Snapshot compressed sensing: performance bounds and algorithms

TL;DR

This paper introduces a theoretical framework and new algorithms for snapshot compressed sensing, enabling efficient recovery of combined video frames with proven convergence and improved performance over existing methods.

Contribution

It develops a compression-based analysis framework and two novel algorithms with convergence guarantees for snapshot CS, tailored for structured video data.

Findings

Algorithms outperform state-of-the-art in noisy and noise-free scenarios.

Customized video compression codes enhance reconstruction quality.

Theoretical guarantees support practical effectiveness.

Abstract

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.