Nowadays, SAR imaging is a well-developed remote sensing technique for providing high spatial resolution images of the Earth’s surface. Fully polarimetric SAR systems which transmit and receive two orthogonal polarizations provide precise information about targets but have some limitations; Transmitting two interleaved waves for each scene doubles the transmitted power, repetition frequency and data volume compared with dual polarized SAR systems which transmit only one polarization and receive two polarizations. On the other hand swath width, which is an important parameter for surveillance applications, for fully polarimetric systems is half of dual polarized systems. Therefore, compact polarimetric systems have been proposed. Compact polarimetric systems are dual polarimetric systems with special transmitted and received polarizations. These combinations of polarizations made the compact polarimetric systems maintain many capabilities of fully polarimetric systems. Three candidates have been proposed for compact polarimetry configurations, namely, π/4, Dual Circular Polarization and Circular Transmit Linear Receive modes. In dual circular polarisation mode one antenna transmits right or left circular polarization and the responses of scatterers are received by two orthogonal right and left circular polarization antennas. There are some deficiencies, regarding the reconstruction of fully polarimetric data from dual circular one in the literature. So in this paper we have explained the reconstruction methods for dual circular polarization data. In order to reconstruct fully polarimetric data from compact polarimetric data, one should consider two approximate assumptions. One of the important assumptions is the reflection symmetry about radar line of sight. This assumption is very necessary for reducing the number of unknowns in the problem of reconstruction. For the second assumption Souyris et al. first linked the magnitude of linear coherence and the cross polarization ratio with a parameter named N and approximately set this parameter to 4. Subsequently Nord modified Souyris’ algorithm by replacing N with the ratio of double bounce scattering power to the volume scattering power and updated it during the calculation process iteratively. These assumptions are not well accurate in reality and thus the reconstruction results have some errors. In this research we noticed that there is a high correlation between N and the ratio of cross polarization power to the sum of co-polarization power. Thus using regression analysis methods, we have linked these two parameters and proposed that N is related to R by a rational model which its nominator and denominator are linear polynomials of R. Using several images from RADARSAT-2 sensor, we have shown that the reflection symmetry assumption is not well accurate for DCP mode and Nord assumption is better than Souyris assumption. Souyris assumption is more appropriate for vegetation areas. We have investigated the accuracies of the proposed and previous assumptions and showed that the proposed assumption is more accurate than the two others. By using the new assumption we have proposed a modified reconstruction algorithm. The proposed and previous reconstruction algorithms have been simulated and quantitative and qualitative analyses have shown that results from the proposed algorithm are closer to the fully polarimetric data and thus the proposed method is more accurate.