## 3 Results and Discussion
### Concentration Distribution Map  
The superiority of hyperspectral images to simultaneously obtain both spectral and spatial information makes it possible to display the results of soil TAs concentration distribution map. This study picks eight soil sample hyperspectral images to generate a TAs concentration distribution map, the maximum TAs concentration soil sample (Figure 6h), minimum TAs concentration soil sample (Figure 6a), and 6 other TAs soil samples. The best model--ETR based on FD preprocessed--was selected to visualize the soil TAs concentration distribution map. The spectral information on each pixel in hyperspectral images was input into ETR model to predict the results. Combined with the prediction results of spatial location information of hyperspectral images, the TAs concentration distribution map could be eventually formed [37, 51]. Then, according to the prediction values, divide the values in the graph into five intervals to statistical analysis, cyan (0-8 \(\upmu\)g/g), green (8-10 \(\upmu\)g/g), yellow (10-12 \(\upmu\)g/g), orange (12-14 \(\upmu\)g/g), and red (14+ \(\upmu\)g/g) (Figure 6). In Figure 6, with more cyan and green sample distribution maps, the sample prediction value is low. Sample distribution maps with more red, orange, and yellow have higher predicted values. According to the results in the Figure 6, mean and standard deviation were statistically analyzed, as shown in Table 4.  
Figure 5: Comparison between the measured values and predicted values of the different regression models. (**a**) ETR; (**b**) RF; (**c**) SVMR; (**d**) PLSR. Shown in Table 4, all soil sample maps with low values (0-10) \(\upmu\)g/g (cyan and green) totaled around 75%. The higher area (more than 10 \(\upmu\)g/g) (yellow, orange, red) is about 25%. Meanwhile, according to Table 4, HSI predicted TAs and measured TAs used the standard deviation plotted as error bars for each sample is drawn (Figure 7). As shown in Figure 7, the mean HSI predicted value increases as the measured value increases, confirming a positive correlation between the two datasets. Furthermore, on the whole, the HSI and measured values are in agreement when considering the standard deviation associated with the HSI prediction. Overall, the results of TAs content in soil samples for measured value were compared with the results shown in the distribution map. The results show that the concentration gradually increases \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multicolumn{2}{c}{**Measured**} & \multirow{2}{*}{**Std.**} & \multirow{2}{*}{**Mean**} & \multirow{2}{*}{**0-8 (\(\upmu\)g/g)**} & \multirow{2}{*}{**8-10 (\(\upmu\)g/g)**} & \multirow{2}{*}{**10-12 (\(\upmu\)g/g)**} & \multirow{2}{*}{**12-14 (\(\upmu\)g/g)**} & \multirow{2}{*}{**14+ (\(\upmu\)g/g)**} \\  & **Value (\(\upmu\)g/g)** & & & & & & \\ \hline a & 7.04 & 4.10 & 8.01 & 37\% & 42\% & 4\% & 13\% & 4\% \\ b & 8.26 & 4.12 & 8.58 & 32\% & 47\% & 5\% & 11\% & 5\% \\ c & 8.69 & 4.13 & 8.59 & 25\% & 56\% & 7\% & 8\% & 4\% \\ d & 9.36 & 4.20 & 8.63 & 23\% & 54\% & 5\% & 11\% & 7\% \\ e & 10.58 & 4.23 & 8.68 & 24\% & 50\% & 10\% & 9\% & 6\% \\ f & 11.05 & 4.36 & 8.92 & 23\% & 51\% & 9\% & 11\% & 6\% \\ g & 11.25 & 4.37 & 8.96 & 25\% & 48\% & 12\% & 10\% & 5\% \\ h & 16.41 & 4.39 & 9.05 & 22\% & 48\% & 9\% & 13\% & 8\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Statistical summary of the TAs distribution maps. Figure 6: Soil TAs concentration distribution maps (Label value is soil sample of arsenic concentration measured with atomic fluorescence spectrometry). (**a**) Sample a 7.04 (\(\upmu\)g/g); (**b**) sample b 8.26 (\(\upmu\)g/g); (**c**) sample c 8.69 (\(\upmu\)g/g); (**d**) sample d 9.36 (\(\upmu\)g/g); (**e**) sample e 10.58 (\(\upmu\)g/g); (**f**) sample f 11.05 (\(\upmu\)g/g); (**g**) sample g 11.25 (\(\upmu\)g/g); (**h**) sample h 16.41 (\(\upmu\)g/g). from soil sample a to soil sample h. This confirms that the model is highly correlated with the real results.