[PP2-2-7-3] Covariance/Coherency matrices

The covariance and coherence matrix are two 4x4 square matrices, which can be built out of the scattering matrix by a lexicographic and a Pauli target scattering vector. They are an alternative representation of a full polarimetric dataset allowing the analysis of incoherent targets (more than one dominant scatterer in the resolution cell) and the phenomenon of depolarisation (transformation of incoming fully polarised wave into a partially polarised wave by creating a variety of different types of polarizations during media interaction). These matrices can be converted into each other without loss of information (by unitary transformations), but not turned back into the scattering matrix due to averaging operations during formation of coherency or covariance matrices.

External resources

• Cloude, S. R. and Pottier, E. (1996). A review of target decomposition theorems in radar polarimetry. IEEE transactions on geoscience and remote sensing, 34(2), 498-518. DOI: 10.1109/36.485127
  Cloude, S. R. and Pottier, E. (1996). A review of target decomposition theorems in radar polarimetry. IEEE transactions on geoscience and remote sensing, 34(2), 498-518. DOI: 10.1109/36.485127
• Jin, Y. Q. and Cloude, S. R. (1994). Numerical eigenanalysis of the coherency matrix for a layer of random nonspherical scatterers. IEEE transactions on geoscience and remote sensing, 32(6), 1179-1185. DOI: 10.1109/36.338366
  Jin, Y. Q. and Cloude, S. R. (1994). Numerical eigenanalysis of the coherency matrix for a layer of random nonspherical scatterers. IEEE transactions on geoscience and remote sensing, 32(6), 1179-1185. DOI: 10.1109/36.338366
• Lee, J. S., Pottier, E. (2009). Polarimetric Radar Imaging. From Basics to Applications. CRC Press. ISBN: 978-142005492 Cloude, S. R. (2009). Polarisation: Applications in Remote Sensing. Oxford University Press, pp. 352. ISBN: 978-0199569731

Learning outcomes

• 1591 - Explain covariance and coherence matrix

  Explain covariance and coherence matrix

• 1593 - Apply covariance and coherence matrix

  Apply covariance and coherence matrix

Self assessment

Outgoing relations

• [PP2-2-7-3] Covariance/Coherency matrices subclassof [PP2-2-7] Polarimetry

Contributors

• Thomas Jagdhuber
  German Aerospace Center
  https://scholar.google.de/citations?user=ZEaPq_4AAAAJ&hl=de