## 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 \multicolumn{2}{c}{**Lena**} & \multicolumn{1}{c}{**Noise Image**} & \multicolumn{1}{c}{**PSO-PCNN**} & \multicolumn{1}{c}{**GACA-PCNN**} & \multicolumn{1}{c}{**tBEMD-NLCDP**} & \multicolumn{1}{c}{**BEMD-GWO-PCNN**} \\ \hline \multirow{4}{*}{\(\delta 2=0.1\)} & STD\({}_{1}\) & 38.874 & 46.596 & 43.899 & 42.191 & 46.626 \\  & MI\({}_{1}\) & 1.612 & 2.877 & 1.983 & 2.487 & 3.147 \\  & SSIM\({}_{1}\) & 0.170 & 0.817 & 0.957 & 0.612 & 0.955 \\  & PSNR\({}_{1}\) & 15.343 & 28.153 & 33.426 & 27.143 & 34.691 \\ \hline \multirow{4}{*}{\(\delta 2=0.2\)} & STD\({}_{2}\) & 35.421 & 38.945 & 46.937 & 36.487 & 54.672 \\  & MI\({}_{2}\) & 1.588 & 2.799 & 1.819 & 3.218 & 4.097 \\  & SSIM\({}_{2}\) & 0.0905 & 0.577 & 0.682 & 0.0667 & 0.806 \\  & PSNR\({}_{2}\) & 12.329 & 16.807 & 22.292 & 15.398 & 29.642 \\ \hline \multirow{4}{*}{\(\delta 2=0.3\)} & STD\({}_{3}\) & 32.709 & 42.861 & 45.364 & 41.315 & 48.498 \\  & MI\({}_{3}\) & 1.097 & 2.614 & 1.864 & 2.446 & 2.695 \\ \cline{1-1}  & SSIM\({}_{3}\) & 0.0605 & 0.726 & 0.592 & 0.782 & 0.793 \\ \cline{1-1}  & PSNR\({}_{3}\) & 10.576 & 20.265 & 23.680 & 18.346 & 26.359 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of the adaptive PCNN combined with BEMD method with other current denoising methods corresponding to different noise intensity values \(\delta\) in Lena. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Results**} & \multicolumn{4}{c}{**Lena**} & \multicolumn{4}{c}{**Pepper**} \\ \cline{2-9}  & _STD_ & _MI_ & _SSIM_ & _P_SNR & _STD_ & _MI_ & _SSIM_ & _PSNR_ \\ \hline Unprocessed image & 28.042 & 0.679 & 0.109 & 13.853 & 5.684 & 1.436 & 0.106 & 10.241 \\ BIMF 1 & 0.187 & 0.643 & \(-\)0.107 & 6.581 & 5.671 & 0.100 & \(-\)0.015 & 5.671 \\ BIMF 2 & 14.619 & 0.078 & 0.034 & 6.840 & 7.241 & 0.413 & 0.023 & 5.685 \\ Residue & 36.361 & 1.305 & 0.186 & 15.749 & 11.029 & 1.644 & 0.286 & 15.357 \\ BEMD-GWO-PCNN & 53.316 & 2.368 & 0.788 & 23.159 & 17.774 & 4.262 & 0.607 & 21.774 \\ GACA-PCNN & 50.006 & 1.804 & 0.599 & 19.532 & 15.685 & 3.240 & 0.596 & 18.029 \\ COR-PCNN & 45.612 & 1.689 & 0.414 & 16.925 & 12.684 & 2.165 & 0.387 & 17.963 \\ PSO-PCNN & 48.469 & 1.971 & 0.683 & 20.007 & 15.357 & 2.514 & 0.439 & 20.684 \\ Median filter & 45.348 & 1.718 & 0.442 & 19.078 & 10.685 & 2.023 & 0.326 & 17.033 \\ tBEMD-NLCDP & 47.366 & 1.793 & 0.527 & 20.223 & 15.388 & 2.854 & 0.546 & 18.003 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Results from an experimental evaluation comparing indicator values of standard deviation (STD), mutual information (MI), structural similarity index measurement (SSIM) and peak signal to noise ratio (PSNR) of the unprocessed images with those from different noise reduction methods. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{2}{c}{**Pepper**} & \multicolumn{1}{c}{**Noise Image**} & \multicolumn{1}{c}{**PSO-PCNN**} & \multicolumn{1}{c}{**GACA-PCNN**} & \multicolumn{1}{c}{**tBEMD-NLCDP**} & \multicolumn{1}{c}{**BEMD-GWO-PCNN**} \\ \hline \multirow{4}{*}{\(\delta 2=0.1\)} & STD\({}_{1}\) & 45.605 & 51.573 & 48.157 & 49.253 & 51.685 \\  & MI\({}_{1}\) & 1.703 & 2.403 & 1.961 & 2.381 & 2.515 \\  & SSIM\({}_{1}\) & 0.0427 & 0.854 & 0.701 & 0.861 & 0.906 \\  & PSNR\({}_{1}\) & 15.246 & 32.224 & 26.358 & 30.269 & 32.362 \\ \hline \multirow{4}{*}{\(\delta 2=0.2\)} & STD\({}_{2}\) & 42.539 & 50.633 & 45.078 & 44.328 & 51.954 \\  & MI\({}_{2}\) & 1.634 & 2.090 & 2.177 & 1.933 & 2.386 \\  & SSIM\({}_{2}\) & 0.0272 & 0.855 & 0.502 & 0.724 & 0.878 \\  & PSNR\({}_{2}\) & 12.274 & 24.009 & 28.086 & 27.913 & 29.966 \\ \hline \multirow{4}{*}{\(\delta 2=0.3\)} & STD\({}_{3}\) & 40.205 & 50.552 & 52.705 & 49.251 & 53.256 \\  & MI\({}_{3}\) & 1.607 & 2.426 & 1.945 & 1.837 & 2.432 \\ \cline{1-1}  & SSIM\({}_{3}\) & 0.0903 & 0.562 & 0.596 & 0.514 & 0.709 \\ \cline{1-1}  & PSNR\({}_{3}\) & 10.566 & 23.823 & 20.817 & 22.037 & 24.108 \\ \hline \hline \end{tabular}
\end{table}