Coherence region shape extraction for vegetation parameter estimation in polarimetric SAR interferometry

Polarimetric SAR interferometry (POLINSAR) provides volumetric information about electromagnetic scattering processes, whereas standard INSAR assumes that only surface scattering is present. Instead of a single complex interferometric coherence for each pixel, POLINSAR observes a polarization-dependent coherence function whose range is called the coherence region. To estimate canopy parameters, the shape of this region must be matched to predictions from scattering models. For computational efficiency, the region must be represented by a small number of samples. Current sampling methods find the stationary points of coherence magnitude or phase; it is questionable whether the coherence region can be characterized adequately with so few samples. We have developed an algorithm for sampling the outer boundary of the coherence region. We formulate the problem of finding the minimum and maximum real part of the coherence as an eigenvalue problem. The solutions specify two points on the boundary. Other points are found by applying a phase shift to the POLINSAR cross-correlation matrix. The mathematical literature shows that the coherence region is convex, and hence the algorithm rinds the entire boundary. We present a comparison of boundary sampling to standard methods on L-band POLINSAR data from the SIR-C platform. It is evident that boundary sampling describes the shape of the coherence region more thoroughly than other methods.