# Blind Deconvolution with Scale Ambiguity
## 4 Discussion and Experimental Results
### Experimental Results  
#### 4.2.1 Quantitative Evaluation on Synthetic Datasets  
To better evaluate the effectiveness of the proposed method, we perform experiments on three mainstream benchmark datasets [8; 19; 44]. For fair comparison, we use the implementations of the state-of-the-art methods to estimate the blur kernels. The non-blind deconvolution method [42] is utilized to generate the final deblurring results.  
We first test our method on the benchmark dataset [19]. This dataset contains 32 blurred images from 4 ground-truth images with 8 blur kernels. We compare our method with 9 state-of-the-art methods including [PERSON] et al. [11], [PERSON] et al. [10], [PERSON] [14], [PERSON] [13], [PERSON] et al. [3], [PERSON] et al. [23], [PERSON] et al. [16], [PERSON] et al. [5] and [PERSON] et al. [17]. We evaluate the effectiveness of the proposed method by both error ratio and average kernel similarity.  
Figure 8 shows the comparisons of the cumulative error ratios and average kernel similarity. The graph in Figure 8a shows that when the error ratio is greater than 2.2, our success rate exceeds 90%. In comparison, the success rate of [PERSON] et al. [16], which performs the best in the 9 compared methods,  
Figure 6: Effects of varying \(\lambda\) on the performances of the proposed method.  
Figure 7: One failure real example. (**a**) An image blurred non-uniformly. (**b**) Our deblurred result of (**a**). Our method can not deal with non-uniform deblurring.  
reaches to 90% until the error ratio being up to 2.8. Similarly, the proposed method has higher average kernel similarity values than other compared methods, as demonstrated in Figure 7(b).  
Next, we test our method on the benchmark dataset [44], which contains 4 images and 12 blur kernels. We also show the performances of the proposed method against 7 state-of-the-art methods including [PERSON] et al. [10], [PERSON] et al. [20], [PERSON] and [PERSON] [14], [PERSON] et al. [3], [PERSON] et al. [5], [PERSON] [23] and [PERSON] et al. [17] in terms of error ratio and average PSNR. As shown in Figure 8(a), our method takes lead with 90% of the output under error ratio 3.8. Figure 8(b) shows that our method has the highest average PSNR among all the methods evaluated.  
Moreover, we evaluate our method on the benchmark dataset provided by [PERSON] et al. [8], which contains 100 images including low-illumination, face, and text images. We compare our method with 7 state-of-the-art methods: [PERSON] and [PERSON] [14], [PERSON] and [PERSON] [13], [PERSON] et al. [5], [PERSON] et al. [3], [PERSON] [23], [PERSON] et al. [16] and [PERSON] et al. [17]. The error ratio and average PSNR are used as performance evaluation criterions on this dataset. Figure 9(a) presents the cumulatively distribution of error ratios, our method is able to exceed 70% success rate when error ratio is greater than 4.6, which performs the best in the 7 compared methods. Figure 9(b) shows that the proposed method performs well in terms of average PSNR.  
In addition, we test our method on some other synthetic images. To provide visual comparisons, we show two examples in Figure 11. The numbers in green presented on the top left corner in each image are the PSNRs values, which quantitatively measure the quality of the deblurring methods. Both visually and quantitatively, Figure 11 shows that the proposed method achieves favorable results against the other deblurring methods.  
Figure 8: Quantitative evaluation on the dataset by [PERSON] et al. [19]. Comparisons on these two quality metrics demonstrate that our method performs well against the other methods.  
Figure 9: Quantitative evaluation on the dataset [44]. In particular, our method is up to 90% success rate at error ratio 3.8. For average PSNR value, our method achieves 30.31 on average, leading among state-of-the-art methods.