High-Accuracy Image Formation Model for Coded Aperture Snapshot Spectral Imaging

Coded aperture snapshot spectral imaging (CASSI) is based on the binary modulation of the spatial-spectral scene, which allows for hyperspectral image reconstruction from 2D compressive measurement. However, the actual optical modulation does not match the current image formation model due to the extra optical phenomena, such as diffraction, distortion, optical misalignment, and dispersion, inside the system. It is a long-lasting problem that the gap between the simplified image formation model and the actual optical modulation degrades the reconstruction quality. In this paper, we propose a high-accuracy image formation model to reduce this gap in CASSI. Specifically, we first reformulate the spectral modulation as channel-wise convolution, in which the convolution kernel represents the point-spread-function (PSF) of each spectral channel. Then, according to our key observation that the calibration images are the blurred versions of the coded aperture, we propose to estimate the PSF by exploring the relationship between these blurred and non-blurred pairs. In addition, we also provide a theoretical analysis of the PSF's influences on the reconstruction quality, which can serve as a guide for CASSI system implementation. Our simulations and real system experiments demonstrate the effectiveness of the proposed model.