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

  • Akira Hirose
  • Ryo Natsuaki
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7202)


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.


Digital Elevation Model Local Correlation Phase Unwrap Interferometric Synthetic Aperture Radar Correlation Learning 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Costantini, M.: A novel phase unwrapping method based on network programming. IEEE Transactions on Geoscience and Remote Sensing 36(3), 813–821 (1998)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Fornaro, G., Franceschetti, G., Lanari, R.: Interferometric SAR phase unwrapping using Green’s formulation. IEEE Transactions on Geoscience and Remote Sensing 34(3), 720–727 (1996)CrossRefGoogle Scholar
  3. 3.
    Ghiglia, D.C., Pritt, M.D.: Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software. John Wiley & Sons, Inc. (1998)Google Scholar
  4. 4.
    Goldstein, R.M., Werner, C.L.: Radar interferogram filtering for geophysical applications. Geophysical Research Letters 25(21), 4035–4038 (1998)CrossRefGoogle Scholar
  5. 5.
    Hirose, A.: Merits of complex-valued neural networks. In: Proceedings of the International Workshop on Intelligence Science and Intelligent Data Engineering (IScIDE), Invited Talk Session 2 (2010)Google Scholar
  6. 6.
    Hirose, A.: Nature of complex number and complex-valued neural networks. Frontiers of Electrical and Electronic Engineering in China 6(1), 171–180 (2011)CrossRefGoogle Scholar
  7. 7.
    Lee, J.S., Papathanassiou, K., Ainsworth, T., Grunes, M., Reigber, A.: A new technique for phase noise filtering of sar interferometric phase images. IEEE Transactions on Geoscience and Remote Sensing 36(5), 1456–1465 (1998)CrossRefGoogle Scholar
  8. 8.
    Pritt, M., Shipman, J.: Least-squares two-dimensional phase unwrapping using FFT’s. IEEE Transactions on Geoscience and Remote Sensing 32(3), 706–708 (1994)CrossRefGoogle Scholar
  9. 9.
    Reigber, A., Moreia, J.: Phase unwrapping by fusion of local and global methods. In: International Geoscience & Remote Sensing Symposium (IGARSS), pp. 869–871 (August 1997)Google Scholar
  10. 10.
    Suksmono, A.B., Hirose, A.: Adaptive noise reduction of InSAR images based on a complex-valued MRF model and its application to phase unwrapping problem. IEEE Transactions on Geoscience and Remote Sensing 40(3), 699–709 (2002)CrossRefGoogle Scholar
  11. 11.
    Suksmono, A.B., Hirose, A.: Progressive transform-based phase unwrapping utilizing a recursive structure. IEICE Transactions on Communications E89-B(3), 929–936 (2006)CrossRefGoogle Scholar
  12. 12.
    Trouvé, E., Nicolas, J., Maître, H.: Improving phase unwrapping techniques by the use of local frequency estimates. IEEE Transactions on Geoscience and Remote Sensing 36(6), 1963–1972 (1998)CrossRefGoogle Scholar
  13. 13.
    Yamaki, R., Hirose, A.: Singular unit restoration in interferograms based on complex-valued Markov random field model for phase unwrapping. IEEE Geoscience and Remote Sensing Letters 6(1), 18–22 (2009)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Akira Hirose
    • 1
  • Ryo Natsuaki
    • 1
  1. 1.Dept. Electrical Engineerinbg and Information SystemsThe University of TokyoBunkyo-kuJapan

Personalised recommendations