Riemannian Quaternion Self-Organizing Map to Overcome Degree-of-Polarization Error in Polarimetric Ground-Penetrating Radar

Ground-penetrating radar (GPR)-based landmine detection has advantages such as high safety and high efficiency. There are various methods to process the data obtained from GPR systems. One of the commonly used methods is to visualize the quaternion-type polarization data by quaternion self-organizing map (QSOM). However, QSOM cannot take into account the geometric property of the polarization data. Then, degree-of-polarization (DoP) error is introduced in the self-organization process of QSOM, which leads to unsatisfactory visualization results. To overcome the limitation, in this article, we propose a novel processing, Riemannian QSOM (RQSOM), which takes into account the geometric property to eliminate the DoP error with the help of logarithmic and exponential maps in Riemannian geometry. We analyze its basic dynamics and compare it with that of QSOM. We conduct experiments to visualize a mock plastic landmine with QSOM and RQSOM. The experimental results show that RQSOM realizes expected self-organization dynamics, thereby achieving better visualization results compared with QSOM.