# A Deconvolutional Deblurring Algorithm Based on Dual-Channel Images
## 2 Basic Model of DCBCD
### The Struction of DCBCD  
Usually, Equation (2) is an ill-posed problem, which cannot be directly solved. Moreover, if the image is a large-scale space-variant or space-invariant image, the restoration results obtained by the method of derivation to obtain the inverse matrix are very poor. Therefore, this paper adopted a split-block strategy, to obtain the kernels of each selected block in the image for dealing with space-variant blurred images. Subsequently, the proposed method classifies similar kernels using a clustering algorithm. Then it assigned different weights to the clusters of kernels to determine the weights of the pixels in each recovered image block. Finally, each pixel value of the final deblurred image was the normalized sum of the corresponding position pixel value from each image block with different weights. As shown in Figure 1, the work of Equation (2) was divided into three parts in this paper: (1) preprocess; (2) kernel estimation; (3) image restoration. Step 1: Preprocessing: De-noising, blocking, and building a pyramid of the input images  
De-noise: In this paper, the image de-noising preprocess was performed using the currently widely used BM3D [12] algorithm. In the process of de-noising, balancing the image sharpness and signal-to-noise ratio after de-noising usually depends on empirical choices. In this paper, the blur kernel estimation process was mostly calculated in the gradient domain. Therefore, the presence of noise affected the sparsity of the gradient domain. Thus, the parameter settings for de-noising tended to enhance the de-noising effect, rather than protecting the image texture. Figure 1: Structure flow chart: This figure describes the flow and components of the proposed algorithm. The input is two blurred images with different blurring patterns, but with the same object. The first step is pre-processing, which focuses on block splitting and de-noising. The second part estimates the blur kernel, block by block. The third step is the classification of the blur kernels using a clustering algorithm and the final restoration. Block: In the process of image blocking, the size of the image blocks must be divided according to the size of the image and the forward step. The choice of block size and the length of the step are usually based on the nature of the image itself. If the similarity of the blur kernel-space change of the image is high, a relatively large step size can be chosen, to reduce the number of blocks and accelerate the calculation speed. If the space change shape is complex, a smaller block can be chosen, to improve the estimation accuracy [13]. Built pyramid: In common image deblur algorithms [2], an image pyramid is usually created by down-sampling in the process of kernel estimation. The kernel is estimated layer by layer, and the initial value of the next kernel is obtained by the up-sampling of the above layer result. The algorithm for estimating the kernel is the same for each layer in all blocks; therefore, the algorithm for the kernel estimation is presented in Section 3, as an example for any layer of any pair of image blocks. Step 2: Block layer kernel estimation (introduced in Section 3)  
Section 3 introduces the kernel estimation method in any block layer of the image pyramid. For space-invariant image blurred images, where the whole image has the same blur pattern, calculating the RSPI block by block is equivalent to calculating the RSPI for the whole image. The specific reasons were described in the section on RSPI below. The split-block step can be omitted if dealing with space-invariant images. The blurring kernel of the whole image is estimated directly by building an image pyramid with the original image size as the initial value layer by layer. With the dual-channel blurred images input, the RSPI between the sliced images was calculated using the total information from selected image blocks as a priori information. The image blur kernel was estimated and restored block by block.