## 3 Theoretical Analysis and Proof
### Experiments with Different Datasets
#### 4.3.1 Sentinel-2  
Figure 3a shows the original remote sensing image acquired from Sentinel-2, while Figure 3b is the corresponding ground-truth image. The image size is 1347 \(\times\) 1347 pixels and the spatial resolution is 10 m. As seen in Figure 3c-f, all four models can consistently identify sea ice with a high degree of accuracy. In addition, from Table 1, metrics of the four \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Performance Index**} & \multicolumn{4}{c}{**Noise-Free \(\psi(t)=0\)**} & \multicolumn{4}{c}{**Random Noise \(\psi(t)\in\mathbb{5\times[-1,1]}\)**} \\ \cline{2-9}  & **EAEND** & **MNI** & **NRI** & **ETZNN** & **EAEND** & **MNI** & **NRI** & **ETZNN** \\ \hline RE & \(1.136869\times 10^{-13}\) & \(2.842171\times 10^{-14}\) & \(2.842171\times 10^{-14}\) & \(2.960869\times 10^{-7}\) & \(\mathbf{5.659684\times 10^{9}}\) & \(1.044903\times 10^{1}\) & \(7.025637\times 10^{9}\) & \(2.006999\times 10^{7}\) \\ OA & \(\mathbf{0.983006}\) & \(\mathbf{0.983006}\) & \(\mathbf{0.983006}\) & \(\mathbf{0.983006}\) & \(\mathbf{0.983006}\) & \(\mathbf{0.964755}\) & \(0.719159\) & \(0.737988\) & \(0.543572\) \\ AA & \(\mathbf{0.984047}\) & \(\mathbf{0.984047}\) & \(\mathbf{0.984047}\) & \(\mathbf{0.984047}\) & \(\mathbf{0.984047}\) & \(\mathbf{0.98407}\) & \(\mathbf{0.962926}\) & \(0.736308\) & \(0.754035\) & \(0.571525\) \\ PP & \(\mathbf{0.964915}\) & \(\mathbf{0.964915}\) & \(\mathbf{0.964915}\) & \(\mathbf{0.964915}\) & \(\mathbf{1.00000}\) & \(0.624656\) & \(0.640781\) & \(0.509592\) \\ Kappa & \(\mathbf{0.965942}\) & \(\mathbf{0.965942}\) & \(\mathbf{0.965942}\) & \(\mathbf{0.965942}\) & \(\mathbf{0.952881}\) & \(0.455939\) & \(0.491205\) & \(0.134977\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Identification metrics and results of four algorithm-assisted CEM method (1) for the Arctic sea ice from HJ-2A. Figure 6: Identification results of four algorithm-assisted CEM method (1) for the Arctic sea ice from HJ-2A. (**a**) Original image. (**b**) Ground truth. (**c–f**) Identification results of EAEND model (10), MNI model (27), NRI model (28), and ETZNN model (29) in the noise-free \(\psi(t)=0\) environment. (**g–j**) Identification results of EAEND model (10), MNI model (27), NRI model (28), and ETZNN model (29) in the random noise \(\psi(t)\in 5\times[-1,1]\) environment. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Performance Index**} & \multicolumn{4}{c}{**Noise-Free \(\psi(t)=0\)**} & \multicolumn{4}{c}{**Random Noise \(\psi(t)\in\mathbb{5\times[-1,1]}\)**} \\ \cline{2-9}  & **EAEND** & **MNI** & **NRI** & **ETZNN** & **EAEND** & **MNI** & **NRI** & **ETZNN** \\ \hline RE & \(2.273738\times 10^{-13}\) & \(5.684385\times 10^{-14}\) & \(5.684353\times 10^{-14}\) & \(1.136990\times 10^{-13}\) & \(\mathbf{5.659684\times 10^{9}}\) & \(1.044903\times 10^{1}\) & \(7.025637\times 10^{9}\models, specifically OA = 0.977508, AA = 0.979355, PP = 0.996358, and Kappa = 0.954620, are the same. Therefore, all comparison models perform well in the noise-free environment. Additionally, as shown in Table 1, all four algorithms have a high convergence accuracy for the RE. Nevertheless, as seen in Figure 3g-j, a significant difference in the performance of the three models emerges in the random noise \(\psi(t)\in 5\times[-1,1]\) environment. Despite MNI model (27) having a noise-suppression term, it cannot maintain good identification performance, with its Kappa coefficient falling to 0.874898 and the other three indicators correspondingly decreasing. Moreover, its RE rose from \(0.537140\times 10^{-12}\) in the noise-free environment to \(1.189779\times 10^{1}\). As shown in Figure 3h, there are some misidentifications and blurred edges in the image.