Microwave imaging techniques, particularly for synthetic aperture radar (SAR), produce high-resolution terrain surface images regardless of the weather conditions. Focusing on a feature of complex SAR images, coherent change detection (CCD) approaches have been developed in recent decades that can detect invisible changes in the same regions by applying phase interferometry to pairs of complex SAR images. On the other hand, various techniques of polarimetric SAR (PolSAR) image analysis have been developed, since fully polarimetric data often include valuable information that cannot be obtained from single polarimetric observations. According to this background, various coherent change detection methods based on fully polarimetric data have been proposed. However, the detection accuracies of these methods often degrade in low signal-to-noise ratio (SNR) situations due to the lower signal levels of cross-polarized components compared with those of co-polarized ones. To overcome the problem mentioned above, this paper proposes a novel CCD method by introducing the Pauli decomposition and the weighting of component with their respective SNR. The experimental data obtained in anechoic chamber show that the proposed method significantly enhances the performance of the receiver operation characteristic (ROC) compared with that obtained by a conventional approach.