Multi-resolution Dynamic Mode Decomposition for Foreground/Background Separation and Object Tracking

We demonstrate that the integration of the recently developed dynamic mode decomposition with a multi-resolution analysis allows for a decomposition of video streams into multi-time scale features and objects. A one-level separation allows for background (low-rank) and foreground (sparse) separation of the video, or robust principal component analysis. Further iteration of the method allows a video data set to be separated into objects moving at different rates against the slowly varying background, thus allowing for multiple-target tracking and detection. The algorithm is computationally efficient and can be integrated with many further innovations including compressive sensing architectures and GPU algorithms.