Circular Property in Complex-Valued Correlation Learning Observed in CMRF-Based Singular Unit Restoration for Phase Unwrapping

Abstract

In the powerful filtering process we proposed previously, i.e., the complex-valued Markov random field (CMRF) -based filtering, we estimate and utilize the local correlation between pixel values in interferogram obtained by satellite interferometric synthetic aperture radar (InSAR) system. From the viewpoint of neural networks, the estimation is regarded as correlation learning in its simplest form. The correlation learning is performed in the complex domain since the InSAR yields complex-amplitude data corresponding to the wave / coherent nature of the electromagnetic-wave propagation. This fact leads to a useful dynamics specific to such coherent radar signal processing, which cannot be realized in real-valued neural networks. One of the properties of coherent wave is circularity. We compare the performance of filters based on complex- and real-valued networks.