## 4 Experimental Results
### Evaluation of Proposed Method
#### 4.4.2 Quantitative Comparison Analysis  
To validate the qualitative comparison above-discussed, we present here a quantitative comparison to assess and rank our proposed dehazing system. In this comparison, we employed two extensively used _FR-IQA_ metrics, namely _SSIM_ and _MSE_. _SSIM_ is used to measure the similarity between the restored image and its ground-truth image, while _MSE_ is used to calculate the error between them. Since _SSIM_ and _MSE_ are quality measures that need a reference image, they are limited to synthetic images only because the ground truths of these images are available. Furthermore, we measured the accuracy of the restored images on synthetic images by exploiting some common _NR-IQA_ (_FADE_[48], \(e\), and \(\bar{r}\)). The indexes \(e\) and \(\bar{r}\) are two contrast enhancement indicators presented by [PERSON] et al. [49], which measure the ability to recover the invisible edges and the quality of the contrast enhancement, respectively. _FADE_ indicator evaluates the ability to remove haze from hazy images. Table 3 sums up the average scores of _SSIM_, _MSE_, \(e\), \(r\), _FADE_, and running time (T) of the comparative methods as well as ours. The high score of _SSIM_ implies a high similarity between the ground-truth and the recovered image. A low value of _FADE_ designates a high ability for removing haze. Whenever the values of \(e\) and \(\bar{r}\) are high, the visibility of the restored images is enhanced. The best values of each indicator are written in bold. As evident from the results in Table 3, among all the comparative methods, our proposed model achieved the best scores of _SSIM_, _MSE_, and _FADE_, and ranked the second in term of visibility enhancement. In addition, it achieved the lowest running time when compared to other comparative methods (T = 0.386). This significant outcome implies that the proposed method can tackle the problem of haze removing, noise suppressing, and visibility-enhancing of recovered images, effectively. Moreover, Table 3 shows that _FADE_ indicator values obtained by [PERSON] et al. [14] and [PERSON] et al. [26] are a little bit high, which means that their results still have some haze residue. In addition, we can see that [PERSON] et al. [35] attained the best score of \(\bar{r}\) indicator, which comes from the over-enhancement, as discussed in the qualitative comparison. [PERSON] et al. 's method [14] has a high \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Method** & **[PERSON] et al. [14]** & **[PERSON] et al. [28]** & **[PERSON] et al. [26]** & **[PERSON] et al. [40]** & **[PERSON] et al. [35]** & **Ours** \\ \hline
**SSIM** & 0.727 & 0.853 & 0.821 & 0.898 & 0.887 & 0.912 \\ \hline
**MSE** & 2.093 & 2.892 & 0.846 & 1.867 & 0.079 & 0.068 \\ \hline
**e** & 1.896 & 1.452 & 1.237 & 2.190 & 2.830 & 2.792 \\ \hline
**\bar** & 2.951 & 2.763 & 2.609 & 3.652 & 4.025 & 3.785 \\ \hline
**FADE** & 1.957 & 0.862 & 1.487 & 0.353 & 0.320 & 0.167 \\ \hline
**T**(s) & 14.901 & 1.004 & 1.830 & 0.469 & 0.541 & 0.386 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The average values of _MSE_, _SSIM_, \(e\), \(r\), _FADE_, and \(T\) on synthetic hazy images of the comparative methods. time complexity (T = 14.901), far from all comparative methods, because of the soft-matting filter. This analysis confirms that the quantitative evaluation validates the previously-discussed qualitative analysis. Moreover, we applied the _NR-IQA_ metrics on real-world hazy images to quantify the performance of the proposed system. To assess the performance quantitatively, we collected from the Internet more than 500 real-world hazy images of average size 640 \(\times\) 480. Table 4 summarizes the average scores of \(e\), \(\bar{r}\), _FADE_, and running time (T) on real-world hazy images of the comparative methods, including our proposed method. As it is visible from the results in Table 4, the proposed system performed quickly compared to other methods and achieved an average of 0.453 s, while [PERSON] et al.