Deep image prior plus sparsity prior: toward single-shot full-Stokes spectropolarimetric imaging with a multiple-order retarder

Compressive full-Stokes spectropolarimetric imaging (SPI), integrating passive polarization modulator (PM) into general imaging spectrometer, is powerful enough to capture high-dimensional information via incomplete measurement; a reconstruction algorithm is needed to recover 3D data cube (x, y, and λ) for each Stokes parameter. However, existing PMs usually consist of complex elements and enslave to accurate polarization calibration, current algorithms suffer from poor imaging quality and are subject to noise perturbation. In this work, we present a single multiple-order retarder followed a polarizer to implement passive spectropolarimetric modulation. After building a unified forward imaging model for SPI, we propose a deep image prior plus sparsity prior algorithm for high-quality reconstruction. The method based on untrained network does not need training data or accurate polarization calibration and can simultaneously reconstruct the 3D data cube and achieve self-calibration. Furthermore, we integrate the simplest PM into our miniature snapshot imaging spectrometer to form a single-shot SPI prototype. Both simulations and experiments verify the feasibility and outperformance of our SPI scheme. It provides a paradigm that allows general spectral imaging systems to become passive full-Stokes SPI systems by integrating the simplest PM without changing their intrinsic mechanism.