We present a semi-parametric spectral estimation algorithm for fully polarimetric synthetic aperture radar (SAR) target feature extraction and image formation. The algorithm is based on a flexible data model that models each target scatterer as a two-dimensional complex sinusoid with arbitrary amplitude and constant phase in cross-range and with constant amplitude and phase in range. The algorithm is a relaxation-based optimization approach that minimizes a nonlinear least squares (NLS) cost function. Due to using the fully polarimetric radar measurements (HH, HV, and VV) simultaneously, the algorithm provides not only more accurate target features, but also more useful information about the target of interest than the single polarization based algorithm. The algorithm has the ability to discriminate corner reflector types by also exploiting the differences in the polarimetric scattering properties of the scatterers of the target of interest. Numerical examples are presented to demonstrate the performance of the proposed algorithm.