Model-Based Decomposition of Polarimetric SAR Covariance Matrices Constrained for Nonnegative Eigenvalues

Model-based decomposition of polarimetric radar covariance matrices holds the promise that specific scattering mechanisms can be isolated for further quantitative analysis. In this paper, we show that current algorithms suffer from a fatal flaw in that some of the scattering components result in negative powers. We propose a simple modification that ensures that all covariance matrices in the decomposition will have nonnegative eigenvalues. We further combine our nonnegative eigenvalue decomposition with eigenvector decomposition to remove additional assumptions that have to be made before the current algorithms can be used to estimate all the scattering components. Our results are illustrated using Airborne Synthetic Aperture Radar data and show that current algorithms typically overestimate the canopy scattering contribution by 10%-20%.