## 4 Experimental Results and Discussion  
To evaluate the proposed algorithm, we conducted two experiments. First, we carried out an experiment with respect to visibility coefficient estimation. The objective of the first experiment was to evaluate the accuracy of the estimated visibility parameter. To achieve this, experimental images were generated from the original images and scattering medium images, as shown in Figure 8. Here, the experimental images are generated based on the \(\alpha\)-blending method using Equation (3), as illustrated in Figure 9. A total of 24 images were generated using Equation (3), with the visibility coefficients adjusted to 0.3, 0.5, and 0.7. The experiment compared the estimation of \(\alpha\) using the previous method with that using the proposed method. And the size of the moving average filter was set to 131 \(\times\) 131 for the proposed method. Figure 6: Probability density function for high-band images: (a) high-band image of baboon; (b) PDF of (a); (c) high-band image of baboon with \(\alpha\)-blending (\(\alpha\) = 0.3); (d) PDF of (c). Figure 7: Histogram stretching. Figure 10 shows some of the resulting images from the experiment, indicating that the quality of the reconstructed images improved subjectively. It can be observed that the resulting images obtained from the previous method with inaccurate visibility coefficients suffered from over-amplification in color. To quantitatively compare these results, we computed the peak signal-to-noise ratio (PSNR) and the structural similarity index measure (SSIM). Table 1 presents the visibility coefficients estimated by the proposed method and the previous method. The proposed method demonstrated more accurate estimated values for \(\alpha\), with averages of 0.32 for \(\alpha\) = 0.3, 0.52 for \(\alpha\) = 0.5, and 0.72 for \(\alpha\) = 0.7, in comparison to the previous method. The PSNR results shown in Table 2 indicate that the proposed method yielded a PSNR improvement of 3.99 dB on average. Table 3 presents the results of the SSIM values between the original images and the resulting images. The SSIM results also demonstrate that the proposed method was superior to the previous method in terms of the improvement in image quality. This is because the visibility coefficients were accurately estimated by the proposed method with the spectral model. These results are also reported in Table 3.  
Figure 8: Test dataset. (**a**) Baboon; (**b**) Lenna; (**c**) kodim22; (**d**) kodim23; (**e**) hazed image1; (**f**) hazed image2; (**g**) hazed image3; (**h**) hazed image4. Figure 9: Generating experimental images through alpha-blending. indicate that accurate estimation of the visibility coefficient plays an important role in improving image quality. In addition, we carried out another experiment by applying the proposed method to CIIR. The objective of the second experiment was to evaluate the performance of the proposed CIIR method. Here, the proposed method was compared with two existing methods. As shown in Figure 11, EIAs were generated from original test images. Then, CIIR methods were used to convert the generated EIA into the reconstructed images. The sizes of the input images were either 512 \(\times\) 512 or 768 \(\times\) 512. The number of elemental