3D Snapshot Compressive Imaging： Reconstructing 3D Scenes from a Single Compressed Image

The capture of high-dimensional data remains a long-standing challenge in signal processing and related fields. Snapshot compressive imaging （SCI）， which integrally captures high-dimensional data using two-dimensional （2D） detectors， from within a single exposure， offers a low-cost and highly efficient computational imaging paradigm. Traditional SCI-reconstruction algorithms primarily focus on recovering 2D video frames from compressed data and often neglect the underlying three-dimensional （3D） geometric structure of the scene. This leads to a lack of consistency in multiview observations and limitations caused by mask singularity. The recent development of 3D scene representation technologies， such as neural radiance fields （NeRF） and 3D Gaussian splatting， has facilitated the recovery of 3D scenes from single-exposure compressed images. This paper provides a systematic review of the emerging field of 3D SCI （SCI-3D）， which not only facilitates high-quality reconstruction of multiview information but also achieves complete 3D modeling， enabling high-fidelity novel view image synthesis. First， a unified mathematical model that systematically describes the framework for solving the inverse problem of mapping a single compressed measurement to a 3D scene representation is reviewed. Second， the technological evolution is thoroughly analyzed， tracing the path from the implicit neural-representation-based SCI-NeRF to the explicit point-cloud-representation-based SCI-Gaussian and SCI-Splat technologies. This analysis focuses on the key technical breakthroughs in addressing core challenges such as highly degraded supervisory signals， unknown camera poses， and absence of geometric priors. Finally， the paper offers an outlook on future research directions， identifying four-dimensional spatiotemporal reconstruction of dynamic scenes and feed-forward networks based on large foundation models as pivotal trends for achieving efficient， robust， and end-to-end 3D reconstruction.