## 4 Data and Methods
### Design of the Performance Evaluation  
#### 4.6.1 Proof of Concept  
The first major part towards the evaluation of the potential of SAR data to remove cloud-obscured pixels from multi-spectral imagery is a reliable test of the algorithm performance. Therefore it is mandatory to prove the potential of the techniques to restore information beneath clouds. In this study, an approach is established that contains two steps. * Cloud removal based on a perfect fill image. * Cloud removal based on a multispectral image. A perfect data source in terms of information restoration is the clouded image itself. This seems paradoxical at first glance, since it raises the question of how an image filled by a certain algorithm with itself shall prove the performance of the algorithm. However, instead of replacing the feature vector of a certain pixel with itself, the algorithm will find the spectrally and spatially closest neighbor. The regions beneath the clouds are masked out for the derivation of the CFV. This methodology makes sure that the fill algorithm will find the most similar pixel \(F_{i,j}\) for the pixel \(F_{x,y}\) under investigation. This approach has numerous advantages. First, it enables the investigation of the overall performance potential of the fill algorithm. Will the result be also perfect, considering a perfect data source? Second, the influence of the two components of the fill algorithm (_i.e._, CFV and IDW) on the fill result can be evaluated in order to define an optimal distance weight (DW). The major shortcoming is the fact that such a perfect data source for cloud removal will hardly exist in the real world, since it assumes the same acquisition date, the same radiometric properties, the same spatial and spectral resolution and exactly the same atmospheric conditions of the fill image \(F\) in comparison with the clouded image \(C\). Nevertheless, this theoretical evaluation of the fill algorithm performance is a significant step towards the evaluation of the algorithm performance. In order to estimate the influence of DW as well as the general potential, a number of constellations are established. First, the amount of cloud cover was fixed at 10%. Only the weight DW is varied. Second, DW is fixed and the amount of cloud cover is varied. The distance weight is varied from \(0.0\) (_i.e._, distance has no influence) over non-linear values (_cf._ Figure 5) up to 2.0. In the latter case the weight of the distance changes with the square of the distance. This property is tested due to the fact that \(DW=2.0\) is the most common setting in spatial interpolation techniques using IDW [14]. The amount of cloud cover was varied from 10% to 50% in order to evaluate the loss of restoration quality due to the limitation of available information. The second step towards the assessment of the potential of SAR data is the evaluation of the performance potential of the algorithm by means of an additional multi-spectral reference. This is useful in terms of testing the robustness of the fill algorithm with regard to variations in the number of available spectral bands, their specific bandwidth, _etc._ Therefore, the knowledge about the potential of the fill algorithm to compensate these variations will be a significant advancement. This second step  
Figure 5: Visual comparison of the original image in comparison with a filled image by means of a perfect data source (_i.e._, the image itself) as a function of the Inverse Distance Weighting. (**a**) Clouded Image; (**b**) Original Image; (**c**) IDW = 0.0; (**d**) IDW = 0.1; (**e**) IDW = 0.2; (**f**) IDW = 0.3; (**g**) IDW = 0.4; (**h**) IDW = 1.0; (**i**) IDW = 2.0.  
was accomplished within this study with the help of a SPOT 4 scene of the test site. This SPOT image was filled by means of the Landsat scene. A major shortcoming is the fact that the overlapping area between the SPOT 4 and the SAR scenes is very small. Therefore the spatial subset varies for this part of the study.