# Comparison of Oil Spill Classifications Using Fully and Compact Polarimetric SAR Images
## 2 Methods
### Dual- and Compact Polarimetric SAR Modes  
Compact polarimetric SAR modes were proposed to solve the contradiction between polarimetric observation capabilities and the swath width, system complexity, power budget and data rate of the radar system. Actually, the idea of transmitting one polarized signal and coherently recording the backscattered signal in \(H\) and \(V\) polarimetric channels was considered by U.S. scientists as far back as 1960. In the 2000s, this operation mode was reconsidered by [PERSON] et al. [16] and was given the new name of \"compact polarimetric\" to differentiate from \"fully polarimetric\" or \"quad-polarimetric\".  
Dual polarimetric (DP) SAR systems transmit a horizontal (\(H\)) or a vertical (\(V\)) linearly-polarized signal and coherently record both horizontal and vertical polarized backscattered signals. They can be treated as a special kind of compact polarimetric SAR mode. In real applications, usually \(HH/HV\) or \(HV/VV\) dual polarization modes are used, for the reason that in these modes, only the \(H\) or \(V\) polarized signal is transmitted. However, on the sea surface, the backscatter of the cross-polarized channel (\(HV\)) is usually much lower than the co-polarized channels [34], sometimes close to the noise  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Pol-SAR Features** & **Clean Sea Surface** & \
\begin{tabular}{c} **Mineral Oil** \\ **(Strong Damping)** \\ \end{tabular} &
\begin{tabular}{c} **Biogenic Slicks** \\ **(Weak Damping)** \\ \end{tabular} \\ \hline Entropy (H) & Lower & High & Low \\ Alpha (\(\alpha\)) & Lower & High & Low \\ DoP & High & Low & High \\ Ellipticity & Negative & Positive & Negative \\ Pedestial Height (PH) & Lower & High & Low \\ Std. CPD & Lower & High & Low \\ Conformity Coefficient & Positive & Negative & Positive \\ Correlation Coefficient & Higher & Low & High \\ Coherence Coefficient & Higher & Low & High \\ \(S_{VV}^{2}\) & High & Low & Low \\ \hline \hline \end{tabular} Note: “lower” and “higher” means that the property of the feature on a certain type of surface is close to the other surface that has the property of “low” or “high”, but slightly lower or higher. “Std. CPD” stands for the standard deviation of CPD.  
\end{table}
Table 1: Behaviors of main polarimetric SAR features on different types of surfaces. DoP, degree of polarization; CPD, co-polarized phase difference.  
floor of the radar instruments. As a result, \(HH/HV\) dual polarimetric modes have limited performance on oil spill classification applications. Although there is no \(HH\)-\(VV\) dual polarimetric SAR operating, except a special experimental imaging mode of TerraSAR-X, this mode is considered for comparative analysis in this paper.  
The 2D measurements vector \(\overset{\rightarrow}{K}\) of \(HH/VV\) dual-polarized, \(\pi/2\) and \(\pi/4\) compact polarimetric SAR modes are provided in Equations (18)-(20), respectively:  
\[\overset{\rightarrow}{K}_{HHVV}=\left(\begin{array}{c}S_{HH}\\ S_{VV}\end{array}\right) \tag{18}\]  
\[\overset{\rightarrow}{K}_{pi/2}=\frac{1}{\sqrt{2}}\Bigg{(}\begin{array}{c} S_{HH}-jS_{HV}\\ S_{HV}-jS_{VV}\end{array}\Bigg{)} \tag{19}\]  
\[\overset{\rightarrow}{K}_{pi/4}=\frac{1}{\sqrt{2}}\Bigg{(}\begin{array}{c} S_{HH}+S_{HV}\\ S_{HV}+S_{VV}\end{array}\Bigg{)} \tag{20}\]  
Table 2 lists several main polarimetric SAR modes, which can be differentiated by their different transmission and receiving polarimetric combinations.  
The covariance matrix can also be used to reflect the second order statistics of the dual and compact polarimetric SAR data, which can be derived from their scattering matrix by:  
\[C_{CP}=2\bigg{\langle}\overset{\rightarrow}{K}_{CP}\overset{\rightarrow}{K }_{CP}^{*}\bigg{\rangle} \tag{21}\]  
where \(\overset{\rightarrow}{K}_{CP}\) stands for measurements vector \(\overset{\rightarrow}{K}\) of different dual- and compact polarimetric SAR modes.