## 1 Introduction
In fact, there are many denoising algorithms that are two steps and similar to the PCNN method, where the first step isolates noisy pixels and the second one suppresses the noise. For example, [PERSON] [27] introduced a non-linear complex diffusion process (NLCDP) technique in the tBEMD domains, where the tBEMD is an adjusted BEMD method built on Student's probability density function (PDF). The tBEMD-NLCDP method has an advantage over the traditional BEMD method. The main contributions in this paper are summarized as follows. Committed to PCNN image noise reduction research, an adaptive PCNN method that is combined with the GWO and BEMD algorithms is developed, which has significant benefits for use in image denoising. But its parameters are difficult to determine which limits its practical application. GWO algorithm is firstly proposed to resolve PCNN parameter issues, which can adaptively optimize parameters exactly, with a global optimal solution and rapid convergence. Through a process of continuous hierarchy screening and multiple iterations, the optimized parameters can have high accuracy via the experimental verification and will enhance the PCNN's denoising performance well. The PCNN application isolates the noisy pixels and the noise-polluted image can be processed more easily. Therefore, a subsequent filter, such as a median filter, can yield better denoising results. Importantly, BEMD will be applied to decompose the raw heavily polluted image into different components. This step is significant, solving the problem of a one-time direct processing, which makes it difficult to reduce the high-intensity image noise thoroughly. The decomposed high and low-frequency components are then denoised using the optimized PCNN filter method. For important novelties, the GWO intelligent algorithm is the first proposed to apply intelligent optimization screening to parameters, which solves the key parameter problem accurately. BEMD application makes the denoising progress more targeted according to the different component conditions. The self-adaptive determination optimized PCNN parameters will make the noise suppression progress fascinating while it is assisted. The proposed BEMD-GWO-PCNN denoising method is mainly applied to complete offline image processing. The method effectively improves the effectiveness of parameter optimization and greatly accelerates the parameter optimization operating speed. Application of BEMD remedies the previous deficiencies of insufficient suppression of high-intensity noise by making the denoising process more specific. The image reconstruction results can finish excellent extraction, preservation of image details, and good noise suppression performance. In this paper, the existing other PCNN based noise reduction methods are compared with our proposed method. In terms of parameter optimization efficiency and actual noise reduction effects, the proposed method applied to image denoising is superior. According to our evaluation indicators, the proposed BEMD-GWO-PCNN method is shown to be feasible and to be more accurate than other conventional and PCNN-based denoising methods. The article is organized as follows: Section 2 is the description of adaptive PCNN combined with GWO and BEMD; Section 3 is the experimental results and analysis; And the last section provides conclusions and challenges for future research.