Trace Coherence: A New Operator for Polarimetric and Interferometric SAR images

Quadratic forms play an important role in the development of several polarimetric and interferometric synthetic aperture radar (Pol-InSAR) methodologies, which are very powerful tools for earth observation. This paper investigates integrals of Pol-InSAR operators based on quadratic forms, with special interest on the Pol-InSAR coherence. A new operator, namely Trace Coherence, is introduced, which provides an approximation for the center of mass of the coherence region (CoRe). The latter is the locus of points on the polar plot containing all the possible coherence values. Such center of mass can be calculated as the integral of Pol-InSAR coherences over the scattering mechanisms (SMs). The trace coherence provides synthetic information regarding the partial target as one single entity. Therefore, it provides a representation, which is not dependent on the selection of one specific polarization channel. It may find application in change detection (e.g., coherent change detection and differential DEM), classification (e.g., building structure parameters), and modeling (e.g., for the retrieval of forest height). In calculating the integral of the Pol-InSAR coherences, an approximate trace coherence expression is derived and shown to improve the calculation speed by several orders of magnitude. The trace coherence approximation is investigated using Monte Carlo simulations and validated ESA (DLR) L-band quad-polarimetric data acquired during the AGRISAR 2006 campaign. The result of the analysis using simulated and real data is that the average error in approximating the integral of the coherence region is 0.025 in magnitude and 3 degrees in phase (in scenarios with sufficiently high coherence).