Diffusion Posterior Sampling for Slitless Spectral Imaging

Imaging spectroscopy is a fundamental technique for investigating various physical phenomena. Traditional imaging spectrographs require a time-consuming scanning process to construct the spatial-spectral data cube, rendering them unsuitable for dynamic scenes. Slitless spectrographs have been proposed as snapshot imagers; however, their measurements consist of overlapped spectra, requiring to solve a limited-angle tomography problem. The existing reconstruction approaches have limited accuracy due to the highly ill-posed nature of the problem. In this work, we adapt the diffusion posterior sampling (DPS) method which uses a trained diffusion model as a prior. Targeting applications where spectrum consists of discrete emissions, we use a Gaussian parametrization for the spectrum, and use DPS to solve the resulting nonlinear inverse problem to estimate the Gaussian line parameters at each spatial location. Effectiveness of the approach is demonstrated on a solar imaging application.