# Wavelet-Based, Blur-Aware Decoupled Network for Video Deblurring
## 3 Wavelet-Based, Blur-Aware Decoupled Network
### Multi-Scale Progressive Fusion Module  
The low-frequency sub-bands obtained through wavelet transform carry the main structural information of the frames. Unlike other video restoration tasks, video deblurring requires not only detailed recovery but also reconstruction of structure distortions caused by blur. Based on this characteristic, we designed the multi-scale progressive fusion (MSPF)  
Figure 1: The architecture of the proposed wavelet-based, blur-aware decoupled network (WBDNet).  
module specifically to address structural information reconstruction in low-frequency sub-band features.  
The core idea of the MSPF module is to utilize redundant structural information from multiple frames to assist in target frame restoration. As shown in Figure 2, we first align features from other frames to the target frame using optical flow information obtained from the preprocessing branch. Considering that low-frequency sub-bands mainly contain structural information, we adopt basic optical flow alignment instead of computationally intensive deformable convolution, maintaining effectiveness while improving computational efficiency. Denoting the target frame features as \(F_{i}^{l}\) and aligned features from other frames as \(\{F_{t}^{l}\}_{l=1,t\
eq i}^{N}\), where \(l=1\) represents the original scale, we construct a three-level feature pyramid (\(l=1,2,3\)) using strided convolution filters for two \(2\times\) downsampling operations to expand the network's receptive field to capture broader structural information.  
We employ a bottom-up fusion strategy, starting from the lowest scale (\(l=3\)) and proceeding level by level. At each scale level, we first concatenate the target frame features with other frame features along the channel dimension and input them into the structure feature fusion block (SFFB) for processing. The fusion process at \(l=2\) can be expressed as follows:  
\[\hat{F}_{i}^{2}=\text{Conv}([H_{SFFB}([F_{1}^{2},\dots,F_{N}^{2},F_{i}^{2}]),( \hat{F}_{i}^{3})^{\dagger 2}]), \tag{4}\]  
where \([\cdot,\cdot\cdot]\) denotes the feature concatenation operation and \((\cdot)^{\dagger 2}\) represents \(2\times\) upsampling. This process continues progressively until output features are obtained at the original scale (\(l=1\)).  
In the SFFB, to emphasize common structural features and suppress interference, we first compute similarity maps between the target frame and other frame features, reflecting structural correlation at each position through similarity distances. By multiplying features with similarity maps, we obtain features with enhanced structural information. This process is represented as follows:  
\[M(t)=\text{Sigmoid}(\theta(F_{i}^{l})\odot\phi(F_{t}^{l})),t\in[1,N]\text{ and }t\
eq i, \tag{5}\]  
\[F_{t}^{l^{\prime}}=F_{t}^{l}\odot M(t), \tag{6}\]  
where \(\theta(\cdot)\) and \(\phi(\cdot)\) are feature embedding functions implemented through convolution layers, \(\odot\) denotes element-wise multiplication, and the sigmoid function normalizes simi  
Figure 2: Schematic diagram of the multi-scale progressive fusion (MSPF) module. For illustration purposes, we only demonstrate the module with two neighboring frames as an example input.  
larity values to the \([0,1]\) interval. The enhanced features are concatenated along the channel dimension and compressed through a convolution layer. To obtain more comprehensive structural representations, SFFB employs parallel convolution kernels of different sizes to extract multi-receptive field features, fusing structural information at different scales for complementary enhancement. This design ensures the network can comprehensively capture and integrate structural information in both temporal and scale domains.