Le . 
pt IA edd NG ed MM 
} 
; 
E 
  
    
  
(a) (b) (c) 
Figure 4. The fractional abundance derived from spatial 
interpolation-based spectral unmixing, where magnification 
factor was set to four (a) water, (b) bare soil / deciduous tree 
and (c) evergreen tree 
  
(a) (b) (c) 
Figure 5. The fractional abundance derived from FCLS (a) 
water, (5) bare soil / deciduous tree and (c) evergreen tree 
(a) 
Figure 6. The fractional abundance derived from hard 
classification (a) water, (b) bare soil / deciduous tree and (c) 
evergreen tree 
As the ASTER image was unmixed, it is necessary to evaluate 
accuracy of different unmixing algorithms. Root mean square 
error (RMSE) was used as the error index using the following 
formula: 
(1) 
where R; is the RMSE value of ith endmember, Pi is the real 
  
fractional abundance of ith endmember in jth pixel, P is the 
estimated fractional abundance of ith endmember in jth pixel. In 
addition, to evaluate the total RMSE value of all endmembers, 
RMSE values of all endmembers should averaged as the 
average RMSE. Then RMSE values of the proposed spatial 
interpolation (SI) algorithm and other algorithms were listed in 
Table 1. 
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXIX-B7, 2012 
XXII ISPRS Congress, 25 August — 01 September 2012, Melbourne, Australia 
  
  
  
  
  
  
  
  
  
  
  
  
RMSE 
Algorithm Evergreen | Deciduous tree / Water [Average 
tree bare soil 
SI (M=2) 0.0599 0.1807 0.1743 | 0.1385 
SI (M=3) 0.0539 0.1136 0.1084 | 0.0920 
SI (M=4) 0.0499 0.0826 0.0768 | 0.0698 
SI (M=5) 0.0542 0.1130 0.1082 | 0.0918 
SI (M=6) 0.0583 0.1178 0.1119 | 0.0960 
FCLS 0.0844 0.2025 0.1705 | 0.1525 
MESMA 0.1560 0.2408 0.2904 | 0.2291 
Hardy 0.0819 0.1965 0.1905 | 0.1563 
classification 
  
  
  
  
  
  
  
Table 1. RMSE values of different spectral unmixing algorithms, 
where M denotes the magnification factor 
From Table 1, it is found that spatial interpolation-based 
spectral unmixing has higher accuracy than that of the MESMA, 
FCLS and hard classification, as the average RMSE values 
show. However, the performance of the proposed algorithm 
depends on the parameter, the magnification factor. The 
unmixing error reaches the bottom line when the magnification 
factor is equal to four, whereas other values of the factor 
resulted in different average RMSE values with large variation. 
Nevertheless, the proposed algorithm has higher accuracy than 
that of the LSU whatever the magnification factor is chosen. 
The result is interesting because only using a simple spatial 
interpolation is efficient to retrieve endmember proportion from 
mixed pixels, as this study shows. Although the spatial 
interpolation will absolutely ignore some detail information in 
the required higher resolution image, it is also effective since 
the resolution conversion in SRSU has reduced the impact of 
detail information in higher resolution. Thus spatial 
interpolation has great potential for spectral unmixing of 
remotely sensed imagery as this experiment shows. 
5. CONCLUSION 
SRSU is a new arising method for spectral unmixing of 
remotely sensed imagery, and has shown good performance in 
previous studies. However, training database in SRSU is a big 
obstacle for convenient use of SRSU. In this study, spatial 
interpolation, much easier to implement, is used as an 
alternative approach to achieve super resolution reconstruction. 
An experiment using ASTER image shows that this simplified 
version of SRSU also performs better than that of linear spectral 
unmixing and hard classification, since the RMSE of the 
proposed algorithm is smaller than that of the linear spectral 
unmixing. Among the different values of magnification factor, it 
was discovered that when the image is resampled to four times 
of the original size, the proposed algorithm shows the highest 
spectral unmixing accuracy. 
This study opens a door to convenient use of SRSU, which will 
make more scholars to recognize the importance and power of 
SRSU. Admittedly, some important issues, such as the optimal 
spatial interpolation method and magnification factor, should be 
considered carefully in future studies. As a result, the land cover 
mapping from remotely sensed imagery will be more accurate 
by use of the improved SISU.