  Snapshot compressed sensing (CS) refers to compressive imaging systems in
which multiple frames are mapped into a single measurement frame. Each pixel in
the acquired frame is a noisy linear mapping of the corresponding pixels in the
frames that are combined together. While the problem can be cast as a CS
problem, due to the very special structure of the sensing matrix, standard CS
theory cannot be employed to study such systems. In this paper, a
compression-based framework is employed for theoretical analysis of snapshot CS
systems. It is shown that this framework leads to two novel,
computationally-efficient and theoretically-analyzable compression-based
recovery algorithms. The proposed methods are iterative and employ compression
codes to define and impose the structure of the desired signal. Theoretical
convergence guarantees are derived for both algorithms. In the simulations, it
is shown that, in the cases of both noise-free and noisy measurements,
combining the proposed algorithms with a customized video compression code,
designed to exploit nonlocal structures of video frames, significantly improves
the state-of-the-art performance.
