# Wavelet-Based, Blur-Aware Decoupled Network for Video Deblurring
## 3 Wavelet-Based, Blur-Aware Decoupled Network
### Blur-Aware Detail Enhancement Module  
High-frequency sub-bands, as crucial components of wavelet transform, contain rich, detailed information on frames. To effectively recover these details, we propose the blur-aware detail enhancement (BADE) module. The core design principle of this module is to fully utilize temporal information from video sequences while considering the impact of motion blur for precise detail recovery. We first concatenate high-frequency sub-band features (\(\{F_{I}^{HL}\}_{t=1}^{N}\), \(\{F_{I}^{LH}\}_{t=1}^{N}\), and \(\{F_{I}^{HH}\}_{t=1}^{N}\)) along the channel dimension as input to the BADE module.  
The specific details of the BADE module are shown in Figure 3. Let \(F_{i}\) denote the target frame features and \(\{F_{I}\}_{t=1,t\
eq i}^{N}\) denote features from other frames. Other frame features first pass through a blur-aware attention block (BAAB). In this block, we incorporate the sharp map (\(S_{t}\)) from the preprocessing branch. This sharp map provides crucial prior information about motion-blurred regions in the video. Using this information, we adaptively modulate inter-frame features to reduce the impact of blurred pixels. Specifically, the computation process of BAAB is expressed as follows:  
\[F_{t}^{att}=\text{Conv2}([\text{Conv1}(F_{t}),S_{t}]), \tag{7}\]  
\[F_{t}^{\prime}=\text{Conv1}(F_{t})\odot F_{t}^{att}+F_{t}, \tag{8}\]  
where \([\cdot,\cdot]\) represents the feature concatenation operation and \(\odot\) denotes element-wise multiplication. This design enables the network to dynamically adjust feature responses based on sharpness information, enhancing representations in sharp regions while suppressing the influence of blurred regions. The residual connection ensures the effective transmission of original feature information.  
Figure 3: Schematic diagram of the blur-aware detail enhancement (BADE) module. For illustration purposes, we only demonstrate the module with two neighboring frames as an example input.  
After obtaining enhanced feature representations, we adopt a residual-flow learning approach to obtain sampling offsets for deformable convolution, which aligns \(\{F_{t}^{\prime}\}_{t=1,t\
eq i}^{N}\) to \(F_{i}\) individually through deformable convolution:  
\[\Delta P_{t}=O_{i\to t}+\mathcal{C}^{p}([F_{t}^{\prime},F_{i}]), \tag{9}\]  
\[\Delta M_{t}=\text{Sigmoid}(\mathcal{C}^{m}([F_{t}^{\prime},F_{i}])), \tag{10}\]  
\[F_{t}^{a}=\text{DConv}(F_{t}^{\prime},\Delta P_{t},\Delta M_{t}), \tag{11}\]  
where \(\mathcal{C}\) denotes a stack of convolutions, and \(\Delta P\) and \(\Delta M\) represent the offset and modulation factor for deformable convolution, respectively. This design offers two key advantages. The first advantage relates to feature enhancement. Through BAAB, detail features in sharp regions become more prominent, which leads to improved feature-matching accuracy. The second advantage concerns motion handling. By using residual-flow learning to guide the offset field estimation in deformable convolution, the network can better adapt to large-scale motion changes in complex scenes. Overall, this design facilitates the effective transmission of detailed information throughout the alignment process.  
Finally, we concatenate all aligned frame features along the channel dimension, compress the channel dimension through one convolution layer, and use cascaded residual blocks for deep feature extraction. This enables the network to fully integrate multi-frame information, further enhancing the expressiveness of detail features.