A multi-spectral Light-Emitting-Diode (LED) array is used for target illumination and spectral modulation while a Digital Micro-mirror Device (DMD) encodes the spatial and temporal frames. Several encoded video frames are captured in a snapshot of an integrating focal plane array (FPA).A high-frame-rate spectral video is reconstructed from the sequence of compressed measurements captured by the grayscale low-frame-rate camera. The imaging system is optimized through the design of the DMD patterns based on the forward model. Laboratory implementation is conducted to validate the performance of the proposed imaging system. We experimentally demonstrate the video acquisition with eight spectral bands and six temporal frames per FPA snapshot, and thus a 256x256x8x6 4D cube is reconstructed from a single 2D measurement.