High-fidelity lensless polarization imaging enabled by differentiable mask optimization and second-order regularized reconstruction.

Lensless coded aperture polarization imaging offers a highly promising avenue for compact optical systems. However, high-fidelity imaging is severely hindered by traditional mask designs that cause spectral zeros in the modulation transfer function (MTF), coupled with the inherently ill-posed reconstruction process that amplifies noise during nonlinear polarization computations. To address these issues, we develop a differentiable physical model to optimize the spatial arrangement of the sub-aperture, avoiding the formation of contiguous transparent regions. This approach effectively eliminates MTF zeros and boosts the energy in mid-to-high frequency bands, providing a solid physical foundation for mitigating noise in the reconstructed images. Furthermore, we propose a total generalized variation momentum primal-dual hybrid gradient (TGV-MPDHG) algorithm by incorporating a second-order regularization into the MPDHG framework to solve the ill-posed reconstruction problem. Experimental results demonstrate that this integrated methodology significantly enhances reconstruction fidelity, reduces background noise, and achieves both faster convergence and stable reconstruction quality across various object sizes.