# Multi-Frame Blind Super-Resolution Based on Joint Motion Estimation and Blur Kernel Estimation
## 5 Experimental Results and Analysis
### Experiments on Synthetic Data  
The ground truth HR images are available on synthetic data, so our proposed algorithm and comparison methods are first measured on synthetic data. In order to evaluate image quality, we employ peak signal-to-noise ratio (PSNR), structural similarity (SSIM) and information fidelity criterion (IFC).  
Thirty-one LR images are created from one HR image. Random motion parameters, blur kernels, mixed noises and down sampling are added to the HR image. Random translations range from \(-3\) to \(+3\) pixels, while random rotation angles range from \(-3^{\circ}\) to \(+3^{\circ}\). The random Gaussian blur kernel \(\sigma_{blur}\) of each LR image ranges from 0.5 to 3.5, and the size of the blur kernel is \(15\times 15\) in this paper. We put in mixed noises in the form of random Gaussian noise and Poisson noise, and random standard deviation of Gaussian noise, \(\sigma_{noise}\), ranges from 0.005 to 0.035. Synthetic LR images are generated by using commonly natural images shown in Figure 3.  
We find that the SR result becomes better gradually by correcting the blur kernel and motion estimation from Figure 4. The artifacts caused by inaccurate estimation of blur kernel disappear gradually in the iterative process.  
We can see that the values of PSNR, SSIM and IFC have been improved on synthetic data in Table 1. The values of PSNR, SSIM and IFC increased by 3.92%, 6.56% and 6.32%.  
We can see from Figure 5, when the noise level is high, the noise outliers of the simple bicubic interpolation are particularly obvious. There are still slight noise points in the BayesSR and SRB methods. The noise level of the DeepSR method is much better, but the image is blurred. The FBSR method is worse than our proposed method in the details of the image. In comparison, the proposed method can preserve the specific details of the image better and suppress the noise as well. The main reason for this is that our algorithm suppresses noise in the manner of iteratively updating the explicit detection of the confidence weight of each low-resolution image and implicit detection using Huber loss function. In addition, motion estimation and blur kernel estimation are modified in the iteration, while the visual effect of the reconstructed high-resolution image is also better.  
Regarding the low-level noise, the influence of blur and motion on the super-resolution reconstruction should be considered here. We can see from Figure 6 that the high-resolution images reconstructed by the bicubic interpolation, BayesSR and DeepSR methods have been blurred. The high-resolution image estimated by the SRB method has obvious point artifacts. The FBSR method gives some ringing artifacts. Our proposed algorithm can better find a balance between deblurring and artifact removal, so the reconstructed high-resolution image has higher quality, which owes much to the combination of motion estimation, blur kernel estimation and image reconstruction.  
Figure 5: Visual comparison of algorithms for the Baby image with \(\sigma_{noise}=0.025\) when the magnification factor is 4. (**a**) The LR image; (**b**) Bicubic interpolation; (**c**) BayesSR; (**d**) SRB; (**e**) DeepSR; (**f**) FBSR; (**g**) Ours; (**h**) ground truth.