## 2 Proposed Fusion Scheme
The structural similarity index measure (SSIM) is used to evaluate the degree to which the reference and fused images have comparable pixel intensities patterns locally. If the value is 1, it means that the reference image and the fused image are analogous. Figure 26 illustrates the relative importance of this metric in comparison with other image fusion techniques. The average improvement of the proposed method concerning SSIM is 7.32% with reference to PA-DCPCNN [20]. The correlation coefficient (CC) measures the degree to which the reference and fused images have the same spectral characteristics. Higher values of CC mean that the fusion method is better. Figure 27 illustrates the relative importance of this metric in comparison with other image fusion techniques. For this parameter, the resultant average value is less than PA-DCPCNN because this indicates that variables move in the opposite direction [20]. The average gradient (\(AG_{F}\)) quantitatively represents the fused image's detail and texture components. The fused image has increased sharpness and clarity proportional to the value of the \(AG_{F}\). Figure 28 illustrates the relative performance of various image fusion techniques based on this metric's value. The average improvement of the proposed method concerning \(AG_{F}\) is 5.95% with reference to PA-DCPCNN [20]. The evaluation of different fusion methods for different parameters based on their average values is depicted in Figure 29. Concerning \(Q_{E}\), the proposed method is 19.50%, 22.89%, 22.17%, and 24.83% superior compared to methods 1, 2, 3, and 4, respectively. Concerning \(AG\), the proposed method is 39.26%, 39.19%, 39.28%, and 38.50% superior compared to methods 1, 2, 3, and 4, respectively. Concerning \(Q^{0}\), the proposed method is

Figure 26: Performance evaluation of image-fusion techniques in reference to _SSIM_. Figure 25: Performance evaluation of image-fusion techniques in reference to \(Q^{ABF}\). 11.41%, 12.50%, 9.50%, and 11.23% superior compared to methods 1, 2, 3, and 4, respectively. Concerning \(Q^{AB/F}\), the proposed method is 21.69%, 24.98%, 23.45%, and 25.58% superior compared to methods 1, 2, 3, and 4, respectively. Concerning \(GM\), the proposed method is 0.27% superior compared to method 1. Concerning \(SD\), the proposed method is 1.70%, 1.54%, 1.35%, and 1.19% superior compared to methods 1, 2, 3, and 4, respectively [22]. Figure 28: Performance evaluation of image-fusion techniques in reference to \(AG_{F}\). Figure 27: Performance evaluation of image-fusion techniques in reference to CC. Figure 21:0 Evaluation of different fusion methods for different parameters based on them average values. ### Computational Efficiency

All of the experiments are carried out in MATLAB R2018b on a computer equipped with an Intel(R)-Core (TM) i5-11320H CPU operating at 3.20 GHz and 16 gigabytes of random-access memory (RAM). Comparing the average amounts of time these various methods take to compute results gives an evaluation of the computational burdens imposed by both existing and proposed approaches. Table 15 contains information on the typical amount of time required to complete these approaches. Since the proposed method integrates _SWT_, _DTCWT_, and _TEM_, the amount of time needed to complete the computations is significantly reduced. As a result, the proposed method has a shorter amount of computing time than existing methods [20]. ## 5 Conclusions

In this paper, _TEM_ laws are used in the hybrid wavelet domain combination of _SWT_ and _DTCWT_ to overcome the drawbacks of the _PA-DCPCNN_ and _MST-CSR_ based methods. The proposed work is implemented on standard images. As a result of using a hybrid algorithm with _TEM_, the proposed fused image can achieve higher visual quality when compared to input images because of its good directionality and a high degree of shift invariance. It is compared with recently published image fusion methods: _PA-DCPCNN_, and _MST-CSR_ (i.e., _DWT-CSR_, _DTCWT-CSR_, _CVT-CSR_, and _NSCT-CSR_).