# No-Reference Blurred Image Quality Assessment by Structural Similarity Index
## 3 The Proposed IQA Metric
### IQA for Blurred Image Restoration  
The purpose of image restoration is to reduce or erase image degeneration during acquisition, compression, transmission, processing, and reproduction. IQA can be used to evaluate image restoration algorithm by assessing qualities of distorted image and restoration image. [PERSON] [30] presented a deconvolution algorithm for decomposition and approximation of space-variant blur using the alternating direction method of multipliers. [PERSON] [31] proposed a blind deconvolution algorithm using the variational Bayesian approximation with the automatic relevance determination model on likelihood and image and blur priors. In this section, we use the proposed NSSIM to evaluate the performance of image restoration. Two groups of images including original image, blurred image and restorations are evaluated by the proposed IQA algorithm NSSIM and PSNR, SSIM and several state-of-the-art NR IQA algorithms. The experimental results are shown in Figures 9 and 10 and Tables 11 and 12.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Algorithm** & **SROCC (_p_-Values)** & **PLCC (_p_-Values)** & **RMSE (_p_-Values)** \\ \hline PSNR & 0.8211 \(\pm\) 0.0796 (0.319167) & 0.8556 \(\pm\) 0.1252 (0.835436) & 0.6481 \(\pm\) 0.5828 (0.929265) \\ SSIM [1] & 0.8636 \(\pm\) 0.0361 (0.356459) & 0.8497 \(\pm\) 0.0404 (0.650212) & 0.8480 \(\pm\) 0.6143 (0.493018) \\ BIQI [14] & 0.8742 \(\pm\) 0.0451 (0.526389) & 0.7768 \(\pm\) 0.0354 (0.335915) & 1.1052 \(\pm\) 0.3834 (0.164435) \\ BRISQUE [4] & 0.8872 \(\pm\) 0.0538 (0.738890) & **0.9150**\(\pm\) 0.0383 (0.385953) & 0.6912 \(\pm\) 0.5226 (0.766324) \\ TIP [2] & 0.8847 \(\pm\) 0.0193 (0.412921) & 0.8756 \(\pm\) 0.0246 (0.310203) & 1.0948 \(\pm\) 0.5053 (0.309981) \\ NIQE [17] & 0.8909 \(\pm\) 0.0519 (0.811307) & 0.9104 \(\pm\) 0.0336 (0.464863) & **0.3562**\(\pm\) 0.2133 (0.230560) \\ BLIIND-II [3] & 0.8841 \(\pm\) 0.0232 (0.296689) & 0.8736 \(\pm\) 0.0347 (0.882062) & 0.5717 \(\pm\) 0.2750 (0.741406) \\
**NSSIM** & **0.8973**\(\pm\) 0.0328 & 0.8814 \(\pm\) 0.0879 & 0.6193 \(\pm\) 0.3621 \\ \hline \end{tabular}
\end{table}
Table 10: Average IQA performance (mean \(\pm\) standard deviation) on four datasets. We take Spearman’s rank order correlation coefficient (SROCC), Pearson linear correlation coefficient (PLCC) and root mean square error (RMSE) as evaluation indexes. In each column, the best performance value is marked in boldface.  
Figure 8: Scatter plots of DMOS vs NSSIM predicted scores on four datasets.  
Figure 10: Group 2 restorations: The original image is 512 \(\times\) 512 \(\times\) 3 which is provided by IVC dataset while the blurred image is produced by a Gaussian low-pass filter of \(11\times 11\) with deviation 1.5. The restorations are produced by [PERSON] [30] and [PERSON] [31], respectively.  
Figure 9: Group 1 restorations: The original image is 480 \(\times\) 720 \(\times\) 3 which is provided by LIVE II dataset while the blurred image is produced by a Gaussian low-pass filter of \(11\times 11\) with deviation 1.5. The restorations are produced by [PERSON] [30] and [PERSON] [31], respectively.  
It can be seen from Figure 9 and Table 11 that PSNR and SSIM [1] fail to evaluate the quality of both restorations since the quality scores are smaller than that of the blurred image. BIQI [14] and NIQE [17] succeed to identity the restoration images but the difference between the two restorations is slight. While BRISQUE [4], BLIIND-II [3], SFA [20] and the proposed metrics NSSIM achieve better precision and the differences between two restorations are distinct. Moreover, the NSSIM-predicted score of blurred image is 0.0709 \(\times\) 10\({}^{-4}\), showing obvious variance between the blurred image and the original image. This demonstrates that NSSIM is extremely sensitive to blur. Similarly, Figure 10 and Table 12 also demonstrate that NSSIM is suitable for blur IQA.