Feature-specific imaging (FSI) or compressive imaging involves measuring relatively few linear projections of a scene compared to the dimensionality of the scene. Researchers have exploited the spatial correlation inherent in natural scenes to design compressive imaging systems using various measurement bases such as Karhunen-Loève (KL) transform, random projections, Discrete Cosine transform (DCT) and Discrete Wavelet transform (DWT) to yield significant improvements in system performance and size, weight, and power (SWaP) compared to conventional non-compressive imaging systems. Here we extend the FSI approach to time-varying natural scenes by exploiting the inherent spatio-temporal correlations to make compressive measurements. The performance of space-time feature-specific/compressive imaging systems is analyzed using the KL measurement basis. We find that the addition of temporal redundancy in natural time-varying scenes yields further compression relative to space-only feature specific imaging. For a relative noise strength of 10% and reconstruction error of 10% using 8×8×16 spatio-temporal blocks we find about a 114x compression compared to a conventional imager while space-only FSI realizes about a 32x compression. We also describe a candidate space-time compressive optical imaging system architecture.