Phasor Quaternion Neural Networks for Singular Point Compensation in Polarimetric-Interferometric Synthetic Aperture Radar

Interferograms obtained by synthetic aperture radar often include many singular points (SPs), which makes it difficult to generate an accurate digital elevation model. This paper proposes a filtering method to compensate SPs adaptively by using polarization and phase information around the SPs. Phase value is essentially related to polarization changes in scattering as well as propagation. In order to handle the polarization and phase information simultaneously in a consistent manner, we define a new number, phasor quaternion (PQ), by combining quaternion and complex amplitude, with which we construct the theory of PQ neural networks (PQNNs). Experiments demonstrate that the proposed PQNN filter compensates SPs very effectively. Even in the situations where the conventional methods deteriorate in their performance, it realizes accurate compensation, thanks to its good generalization characteristics in integrated Poincare-sphere polarization space and the complex-amplitude space. We find that PQNN is an excellent framework to deal with the polarization and phase of electromagnetic wave adaptively and consistently.