## 4 Data and Methods
### Methodological Considerations and Requirements  
To achieve the mentioned objectives, certain fundamental assumptions are mandatory. The most essential step towards a successful cloud removal is their detection [23]. Within this study, the cloud detection is regarded as given, since the work was not supposed to focus on cloud detection algorithms. Hence, cloud cover was simulated in the framework of this study. Detailed disquisitions of this topic are beyond the scope of this paper. Furthermore, cloud shadows were neglected completely. This assumption is justified by the abstraction of clouds (and their shadows) to areas of no information. Moreover, this study is focused on the removal of optically thick clouds with no contribution of the ground beneath a cloud to the signal received at a sensor. Therefore all evaluations are based on the consideration of small, optically thick fair weather cumulus clouds. \begin{table}
\begin{tabular}{l l l} \hline \hline
**Property** & **Landsat TM 5** & **SPOT 4** \\ \hline Acquisition Date & 2010-07-08 & 2010-07-09 \\ Original Resolution & 30 m & 20 m \\ Final Resolution & 30 m & 30 m \\ Spectral Bands (\(\mu\)m) & Blue (0.45–0.52) & \\  & Green (0.52–0.60) & Green (0.50–0.59) \\  & Red (0.63–0.69) & Red (0.61–0.68) \\  & NIR (0.76–0.90) & NIR (0.78–0.89) \\  & SWIR-1 (1.55–1.75) & SWIR (1.58–1.75) \\  & Thermal (10.4–12.5) & \\  & SWIR-2 (2.08–2.35) & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Overview of the multi-spectral data used in this study. \begin{table}
\begin{tabular}{l l l l} \hline \hline
**Property** & **TSX** & **ERS** & **ALOS** \\ \hline Acquisition Date & 2010-07-10 & 2010-06-09 & 2010-07-09 \\ Acquisition Mode & SM * & IM ** & FBD *** \\ Polarization State & HH/HV & VV & HH/HV \\ Incidence Angle & 22.13\({}^{\circ}\) & 23.18\({}^{\circ}\) & 38.74\({}^{\circ}\) \\ Band Name & X-Band & C-Band & L-Band \\ Frequency & 9.6 GHz & 5.3 GHz & 1.27 GHz \\ Wavelength & 3 cm & 5.6 cm & 23.6 cm \\ Pass Direction & Descending & Ascending & Ascending \\ Looking Direction & Right & Right & Right \\ R\({}^{+}\)/A\({}^{++}\) Resolution & 4.22 m/4.39 m & 20.01 m/19.85 m & 15.2 m/12.53 m \\ R/A ML\({}^{+++}\)-Factor & 12/12 & 1/5 & 2/8 \\ Original Resolution & 1.1 \({}^{+}\)/2.4 \({}^{++}\) m & 3.9 \({}^{+}\)/7.9 \({}^{++}\) m & 9.3 \({}^{+}\)/3.1 \({}^{++}\) m \\ Final Resolution & 30 m & 30 m & 30 m \\ \hline \hline \end{tabular}  
* SM—StripMap; ** IM—Image Mode; *** FBD—Fine Beam Dual;  
\({}^{+}\) R—Range Direction; A\({}^{++}\)—Azimuth Direction; ML\({}^{+++}\)—Multilooking.  
\end{table} 
Table 2: Overview of the SAR data used in this study. Based on these assumptions, the following methodological requirements arise for the framework of this study:  
* Implementation of a generic pixel-based cloud removal algorithm as a step towards the compensation of the drawbacks of substitution and interpolation techniques. The algorithm is supposed to be:
* sensor independent,
* based on physical interrelations,
* independent from the land cover,
* methodologically simple, and
* generating reproducible outputs;
* Establishment of a framework for the statistical evaluation of the performance of the cloud cover removal algorithm;
* Evaluation of the potential of mono-temporal, multi-frequency SAR imagery to serve as data basis for the image restoration of a multi-spectral image. To achieve the abovementioned objectives, certain basic requirements on data and methodology can be inferred. In order to consider land cover change as negligible, it is mandatory to include data with very short temporal baselines in relation to the cloud obscured multi-spectral image. Another data related premise is the endeavor to keep the demand for cloud-free reference data as minimal as possible but to include as much data as necessary. On the methodological side, it is desirable to reduce the complexity of the algorithm as much as possible. In order to achieve a logical intuitive restoration of missing information, the number of variables should be minimized.