*3.3. Spectral Synthesis*

The spectral synthesis results are shown in Table 9 below.


**Table 9.** Spectral synthesis: ERGAS.

The best result is indicated by the smallest value. The results indicate that IMVM pansharpening method produced the best spectral synthesis followed by the RCS method. The Brovey method produced the worst synthesis.

The best spectral synthesis in IMVM was reflected by ERGAS 3.921, RCS 6.180, BAY 6.426, EHLERS 6.846, and GRS 7.069.

The IMVM algorithm produced the best pansharpening results in terms of spectral consistency and synthesis as revealed by the CC, bias, DIV, ERGAS, UIQI, RASE, and RMSE results. In terms of spectral consistency, one of the properties tested under Ward's criteria, the results of this study also show that the IMVM pansharpening technique had an average high correlation coefficient of 0.969 in the visible bands, the highest among the fusion algorithms tested in the study. The performance of the IMVM algorithm is further shown by the fact that it had the lowest bias and DIV values of 0.004 and 0.616, respectively. The superiority of the IMVM algorithm is further attested to by a very high UIQI value of 0.972. Such a high UIQI value demonstrates high spectral consistency as it considers factors such as loss of correlation, luminance, and contrast distortion. The IMVM algorithm had the best RMSE, RASE, and ERGAS values of 11.674, 3.741, and 1.062, respectively, the lowest amongst the tested pansharpened methods. The pansharpened image maintains almost the same natural color as the original multispectral images and the same level of spatial detail as the original panchromatic images. Results of the assessment also revealed that the IMVM algorithm had the best synthesis as shown by an ERGAS of 3.921, the lowest in the analysis, indicating that the fused image had minimum distortions and is quite similar to the reference image.

The RCS algorithm ranked second in the assessment and showed good results in terms of spectral consistency and synthesis. The ability of the algorithm to retain spectral information is shown by a correlation coefficient of 0.855, bias of 0.007, DIV of 1.270, ERGAS of 2.296, UIQI of 0.856, RASE of 8.239, and RMSE of 26.009. The other pansharpening methods that performed comparatively well in terms of spectral consistency were the wavelet principal components, MIHS, and PANSHARP methods. The PCA and Brovey methods produced consistently poor results in terms of spectral consistency as shown by the CC, bias, DIV, ERGAS, UIQI, RASE, and RMSE results.

Spectral synthesis is one of the properties that needs to be analyzed under Ward's three property criteria. As pointed out earlier, our results indicate that the IMVM algorithm produces the best spectral synthesis as shown by a very low ERGAS value of 3.921. Once again, the RCS algorithm ranked second with an ERGAS value of 6.180. Good spectral synthesis results were also obtained by the BAY, EHLERS, GRS, PANSHARP, and MIHS fusion techniques. The spectral synthesis results also revealed the poor performance of the Brovey, CNS, and PCA methods as shown by ERGAS values of 27.034, 25.122, and 19.177, respectively.

The third property evaluated in this study in terms of Ward's three property criteria related to spatial consistency. The correlation coefficient results ranked BAY, GRS, CNS, PANSHARP, RCS, PCA, and MIHS algorithms among the top-performing fusion techniques in terms of spatial consistency. While the Bayer algorithm was considered the best in terms of spectral consistency, most of the algorithms showed high spatial correlation with a correlation coefficient above 0.8 and the wavelet principal component method having the lowest value of 0.542. In contrast to the spectral consistency and synthesis results, the IMVM algorithm did not feature among the top-performing algorithms although it still had a high correlation coefficient of 0.784. This result seems to suggest there is a trade-off between spectral consistency and synthesis with spatial consistency.

While the IMVM and RCS pansharpening methods showed superior performance compared to the other fusion methods such as the PANSHARP, MIHS, GRS, wavelet transform, Bayesian, and EHLERS pansharpening techniques, the results of this study clearly show the credibility of these methods in terms of preservation of spectral and spatial information. When selecting the most ideal pansharpening method to use for practical applications, a trade-off is required in terms of factors such as the need for retention of scene radiometry, image sharpness, spatial and spectral consistency, and computational overhead.

Color distortion due to pansharpening could be attributed to the broadening of the panchromatic band into the near-infrared wavelength region in some modern sensors [26]. In the case of SPOT 6/7, the panchromatic bands have a spectral range of 450 nm to 745 nm, clearly overshooting the bands in the visible spectrum and encroaching into the near-infrared region that starts from the nominal red edge at 700 nm. This spectral coverage essentially spans over the visible spectrum that contains the blue (450–450 nm), green (530–590 nm), and red (625–695 nm) spectral channels. The extension of the panchromatic band affects the grey values of the panchromatic channel rendering some traditional pansharpening techniques less effective. The PANSHARP algorithm, for instance, is resilient to this challenge in that it is a statistics-based technique that uses the least-squares method to determine the best fit between the grey level values of the spectral bands being merged and adjusts the contribution of each band to the pansharpening result to minimize color distortions. Zhang [26,27] also highlights that the statistics-based approach utilized in the PANSHARP algorithm lessens the influence of dataset discrepancy and automates the pansharpening process. This assertion is supported in this study as shown by the superior performance of the IMVM, RCS, and Bayer's fusion techniques. The high performance of the IMVM image fusion algorithm was confirmed in similar studies. Witharana [44] reported that the IMVM algorithm produced some of the best fusion results when compared to a range of pansharpening algorithms when evaluated using CC, RMSE, Deviation Index (DI), SD, and DIV metrics. Nikolakopoulos and Oikonomidis [43] compared fusion techniques and confirmed that the LMVM algorithm produced the best spectral consistency and synthesis when applied to Worldview-2 data. As in our case, other techniques that produced favorable spectral consistency and synthesis results included PANSHARP, MIHS, EHLERS, GRM, and wavelet principal components techniques [44,45].

The shortcomings of traditional fusion techniques such as PCA, Brovey transform, and wavelet fusion are well described by Zhang [26]. To improve the quality of pansharpening results of traditional pansharpening methods some propositions recommended include stretching the principal components in PCA pansharpening to give them a spherical distribution. Alternatively, the first principal component could be cast-off. Modifications of traditional pansharpening techniques are necessary to deal with some of the limitations confronted in dealing with new satellite sensors. In a general sense, the quality of image geometric and radiometric rectifications done before the pansharpening directly impacts on the quality of all pansharpening results for all the image fusion techniques.

Lastly, the spectral integrity of pansharpened images is an important requirement for most quantitative remote sensing applications. While this study used an array of reference-based metrics to assess the image quality of various pansharpened images in terms of spectral consistency, spatial consistency, and image synthesis, the information content within the images was not quantified. The use of image information metrics such as Shannon entropy and Boltzmann entropy [46–50] enables the quantification of the average amount of information in the fused images and could be used to effectively assess the efficacy of various pansharpening methods in terms of the ability to retain or enhance both spectral and spatial information.

#### **4. Conclusions**

Pansharpening in increasingly becoming an important procedure critical in meeting the ever-increasing demands for high-resolution satellite imagery. Preservation of spectral and spatial information is an important requirement for most quantitative remote sensing applications. In this study, image quality metrics were used to evaluate the performance of twelve image fusion techniques. Twelve pansharpening algorithms were presented in this study and the IMVM algorithm was the best in terms of spectral consistency and synthesis followed by the RCS algorithm. Although the IMVM and RCS image fusion techniques showed better results compared to the other pansharpening methods, it is pertinent to highlight that our study also showed the credibility of the other pansharpening algorithms in terms of spatial and spectral consistency as shown by the high correlation coefficients achieved in all methods. The spatial and spectral quality of the pansharpening could, therefore, be

improved by implementing some modifications to the traditional pansharpening techniques to deal with the discrepancy that arises due to the broadened panchromatic band that extends to the near-red region. The use of statistics-based techniques such as the IMVM, PANSHARP, and Bayers algorithms used in this study could address this shortcoming. In terms of spatial consistency, BAY, GRS, CNS, PANSHARP, RCS, PCA, and MIHS algorithms showed very good spatial consistency as shown by the high spatial correlation coefficients. The study noted that the algorithms that ranked higher in terms of spectral consistency were outperformed by other competing algorithms in terms of spatial consistency. We, therefore, conclude that the selection of image fusion techniques is driven by the requirements of remote sensing application and a careful trade-off is necessary to account for the impact of scene radiometry, image sharpness, spatial and spectral consistency, and computational overhead.

**Author Contributions:** Conceptualization, P.M.; methodology, P.M.; validation, P.M., W.M., and N.M.; formal analysis, P.M.; investigation, P.M., W.M., and N.M.; resources, P.M.; writing—original draft preparation, P.M.; writing—review and editing, P.M., W.M., and N.M.; project administration, P.M. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflicts of interest.
