Two-pixel polarimetric camera by compressive sensing

We propose an original concept of compressive sensing (CS) polarimetric imaging based on a digital micro-mirror (DMD) array and two single-pixel detectors. The polarimetric sensitivity of the proposed setup is due to an experimental imperfection of reflecting mirrors which is exploited here to form an original reconstruction problem, including a CS problem and a source separation task. We show that a two-step approach tackling each problem successively is outperformed by a dedicated combined reconstruction method, which is explicited in this article and preferably implemented through a reweighted FISTA algorithm. The combined reconstruction approach is then further improved by including physical constraints specific to the polarimetric imaging context considered, which are implemented in an original constrained GFB algorithm. Numerical simulations demonstrate the efficiency of the 2-pixel CS polarimetric imaging setup to retrieve polarimetric contrast data with significant compression rate and good reconstruction quality. The influence of experimental imperfections of the DMD are also analyzed through numerical simulations, and 2D polarimetric imaging reconstruction results are finally presented.