## 2 Adaptive PCNN Combined with GWO and BEMD
### The Proposed BEMD-GWO-PCNN Algorithm
A quantitative analysis of the different de-noising methods is presented in Table 3. The table clearly shows that the proposed BEMD-GWO-PCNN algorithm yields a better denoising performance, with higher STD and PSNR values, which means higher contrast with regard to each image's pixel gray level and reduced noise content. In addition, the MI and SSIM values of the proposed method are higher than those of the other methods. Analysis of the indicators shows that the denoised image obtained using the proposed BEMD-GWO-PCNN algorithm has a higher degree of fitness with respect to the original image. The PSO-PCNN algorithm also provides an excellent denoising performance, which benefits greatly from the intelligent swarm model optimization used to improve the PCNN denoising performance. The GACA-PCNN algorithm can also produce a relatively good effect; nevertheless, the whole optimization algorithm is difficult to run because of multiple overlapping iterative combinations. Meanwhile, the above methods cannot achieve the desired goal in the image detail extraction. And the operation of the entire GACA-PCNN program is multi-regional and complex. The tBEMD-NLCDP method can also yield some results, the detail is well presented, but it did not perform well for salt and pepper noise removal. At the same time, the tBEMD-NLCDP method obviously lacks enough ability in the face of high-intensity noise. To produce a more comprehensive analysis, different intensities of \(\delta\)2 = 0.1, 0.2, and 0.3 for salt-pepper noise are added to the original Lena and Pepper images. In Tables 4 and 5, PSO-PCNN and GACA-PCNN are compared with our proposed BEMD-GWO-PCNN method to verify their noise reduction capabilities for high-intensity noise. From the data analysis, the proposed BEMD-GWO-PCNN method does provide a fairly good denoising effect. When compared with the original noisy images, the indicator values of the STD, MI, SSIM, and PSNR provide a good reflection of the image quality improvements produced by the noise reduction. The PSNR and STD values of the proposed algorithm are relatively high, which means lower noise residue. At the same time, the MI and SSIM values describe the degree of recovery of the image details. From the indicator data analysis, the BEMD-GWO-PCNN method enables effective image detail extraction and noise

Figure 8: Pepper image: (**a–c**) the noise-suppression BIMF 1 to 2 and the residue, (**d**) The proposed BEMD-GWO-PCNN reconstruction image, (**e**) median filter, (**f**) PSO-PCNN method, (**g**) GACA-PCNN, (**h**) COR-PCNN, (**i**) tBEMD-NLCDP. reduction. In the Lena and Pepper images, the PSO-PCNN, GACA-PCNN, tBEMD-NLCDP method and BEMD-GWO-PCNN methods all performed well. However, multiple experiments demonstrated that our method is more feasible and provides superior performance to the GACA-PCNN PSO-PCNN, and tBEMD-NLCDP methods. In fact, our method has shown that the noise interference is well eliminated, and that the extraction of the image stripe details is well completed. At the same time, the PSO-PCNN, GACA-PCNN and tBEMD-NLCDP method lacks enough ability in the face of high-intensity noise, whose performances are relatively weak.