## 2 Materials and Methods
### Regularization and Uncertainty Quantification Module  
Incorporating various regularization and uncertainty modeling strategies into the network is essential for improving generalization and quantifying prediction uncertainty. These strategies are evaluated through a series of experiments, detailed below. _Experiment A: Fixed Dropout_  
Dropout is widely employed as a regularization technique, where the random omission of neuron activations helps reduce overfitting. Research indicates that placing a dropout layer near the output of feature extraction and reconstruction networks improves performance [40]. Therefore, a fixed dropout rate of 0.01 is applied between the Residual-Block and SubPixelConv layers. This introduces randomness during training, enhancing robustness and preventing overfitting on the training set. _Experiment B: Layer-wise Progressive Dropout_  
This strategy adjusts dropout rates based on the depth and complexity of the network layers. In shallow layers, lower dropout rates are used, which gradually increase as the network deepens [22; 41]. Specifically, after the initial 3 \(\times\) 3 convolution (64 output feature maps), a Dropout2d layer with \(p\) = 0.01 is applied to prevent overfitting in early layers. The next eight residual blocks utilize Dropout2d with \(p\) = 0.05, while the subsequent blocks increase the dropout rate to \(p\) = 0.1. Finally, Dropout2d (\(p\) = 0.1) is applied after sub-pixel up-sampling to further regularize the output. _Experiment C: Activation Intensity-driven Adaptive Dropout_  
This method introduces a novel approach to regularization by adjusting the dropout rate based on the local activation intensity. The dropout probability for each spatial location is dynamically modulated according to the mean activation value on the feature map [42; 43]. The corresponding formula is  
\[p_{adaptive}=clip(p_{base}\cdot e^{-k\cdot mean(\mid F\mid)},0,1) \tag{5}\]  
In this case, \(p_{base}\) is the base dropout rate, and k is a decay coefficient that controls the dropout rate in different regions. High-activation areas (such as edges) experience a reduced dropout rate (\(\sim\)5%), while low-activation regions (such as smooth backgrounds) see an increased rate (\(\sim\)35%). This allows for more granular regularization, enabling the model to preserve edge and detail information while controlling the background. _Experiment D: Dynamic Gate Network_  
The dynamic gated network introduces a gating module (Figure 1f) to adjust the importance of each channel. Using learned gating coefficients, the module can fine-tune feature selection, focusing on relevant information. This gating mechanism is applied after the residual block stack and before the up-sampling stage. A \(1\times 1\) convolution generates initial gating weights, which are normalized through Batch Normalization [44], followed by ReLU activation and Sigmoid to produce gating coefficients G within the range of [0, 1]:  
\[G=\sigma(BN(Conv_{1\times 1}(F))) \tag{6}\]  
where \(F\) is the output feature of the residual block and \(G\) is used to weigh \(F\) on a channel-by-channel basis. This mechanism allows for the selective enhancement of important features and the suppression of less relevant ones, improving feature extraction performance in complex data [45; 46]. Experiment E: Multi-stage Uncertainty Quantification  
Multi-stage uncertainty quantification incorporates strategies for modeling both epistemic uncertainty with MC-Dropout and aleatoric uncertainty with heteroscedastic noise. This design not only facilitates an assessment of the reliability and certainty of predictions but also offers a probabilistic interpretation of the outputs, thereby enhancing both the transparency and practical robustness of the model [22; 47; 48]. As a result, the experiments adopt a two-stage uncertainty modeling strategy that bolsters the model's ability to evaluate prediction uncertainty and overall robustness.