Snapshot Compressive Imaging under Saturation: Theory, Mask Design, and Reconstruction

Abstract

Snapshot compressive imaging (SCI) acquires high-dimensional data cubes, such as videos and hyperspectral images, by optically multiplexing multiple coded frames into a single two-dimensional measurement. While this multiplexing enables high acquisition efficiency, it also increases the risk of sensor saturation: the accumulated intensity may exceed the detector dynamic range, causing clipped measurements that violate the standard linear SCI model. This paper studies SCI reconstruction under such saturated measurements from both theoretical and algorithmic perspectives. We model saturation as an element-wise clipping nonlinearity and derive a finite-sample recovery bound for compression-based SCI. The bound explicitly relates the reconstruction error to the Bernoulli mask density, the compression rate of the signal class, measurement noise, and the expected fraction of saturated measurements. The analysis reveals a principled mask-design rule: under saturation, the optimal Bernoulli mask density remains below one-half and decreases as saturation becomes stronger. Motivated by this result, we optimize mask patterns for saturated acquisition and introduce a saturation-aware plug-and-play reconstruction framework, termed \emph{Saturation-Aware PnP Net} (SAPnet), which enforces consistency with both unsaturated and clipped measurements. Experiments on standard video SCI benchmarks validate the theoretical predictions and show that SAPnet substantially improves reconstruction quality over conventional PnP-based methods, especially in strongly saturated regimes.