  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.
