# No-Reference Blurred Image Quality Assessment by Structural Similarity Index
## 3 The Proposed IQA Metric
### Comparison with the State-of-the-Arts  
We compared the performance of NSSIM against PSNR, original SSIM [1], and several state-of-the-art NR IQA models such as BRISQUE [4], BLIIND-II [3], MCNN [19], IQA-CWT [7], SFA [20], etc. In order to evaluate the statistically significant difference between the proposed metric and the existing IQA algorithms, we performed statistical analysis by paired-sample \(t\)-tests and reporting the \(p\)-values. The null hypothesis in our \(t\)-tests is that the pairwise difference between the proposed metric and others has a mean equal to zero, i.e., the differences in performances presented in the results are not statistically significant. \(p\)-values \(<0.05\) indicates the rejection of the null hypothesis at the 5% significance level, meaning that the differences are statistically significant. It should be noticed that results of some IQA algorithms, such as NR-CSR [18], MCNN [19], IQA-CWT [7], and SFA [20], are collected from the corresponding references, thus their \(p\)-values are not shown in the result tables. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**deviation\(\backslash\)Size(Pixels)** & **5** & **7** & **9** & **11** & **13** & **15** \\ \hline
0.5 & 2.2956 & 2.2740 & 2.2875 & 2.3679 & 2.3840 & 2.3569 \\
1.0 & 2.2553 & 2.3779 & 2.2955 & 2.2769 & 2.3800 & 2.3440 \\
1.5 & 2.2537 & 2.3232 & 2.2743 & **2.2495** & 2.3779 & 2.3457 \\
2.0 & 2.2560 & 2.4236 & 2.2846 & 2.2967 & 2.4144 & 2.3379 \\
2.5 & 2.2574 & 2.4542 & 2.3055 & 2.3547 & 2.4531 & 2.4553 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The impact of size and deviation of the Gaussian low-pass filter on running time (seconds), which is tested on LIVE II dataset. The minimum running time is marked in boldface. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Patch Quantity** & **4 \(\times\) 4** & **8 \(\times\) 8** & **12 \(\times\) 12** & **16 \(\times\) 16** & **20 \(\times\) 20** & **32 \(\times\) 32** & **64 \(\times\) 64** \\ \hline Running Time (seconds) & 3.4769 & 3.8733 & 3.6547 & **2.4373** & 4.5235 & 5.4144 & 18.3218 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison of running time in LIVE II dataset with different patch quantity from 4 \(\times\) 4 to 64 \(\times\) 64. The minimum running time is marked in boldface. As seen from Table 6, NSSIM achieves 0.8971 of PLCC and 0.1266 of RMSE on CSIQ [25] dataset, better than SSIM and MCNN metrics. We randomly sampled 100 images from CSIQ dataset by 10 times for the \(t\)-test, so that 10 samples of SROCC, PLCCs and RMSE were achieved for each algorithm in comparison. \(p\)-values in Table 6 show that \(t\)-tests reject the null hypothesis at 5% significance level, i.e., the alternative hypothesis is accepted that the pairwise difference between NSSIM and the other metrics does not have a mean equal to zero. This ascertains the differences of various metrics are the statistically significant. Table 7 shows that NSSIM achieves 0.9689 of PLCC which performs better than the other ten algorithms on LIVE II [26] dataset, and 0.9464 of SROCC holds the third position among the 11 metrics. A paired-sample \(t\)-test was also applied the same as we done on CSIQ [25] dataset. The \(p\)-values demonstrate the statistically significant improvement of the proposed metric in terms of PLCC. Table 8 indicates that NSSIM achieves 0.9239 of PLCC and 0.4367 of RMSE, which are the best among all nine algorithms tested on IVC [27] dataset. We also run a paired-sample \(t\)-test via randomly sampling 15 images from IVC dataset by 10 times. The \(p\)-values proves the statistically significant improvement of the proposed metric in terms of PLCC and RMSE.