-denoising process can be completed; then, a median

Figure 4: **(a)** The 3D surface plot of the tested function in the parameter space: \(Y=sum(ans((x+0.5))^{\wedge 2})\), \(x_{1},x_{2}\in[-100,100]\), \(step=2\); **(b)** the calculated convergence curve through 500 iterations of the grey wolf optimization (GWO), genetic ant colony algorithm (GACA), and particle swarm optimization (PSO) method. filter will be applied for noise reduction. The BEMD is performed within the PCNN to improve its performance. The experimental implementation results (Figures 5 and 6) for the proposed method are validated. The original Lena image and the Pepper image are in JPG format and the original image sizes are \(3\times 512\times 512\) and \(3\times 750\times 1020\), respectively. The images were both conducted gray processing in advance then are preprocessed by decomposition using the BEMD.