Sub-Pixel Dispersion Model for Coded Aperture Snapshot Spectral Imaging

Coded aperture snapshot spectral imaging (CASSI) aims to reconstruct three-dimensional spatial-spectral images from a single snapshot measurement. Traditional CASSI systems model the imaging process as a sum of binary spatial modulation and ideal stair-stepping spectral shifts of the scene pixels. However, the actual optical reality does not match the current imaging model as the dispersion in the system is continuous. Certain spectral bands are shifted to align the sensor pixels perfectly, while others are pixel-misaligned and projected into two adjacent pixels. Existing imaging models have ignored the pixel-misaligned spectral bands, resulting in the limitations of the reconstruction quality and spectral band number. In this paper, we present a sub-pixel dispersion model that accounts for the continuous dispersion in the CASSI system. We discretize the scene spectrum with dense sampling and express the spectral shifts in the sub-pixel level to consider both the pixel-aligned and pixel-misaligned spectral bands, thus accurately modeling the CASSI imaging process towards actual optical reality. We integrate the proposed model into two mainstream reconstruction algorithms, including the traditional handcrafted prior and deep image prior. The proposed precise model makes the reconstruction targets of these algorithms closer to the optical reality, which increases the reconstruction accuracy and spectral bands. Both simulations and experiments with actual systems demonstrate the effectiveness of the proposed model.