# A Deconvolutional Deblurring Algorithm Based on Dual-Channel Images
## 3 The Block Layer Kernel Estimation
### The RSPI of Total Images
#### 3.2.2 Block Layer Iter-Image Estimation with WB-NGM  
As mentioned above, the ordinary regularization term NGM was improved upon with the WB-NGM. As shown in Figure 2, the \(\lambda_{2}\!\left|\
abla X_{2-block-layer}^{iter-pixel}\right|\) from channel-2 of the proposed WG-NGM method was found to effectively improve the texture restoration effect of the iterative image and improve the restoration accuracy of the iterative kernel. The calculation method of WB-NGM is as follows:  
\[T(X_{iter})=\frac{\left|\
abla X_{1-block-layer}^{iter-pixel}\right|}{\left| \lambda_{1}\right|\!\left|\
abla X_{1-block-layer}^{iter-pixel}\right|+ \lambda_{2}\!\left|\
abla X_{2-block-layer}^{iter-pixel}\right|+E\!\left[ \
abla Y_{1-block-img}^{iter-temp}\right]} \tag{15}\]  
where \(E\!\left[\
abla Y_{1-block-img}^{iter-temp}\right]\) indicates the mathematical expectation operation performed on the channel-1 iterative blurred block layer image gradient map \(\
abla Y_{1-block-img}^{iter-temp}\) in the block layer iter-image estimation process, and the value is the mean of the gradients of all pixels of the \(\
abla Y_{1-block-img}^{iter-temp}\cdot\
abla X_{1-block-layer}^{iter-pixel}\) and \(\
abla X_{2-block-layer}^{iter-pixel}\) are the pixel values of the selected location in the gradient images of the block layer iter-images from channel-1 and channel-2. \(\lambda_{1}\) and \(\lambda_{2}\) (determined by experience) are weighting factors to control the ratio of two pixels. If the located pixel's gradient value \(\
abla X_{1-block-layer}^{iter-pixel}\) is larger than the \(E\!\left[\
abla Y_{1-block-img}^{iter-temp}\right]\), the pixel is retained; otherwise, it is discarded. By updating the threshold and iterative formula repeatedly, only small parts of the pixels are retained in the final result, which improves the accuracy of the blur kernel estimation, while ensuring sparsity. The WG-NGM could be applied to rewrite the block layer iter-image model as:  
\[\begin{split}\
abla X_{1-block-layer}^{iter}=\underset{h\in \mathcal{H}}{\mathrm{argmin}}(\left\|\
abla X_{1-block-layer}^{temp-pixel} \right.\left.\left.\left.\left.\left.\left.\left\langle X_{1-block-layer}^{ iter-pixel}\right|\right.\right.\right.\right.\right.\right.\\ \left.\left.\left.\left.\left.\left.\left.\left.\left.\left.\left. \left\langle X_{1-block-layer}^{iter-pixel}\right|\right.\right.\right.\right. \right.\right.\right.\right.\right.\\ \left.\left.\left.\left.\left.\left.\was set to 10 times, based on the design experience in the references, and the minimum threshold was \(10^{-2}\). In order to verify that the introduced multi-channel information could improve the estimation of iterative images, two images from the [PERSON] image set were selected for testing in this paper. As shown in Figure 3, it was found that the iterative results estimated by the WG-NGM term performed better than those estimated by the NGM term (the different scales caused the step-like performance in the image pyramid, as Figure 3 shows, because the smaller images had a better performance). The data were displayed for approximately 90 iterations (the pyramid was divided into nine layers, and the number of iterations estimated for each layer of the iterative image was ten, so there were 90 iterations), which was in line with the results of the Group-1 experiment below. The same parameters were used to create a pyramid of images of the same size as the baseline. The performance of the WG-NGM and NGM algorithms was compared separately to the iterative images for 90 iterations. PSNR and SSIM were chosen as the test indicators. As the figure shows, the WG-NGM method performed better in terms of PSNR, and the final three results in the SSIM were compared, as follows:  
The value of SSIM is usually small, so the difference in the final stages in the Figure 3 appears to be small. Table 2 lists the comparison of the SSIM values of the last three terms of the two methods. It can be noticed that WG-NGN performed better.