Least-Squares Estimation for Pseudo Quad-Pol Image Reconstruction from Linear Compact Polarimetric SAR

Compact polarimetry is a hybrid dual-polarization imaging mode, which is used to enable wide swath coverages and provide more polarimetric information compared with the conventional dual-polarimetric imaging modes (HH/HV and VH/VV). In applications of compact polarimetric synthetic aperture radar (Pol-SAR), pseudo quad-polarimetric (quad-pol) image reconstruction is an important technique. In this study, we propose a least-squares (LS) based method to estimate the quad-pol covariance elements for the linear π/4 compact polarimetric mode. Different from existing quad-pol reconstruction approaches, which use an iterative approach to refine the model solution based on multi-look data, the LS method uses a set of data points to best fit the reconstruction model and is applicable to both multi-look and single-look complex data. In this study, a decomposition-based three-component reconstruction model is exploited to construct the system of non-linear equations. Then, the minimization problem is addressed in a local window for the cross-polarized term, which is optimized with bound constraints. Furthermore, the $m - {\alpha _s}$ decomposition for the linear compact mode is developed, which is used to approximate the reconstruction model parameter for the LS model function. Experiments are performed on C-band RADARSAT-2 data collected over agriculture fields, an urban area, and an area with complex terrain types. In comparison with the iterative-based methods, the LS-based reconstruction method shows its superiority in estimating both the cross-polarized term and the co-polarized phase difference.