## 2 Adaptive PCNN Combined with GWO and BEMD
### Noise Reduction Mechanism of PCNN  
In the PCNN model, each neuron corresponds to a single image pixel, and the excitation of one neuron causes excitation of neighboring pixels with similar gray values; these responses are called synchronization release pulse characteristics [37]. Through application of these characteristics, a variety of the image processing methods mentioned above can be realized. In this work, all of the neurons adopt the same connection behavior. The brightness information of every pixel will be input to the corresponding neurons. Every neuron will then be connected with the neurons in a \(3\times 3\) neighboring region. The state of a neuron (i.e., firing or extinguishing) is dependent on the output of the firing system. The \(F_{ij}[c]\) of every neuron corresponds to the highlight of the pixel points. \(L_{ij}[c]\) is equal to the sum of the output responses from the \(3\times 3\) neighboring neurons in channel \(L\). To overcome the noise disturbance and recover the detailed information as far as possible, noise elimination is necessary. By adjusting the brightness values of the image pixels, contaminated images can, to a certain extent, be recovered [38]. In most cases, the brightness values of the contaminated pixels differ from those of the neighboring normal pixels. Therefore, the outputs of noisy pixels differ from those of normal pixels. Based on the output states of each neuron and its neighboring neurons (i.e., ignited or unignited), the brightness values of the corresponding pixels are adjusted. The consequent improvement in the pixel values can eliminate the noise and promote detail preservation performance. When the neuron output values are considered, the corresponding pixel brightness values will be declined when one neuron is ignited but most of its neighboring neurons are unignited; the corresponding pixel brightness values will increase when one neuron misfires, but most neighboring neurons do fire. In other cases, the brightness values will not change. Therefore, through application of the PCNN, the ignited matrix of the raw image can be obtained. From this perspective, the simplified PCNN model can locate the isolated noisy pixels accurately and suppress these isolated noisy pixel points. In the actual denoising process, the PCNN processing acts as the pre-processing procedure, and a filter operation is often used on the isolated pixels to achieve an improved noise reduction effect. In general, median filtering can be applied to the isolated points using the marked difference between the ignited pixels and the normal pixels. Many experiments have shown that the combination of the PCNN and a median filter is practical. A table showing the PCNN noise reduction algorithm with conventional random parameters (COR-PCNN; Algorithm 1) is introduced here in detail. From the model and the associated mechanism analysis, the parameters play a critical role in the PCNN treatment. In this study, we invested considerable effort in optimization of the critical parameters \(\alpha_{T}\), \(\beta_{T}\) and \(\
u_{T}\), which performed well in our proposed GWO strategy.