## 4 Discussion
### Image Analysis  
MNF transformation was used on the masked images to determine the inherent dimensionality of image data, to segregate noise in the data, and to reduce the computational requirements for subsequent processing [33]. The MNF transformation is essentially a two-phase Principal Component Analysis that segregates the noise from the data resulting in a reduced number of bands, which contained the most meaningful information [60]. The first transformation, based on an estimated noise covariance matrix, de-correlated and rescaled the noise in the data. This step resulted in transformed data in which the noise had unit variance and no band-to-band correlations. The second step was a standard Principal Component transformation of the noise-whitened data. For the purposes of further spectral processing, the inherent dimensionality of the data was determined by examination of the final values and the associated image. The data space was divided into two parts: one part associated with large values and coherent images, and a complementary part with near-unity values and noise-dominated images. By using only the coherent portions, the noise was separated from the data, thus improving spectral processing results. The MTMF score in Figure 4 measures how spectrally abundant the measured material (endmember) is in the image pixel. Spectral abundance in an image pixel corresponds to physical abundance in the same location on the ground. A score of zero means no match to the input endmember and no presence of the material in a pixel, while a score closer to one indicates a better match to the input endmember and greater abundance of the material in the pixel. The infeasibility (IF) value generated as part of the MTMF analysis, shows how likely or unlikely the match is. In general, pixels with a combination of high MTMF scores with low IF values are a better match to the endmember spectrum [61]. The MTMF processed datasets reflected mostly soil and scorched vegetation endmembers. The scores of MTMF summation at each pixel was almost less than unity since almost all pixels had unidentified background material. MTMF combines features of Linear Spectral Mixing model and Matched Filter model while avoiding the drawbacks of each of these methods. Unlike traditional Spectra Mixture modeling, it has the ability to acquire a single known target without acquiring other background endmember signature [62]. It can leverage the constraints on feasibility including the unit-sum and positivity requirements. As a result, MTMF can outperform traditional mixing model methods, especially in cases of subtle, sub-pixel occurrences such as wildfires. The fire severity map derived in this study indicated that combining unmixing techniques with noise segregation greatly improved accuracy. The results found in this study successfully constitute to initial fire risk zone assessment using multispectral remote sensing imagery. The evaluation of dNBR, RdNBR, and MTMF of scorched vegetation and soil cover produced suitable matches to burn severity areas. The advantage of using MTMF with respect to dNBR and RdNBR is that it discriminates physical ground characteristics (i.e., ash, soil, and scorched/green vegetation) of dNBR and RdNBR classes while improving the burn severity map than previous mapping methods [63; 64]. The dNBR reflective values for vegetation (0.75) fit best with ground values of burn severity. The RdNBR reflective values for vegetation and soil were slightly higher than dNBR (Table 2), which resulted in better classification accuracies for mixed vegetation types as highlighted by several studies [18; 20; 21; 22]. RdNBR results showed a slight lower correlation to pre-fire NBR than dNBR, proving RdNBR is more effective at high severity burn detection, similar to a previous study [19]. Unmixing results greatly improve severity detection in fire-prone Xeric and secondary forest region by identifying the relative abundance of ground components (scorched vegetation and soil).