Scaling-based two-step reconstruction in full polarization-compressed hyperspectral imaging

Polarized hyperspectral images can reflect the rich physicochemical characteristics of targets. Meanwhile, the contained plentiful information also brings great challenges to signal processing. Although compressive sensing theory provides a good idea for image processing, the simplified compression imaging system has difficulty in reconstructing full polarization information. Focused on this problem, we propose a two-step reconstruction method to handle polarization characteristics of different scales progressively. This paper uses a quarter-wave plate and a liquid crystal tunable filter to achieve full polarization compression and hyperspectral imaging. According to their numerical features, the Stokes parameters and their modulation coefficients are simultaneously scaled. The first Stokes parameter is reconstructed in the first step based on compressive sensing. Then, the last three Stokes parameters with similar order of magnitude are reconstructed in the second step based on previous results. The simulation results show that the two-step reconstruction method improves the reconstruction accuracy by 7.6 dB for the parameters that failed to be reconstructed by the non-optimized method, and reduces the reconstruction time by 8.25 h without losing the high accuracy obtained by the current optimization method. This feature scaling method provides a reference for the fast and high-quality reconstruction of physical quantities with obvious numerical differences.