Polarizer-free two-pixel polarimetric camera by compressive sensing

We propose an original concept of compressive sensing (CS) polarimetric imaging based on a digital micromirror (DMD) array and two single-pixel detectors, without using any polarizer. The polarimetric sensitivity of the proposed setup is due to the tiny difference in Fresnel's coefficients 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 demonstrated in this paper and preferably implemented through a reweighted fast iterative shrinkage-thresholding 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 generalized forward-backward algorithm. Numerical simulations demonstrate the efficiency of the two-pixel CS polarimetric imaging setup at retrieving polarimetric contrast data with significant compression rate and good reconstruction quality. The influence of experimental imperfections of the DMD is also analyzed through numerical simulations, and 2D polarimetric imaging reconstruction results are finally presented.