# Real Image Deblurring Based on Implicit Degradation Representations and Reblur Estimation
## 3 Proposed Method  
### Network Structure  
As shown in Figure 1, IDR\({}^{2}\)ENet contains a degradation representation estimation process, a reblurring process and a deblurring process during training, whose architecture is mainly inspired by [24; 25; 26; 33]. The degradation representation estimation process is dominated by the degradation estimation subnetwork, whose input is a real blurred image \(y\), and whose output is implicit degradation representations \(E\) estimated by learning on \(y\).  
The deblurring process takes the real blurred image \(y\) and the degradation representation \(E\) as input, and outputs a sharp image \(x_{de}\) after deblurring. \(E\) enables the multi-scale degradation-representation-guided deblurring subnetwork to learn the corresponding blur features in blurred images, so that it can adaptively handle a wide range of blurred images. It is worth mentioning that the multi-scale degradation-guided deblurring subnetwork does not learn a complete mapping from the real blurred image \(y\) to the deblurred image \(x_{de}\); instead, it only learns the residuals between them, which can be expressed by the following equation:  
\[x_{de}=\mathcal{N}_{\text{Deb}}(y,E) \tag{4}\]  
where \(\mathcal{N}_{\text{Deb}}\) denotes the multi-scale degradation-guided deblurring subnetwork.  
In order to better learn degradation representations, the design uses the reblurring process. An immediate idea is that the reblurring subnetwork learns to generate the reblurred image \(y_{re}\) using only the sharp image \(x\) as input. However, since a sharp image can correspond to countless blurred images, in order to reduce training difficulty and assist the degradation estimation subnetwork to better estimate the degradation representations, the real sharp image \(x\) and degradation representation \(E\) are used together as the input of the reblurring subnetwork, which is also expressed as a multi-scale degradation-representation-guided reblurring subnetwork, with \(y\) as the target and the output as the reblurred image \(y_{re}\). Likewise, the multi-scale degradation-guided reblurring subnetwork learns only residuals between the sharp image \(x\) and reblurred image \(y_{re}\) to better implement degradation representation \(E\) to guide reconstruction. The equation of the deblurring process is expressed as follows:  
\[y_{re}=\mathcal{N}_{\text{Reb}}(x,E) \tag{5}\]  
Figure 1: Network structure of IDR\({}^{2}\)ENet, which is the Implicit Degradation Representations and Reblur Estimation Network for real image deblurring.  
where \(\mathcal{N}_{\text{Reb}}\) represents the multi-scale degradation-guided reblurring subnetwork. This is intended to, on the one hand, guide the degradation estimation subnetwork to focus more on learning in order to extract the degradation representation \(E\) in the image during the reblurring process and ignore the content of the image itself, and on the other hand, to make the training process faster and more stable.  
During training, the degradation estimation subnetwork, multi-scale degradation-guided reblurring and deblurring subnetwork are trained jointly. This has the advantage of constraining the degradation estimation subnetwork to better estimate \(E\) in the joint training on the one hand, and enable the multi-scale degradation-guided deblurring subnetwork to better utilize degradation representations for reconstruction on the other. For testing, IDR\({}^{2}\)ENet only retains the degradation estimation and deblurring process.