Compton imaging is a useful method to localize gamma sources without using mechanical collimators. In conventional Compton imaging, the incident directions of gamma rays are estimated in a cone for each event by analyzing the sequence of interactions of each gamma ray followed by Compton kinematics. Since the information of the ejection directions of the recoil electrons is lost, many artifacts in the shape of cone traces are generated, which reduces signal-to-noise ratio (SNR) and angular resolution. We have developed an advanced Compton imaging system with the capability of tracking recoil electrons by using a combination of a trigger-mode silicon-on-insulator (SOI) pixel detector and a GAGG detector. This system covers the 660-1330 keV energy range for localization of contamination nuclides such as 137Cs and 134Cs inside the Fukushima Daiichi Nuclear Power Plant in Japan. The ejection directions of recoil electrons caused by Compton scattering are detected on the micro-pixelated SOI detector, which can theoretically be used to determine the incident directions of the gamma rays in a line for each event and can reduce the appearance of artifacts. We obtained 2-D reconstructed images from the first iteration of the proposed system for 137Cs, and the SNR and angular resolution were enhanced compared with those of conventional Compton imaging systems.