The Dynamic Mode Decomposition (DMD) is a spatiotemporal matrix decomposition method capable of background modeling in video streams. DMD is a regression technique that integrates Fourier transforms and singular value decomposition. Innovations in compressed sensing allow for a scalable and rapid decomposition of video streams that scales with the intrinsic rank of the matrix, rather than the size of the actual video. Our results show that the quality of the resulting background model is competitive, quantified by the F-measure, recall and precision. A GPU (graphics processing unit) accelerated implementation is also possible allowing the algorithm to operate efficiently on streaming data. In addition, it is possible to leverage the native compressed format of many data streams, such as HD video and computational physics codes that are represented sparsely in the Fourier domain, to massively reduce data transfer from CPU to GPU and to enable sparse matrix multiplications.