3.1.5. Tradeoff Parameter

In the tradeoff process, the intensity images obtained by SCMP and CS were combined by Equation (17) using the tradeoff parameter τ (0 ≤ τ ≤ 1). The tradeoff parameter is a hyperparameter that should be determined in advance. In general, experimental validation is carried out via cross-validation when there are hyperparameters. Since we used two kinds of satellite images (Ninohmatsu and Yokohama), the value of τ was determined using one of these datasets, and the other dataset was processed using the determined value. In our experiment, the tradeoff parameter was determined using the correlation coefficient (CC) and ERGAS [38]. The results of applying the tradeoff parameter with a step size of 0.1 for image quality evaluation are shown in Table 3. From this result, it was found that the resolution and numerical evaluation were improved when the sum of squares of 1-CC and ERGAS was the smallest. This relationship is shown in Equations (23) and (24).

$$\underset{\tau}{\operatorname{argmin}} \mathcal{S}(\tau) \text{ s.t. } 0 \le \mathcal{S}(\tau) \le 2 \tag{23}$$

$$S(\tau) = \left(\frac{1 - CC(\tau)}{\max(1 - CC)}\right)^2 + \left(\frac{ERGAS(\tau)}{\max ERGAS}\right)^2\tag{24}$$

The tradeoff parameter was determined as the value that minimizes Equation (24). Figure 4 displays the results of evaluation of the intensity of RGB images with various tradeoff parameters. The red line shows Nihonmatsu, the blue line shows Yokohama, the solid line is the result of CC, and the dotted line is the result of ERGAS. Figure 5 shows three images with some tradeoff parameter values. The lower the evaluation index S, the better the visual appearance. From these results, the value that minimized *S*(τ) was τ = 0.4 for Nihonmatsu and τ = 0.3 for Yokohama. Therefore, in the following experimetns, τ = 0.3 was used for Nihonmatsu and τ = 0.4 was used for Yokohama.


**Table 3.** CC, ERGAS, and the evaluation index S that determines the tradeoff parameter. The best values are given in bold.

**Figure 4.** The values of CC and ERGAS obtained in the tradeoff process. CC: solid line, ERGAS: dotted line; Nihonmatsu: blue line, Yokohama: red line.

**Figure 5.** Comparison of intensity of RGB images against the tradeoff parameter. *S* represents the index that determines the tradeoff parameter. (**a**) Nihonmatsu, (**b**) Yokohama.
