  Spatial multiplexing cameras (SMCs) acquire a (typically static) scene
through a series of coded projections using a spatial light modulator (e.g., a
digital micro-mirror device) and a few optical sensors. This approach finds use
in imaging applications where full-frame sensors are either too expensive
(e.g., for short-wave infrared wavelengths) or unavailable. Existing SMC
systems reconstruct static scenes using techniques from compressive sensing
(CS). For videos, however, existing acquisition and recovery methods deliver
poor quality. In this paper, we propose the CS multi-scale video (CS-MUVI)
sensing and recovery framework for high-quality video acquisition and recovery
using SMCs. Our framework features novel sensing matrices that enable the
efficient computation of a low-resolution video preview, while enabling
high-resolution video recovery using convex optimization. To further improve
the quality of the reconstructed videos, we extract optical-flow estimates from
the low-resolution previews and impose them as constraints in the recovery
procedure. We demonstrate the efficacy of our CS-MUVI framework for a host of
synthetic and real measured SMC video data, and we show that high-quality
videos can be recovered at roughly $60\times$ compression.
