# A Deconvolutional Deblurring Algorithm Based on Dual-Channel Images
## 3 The Block Layer Kernel Estimation  
The main improvements of the proposed method in this section, which deals with the space-variant blurred images, are the modified regularization terms in the kernel estimation process.  
Specifically, in the kernel estimation algorithm for each layer of the image block pyramid, this paper makes the following contributions:  
1. In the block layer iter-kernel estimation process, using the RSPI of each pair of blocks to calculate the correlation coefficient, the integrity of the total information of the selected block was preserved to the greatest extent. Furthermore, the interference caused by the information from the other parts of the global image was avoided.
2. In the block layer iter-image estimation process, the advanced modified regularization term is proposed with the dual-channel images information introduced in this paper. With the improvements, the accuracy of the clock-layer kernel estimation was improved.  
For the block layer kernel estimation problem, the estimation model from Equation (2) can be written in the following iterative form:  
\[H=\underset{\
abla X\coloneqq h}{argmin}\|h_{iter}\varoquigarrow X_{iter}-Y_{L} \|_{2}^{2}+\lambda_{x}\|T(X_{iter})\|+\lambda_{h}\|F(h_{iter})\| \tag{4}\]  
where \(H\) is the result of the kernel estimation in this block layer, and \(Y_{L}\) is the blurred image in this block layer, with it representing the alternate iterative minimization of the block layer iterative image \(X_{iter}\) and the block layer iterative kernel. \(\lambda_{x}\) and \(\lambda_{h}\) are regularization coefficients for iterative image estimation and kernel estimation in each block layer. \(T(X_{iter})\) and \(F(h_{iter})\) are regularization terms for the block layer iterative image estimation and layer-kernel estimation models, respectively. The choice of these coefficients is usually based on experience, depending on the design purpose of the regularization term and the characteristics of the image itself.  
The design requirement of the regularization term \(F(h_{iter})\) in the block layer iter-image estimation process aims to improve the reliability of the block layer iter-image. Regularization terms, such as the TV operator, are usually chosen to emphasize the gradient part of the blurred image. However, such features are derived from the gradient of the blurred image itself and lack reference side information to which to refer. Therefore, if the dual-channel blurred images are the input content with weak coprime, the two images will be more correlated. Furthermore, the more reliable information can be preserved using RSPI as the regularization term. In Section 3.1, this paper proposed a block layer iter-kernel estimation model with an RSPI regularization term for optimizing the block layer iter-kernel estimation process.  
The design requirements of the regularization term \(T(X_{iter})\) in the block layer iter-image estimation process usually need to consider the feature of the gradient image from the block layer iter-image. This paper introduced the side information from the input dual-channel corresponding image, to modify the regularization term NGM, which is used in [14]. The modified regularization term WG-NGM receives information from two-channel input images, making it more reliable than the NGM.  
Therefore, through the improvements above, and by continuously iterating alternately to convergence, the optimal solution of the block layer kernel \(H\) can be obtained.  
Finally, with the repetition of the up-sample and iterative solving process, the kernels of the blurred image blocks could be estimated.