Snapshot compressed sensing: performance bounds and algorithms
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Snapshot compressed sensing (CS) refers to compressive imaging systems where multiple frames are mapped into a single measurement frame. Each pixel in the acquired frame is a linear combination of the corresponding pixels in the frames that are collapsed 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 proposed that enable a theoretical analysis of snapshot compressive sensing systems. This new framework leads to two novel, computationally-efficient and theoretically-analyzable snapshot compressive sensing recovery algorithms. The proposed algorithms are iterative and employ compression codes to impose structure on the recovered frames. Theoretical convergence guarantees are derived for both algorithms. In simulations, it is shown that 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.
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