## 2 Materials and Methods
The panchromatic band is fused into low-resolution multispectral channels by performing a reverse PCA transform. A high-resolution fused image is generated after the reverse PCA transformation [29]. The color normalized spectral sharpening (CNS) algorithm implemented in Environment for Visualizing Images (ENVI) software is employed to simultaneously sharpen any defined number of bands and retain the characteristics of the original bands in terms of data type and dynamic range. In this case, the higher resolution bands are used to sharpen the lower resolution bands and in the ENVI implementation, the lower resolution multispectral bands are expected to fall in the same spectral range with the high-resolution panchromatic channel [30; 31]. The multispectral bands are clustered into spectral segments defined by the spectral range of the high-resolution panchromatic sharpening band. The pansharpened image is generated by multiplying the high-resolution panchromatic with each lower resolution multispectral band before normalizing the computation by dividing the sum of the input spectral channels in each segment. The wavelet resolution merge (WAVELET) fusion approach sharpens low-resolution multispectral bands using a matching high-resolution panchromatic band by first decomposing the high-resolution panchromatic band into a set of low-resolution multispectral bands with corresponding wavelet coefficients (spatial details) for each level. This is done by infusing the high-resolution spatial into each of the multispectral bands by performing a reverse wavelet transform on each MS band together with the corresponding wavelet coefficients. In a sense, wavelet-based processing is akin to Fourier transform analysis, except fast Fourier transform analysis uses long continuous (sine and cosine) waves, whereas wavelet transform analysis applies short and discrete wavelets [32; 33; 34; 35]. The Gram-Schmidt (GRS) pansharpening algorithm available in the ENVI fuses the high-resolution panchromatic band to the lower resolution multispectral bands by simulating the panchromatic band from the multispectral band by averaging the multispectral bands. A Gram-Schmidt transformation is computed from the simulated panchromatic band and the multispectral band, whereby the simulated panchromatic band is used as the first band. Further, the high spatial resolution panchromatic band is substituted with the first Gram-Schmidt band before applying an inverse Gram-Schmidt transformation to generate the pansharpened multispectral bands [36; 37]. The ratio component substitution (RCS) pansharpening algorithm implemented in Orfeo ToolBox [38] fuses orthorectified panchromatic (PAN) and multispectral (XS) images using a low pass sharpening filter as shown in the computation below (OTB, 2019). \[\frac{\text{XS}}{\text{Filtered (PAN)}}\text{PAN E} \tag{1}\]  
where E is a vector of random errors that is considered to be stochastically independent of Z. The Bayesian fusion (BAY) applies elementary calculus in the fusion of the panchromatic and multispectral images to generate a pansharpened image [38]. This fusion approach uses the statistical relationships amongst the spectral bands and the panchromatic band. Bayesian pansharpening techniques use three images that include a panchromatic band and a multispectral image resampled to the same spatial resolution as the panchromatic band. The panchromatic band is weighted in comparison to the multispectral bands. A thorough mathematical description of the Bayesian pansharpening algorithm implemented in Orfeo ToolBox is provided by [39]. This pansharpeningtechnique is dependent on the notion that the variables of interest, expressed as vector Z, are not directly observable and related to observable variable Y through an error-like equation. \[\mathrm{Y=g(Z)+E} \tag{2}\]  
where g(Z) is considered a set of functionals.