# Real Image Deblurring Based on Implicit Degradation Representations and Reblur Estimation
## 3 Proposed Method
### Multi-Scale Degradation-Representation-Guided Deblurring (Reblurring) Subnetwork  
As shown in Figure 3, the multi-scale degradation-representation-guided reblurring and deblurring subnetworks share the same network structure but they do not share weights. For better illustration, this structure is subsequently referred to as the multi-scale degradation-guided reconstruction subnetwork. Following the design of the high-dimensional non-blind denoising (HDNBD) engine in [25], the multi-scale degradation-guided reconstruction sub-network adopts a U-net-based codec structure and follows core modules such as the feature enhancement module, enhanced residual bridge connection and attention module. DWT and IDWT are also used as down-sampling and up-sampling methods, respectively. What is different is that the multi-scale degradation-guided reconstruction subnetwork takes both the image (_sharp image x or blurred image y_) and degradation representation \(E\) as input. Moreover, our design uses a multi-scale degradation representation fusion module for a better use of degradation representations. Figure 2: Network structure of degradation estimation subnetwork. At the encoding end, the input of each layer first goes through a feature enhancement module to initially extract features, and then the dimension is halved after DWT down-sampling as the input of the next layer. Both the encoding end and the decoding end are five layers in depth. The bottom layer of the encoding end goes through one Conv \(3\times 3\) and ReLU to become the bottom layer of the decoder. Apart from the bottom layer, the input of each layer at the decoder end is the concatenation of the up-sampling value of the lower layer and the output of the multi-scale degradation representation block and the enhanced residual bridge connection block cascaded with it. After concatenation, the decoder-side feature is cascaded through a Conv \(1\times 1\) and a feature enhancement module, and then the input is up-sampled to the upper layer. The encoder side and the decoder side are set up with a jump connection section. The jump connection part of each layer consists of a feature enhancement module, the first enhanced residual bridge connection, the multi-scale degradation representation fusion module, and the second enhanced residual bridge connection cascade in turn. In particular, it should be noted that the input of the multi-scale degradation representation fusion module is not only the encoder-side features of that layer, but also the encoder-side features of the remaining layers and the implicit degradation representation \(E\). The code-side features of each subsequent layer are denoted as \(R_{i}\) subsequently, where \(i\) refers to the number of code-decoder layers, which increases from top to bottom. According to Figure 3, the dimensionality of \(E\) and \(R_{i}\) is shown as  
\[ \begin{split}& E\in\mathbb{R}^{64\times H\times W}\\ & R_{i}\in\mathbb{R}^{64\times H_{i}\times W_{i}}\quad i=1,\dots,4\end{split}  \tag{6}\]  
where \(H\) and \(W\) denote the height and width of the input image, respectively. At the top layer (i.e., the layer with \(i=1\)), the output decoder-side feature after the feature enhancement module is again changed back to 64 channels after being passed through a Conv \(1\times 1\), which is then passed through a Conv \(3\times 3\) and then used as the input of the attention module. The output of the attention module is added element-wise to the features initially inputted at the encoder side, which is used as a global short connection to further enhance feature fusion between the encoder and decoder. Finally, the output image is obtained after one more Conv \(1\times 1\): if the input image is \(x\), the corresponding output is the reblurred image \(y_{re}\), and the deblurred image \(y_{de}\) is obtained when inputting the blurred image \(y\). The structure of the sub-modules is analyzed below. Figure 3: Network structure of multi-scale degradation-representation-guided deblurring (reblurring) subnetwork.