Volume Scattering Power Constraint Based on the Principal Minors of the Coherency Matrix

This letter proposes a constraint for a volume scattering power employing the principal minors, which can be used for polarimetric synthetic aperture radar (POLSAR) model-based decomposition. This constraint effectively allows for avoiding unreasonable results which yield negative eigenvalues. The proposed constraint is derived so that all the principal minors of the coherency matrix after volume scattering subtraction are nonnegative. Mathematically, the constraint is exactly the same as that based on the nonnegative eigenvalues. Thus, it is guaranteed that the result is physically reasonable and that the volume scattering power is not overestimated. A significant advantage of the proposed method compared to the constraint based on the nonnegative eigenvalues is the high computation efficiency, since the maximal volume scattering power can be derived analytically, while the nonnegative eigenvalue constraint requires a numerical calculation. In our experiment, the computation of the maximal power is six times faster using the approach based on the principal minors than that based on the nonnegative eigenvalues.