Computationally Efficient and High Fidelity Log-based Demosaicking for Degree of Linear Polarization

In polarimetric imaging, degree and angle of linear polarization (DoLP and AoLP, respectively) are computed from ratios of Stokes parameters. In snapshot imagers, however, DoLP and AoLP are degraded by inherent mismatches between the spatial bandwidth supports of S-0, S-1, and S-2 parameters reconstructed by demosaicking from microgrid polarizer array (MPA)-sampled data. To overcome this shortcoming, we rigorously show that log-MPA-sampled data approximately decouples DoLP and AoLP from the intensity component (S-0) in the spatial Fourier domain. Based on this analysis, we propose an alternative demosaicking strategy aimed at estimating DoLP and AoLP directly from MPA-sampled data. Our method bypasses Stokes parameter estimation, alleviating the spatial bandwidth mismatch problems altogether and reducing the computational complexity. We experimentally verify the superior DoLP and AoLP reconstructions of the proposed log-MPA demosaicking compared to the conventional Stokes parameter demosaicking approach in simulation. We simulated the conventional 2 x 2 MPA patterns as well as the more recently introduced 2 x 4 MPA patterns, and report quantitative (mean squared error, structural similarity index, and polarization angular error) and qualitative results. We also provide a closed-form approximation error analysis on the log-MPA-sampled data to demonstrate that the approximation error is negligible for real practical applications.