Cocosvi: Single Snapshot Compressive Spectral Video Via Covariance Matrix Estimation

This paper proposes a snapshot spectral video imager based on the compressive covariance sampling (CCS) theory, named compressive covariance spectral video (CoCoS-Vi), and a low-rank optimization problem that exploits the covariance matrix (CM) spectrotemporal correlation to improve the reconstruction accuracy. Specifically, CoCoS-Vi relies on a lenslet array to simultaneously obtain multiple compressed measurements for each frame. Moreover, a dual-dispersive sensing geometry based on a single prism and the coded aperture is designed to recast the vectorial sensing problem into a matrix CCS model. Several computational simulations validate the CoCoSVi accuracy and speed, achieving up to 4 and 8 dB of PSNR compared to traditional ADMM and CM-based algorithms, respectively, and a speedup of up to 371x. A CoCoSVi testbed implementation was developed to validate the acquisition and reconstruction methodology. CoCoSVi experiments show a speedup of 231x against a traditional PnP-ADMMM algorithm.