Circular property of complex-valued correlation learning in CMRF-based filtering for synthetic aperture radar interferometry

To deal with satellite interferometric synthetic aperture radar (InSAR), we previously proposed a powerful filtering process, namely the complex-valued Markov random field (CMRF) -based filter. There we estimate and utilize the local correlation between pixel values in interferogram. 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 system 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. We also evaluate the performance of the filter based on phase-amplitude network to demonstrate the importance of treating the data as complex-amplitude information in filtering SAR interferogram.