2D Orthogonal Matching Pursuit for Fully Polarimetric SAR Image Formation

Fully polarimetric SAR provides richer scattering information than single-polarisation imaging, but multichannel sparse image formation can be computationally and memory demanding, especially when channels are processed jointly. In our previous work, we introduced Orthogonal Matching Pursuit 2D Fully Polarimetric (OMP2D-FP), a greedy reconstruction algorithm that enforces a shared spatial support across polarimetric channels while exploiting a separable 2D formulation to avoid vectorisation and reduce computational burden and memory footprint relative to vectorised OMP-based formulations. In this paper, we extend its validation to real measurements and further develop its theoretical foundations by recasting the atom-selection step as a detection–estimation problem, thereby defining a cumulative objective function (COF) design space that enables the incorporation of disturbance statistics and prior knowledge into sparse recovery. Experiments on fully polarimetric SAR data of a T-72 tank over a wide range of aspect angles, SNR levels, and measurement percentages show that joint support selection improves reconstruction fidelity and polarimetric information preservation over independent per-channel processing, with particularly clear gains under challenging conditions. Preliminary applications of the COF framework (a whitening COF incorporating polarimetric clutter statistics and a mask-based COF incorporating spatial prior knowledge) yield encouraging results, motivating further systematic investigation of adaptive COF designs.