Compressive imaging systems typically exploit the spatial correlation of the scene to facilitate a lower dimensional measurement relative to a conventional imaging system. In natural time-varying scenes there is a high degree of temporal correlation that may also be exploited to further reduce the number of measurements. In this work we analyze space–time compressive imaging using Karhunen–Loève (KL) projections for the read-noise-limited measurement case. Based on a comprehensive simulation study, we show that a KL-based space–time compressive imager offers higher compression relative to space-only compressive imaging. For a relative noise strength of 10% and reconstruction error of 10%, we find that space–time compressive imaging with $8\times 8\times 16$ spatiotemporal blocks yields about $292\times$ compression compared to a conventional imager, while space-only compressive imaging provides only $32\times$ compression. Additionally, under high read-noise conditions, a space–time compressive imaging system yields lower reconstruction error than a conventional imaging system due to the multiplexing advantage. We also discuss three electro-optic space-time compressive imaging architecture classes, including charge-domain processing by a smart focal plane array (FPA). Space–time compressive imaging using a smart FPA provides an alternative method to capture the nonredundant portions of time-varying scenes.