Noise Removal for Dynamic Mode Decomposition Based on Plug-and-Play ADMM

Dynamic mode decomposition (DMD) is useful for video background/foreground separation. This decomposition algorithm can decompose a video into a set of dynamic modes, called the DMD mode, and then separate the near-zero mode as the stationary background and the other modes as the moving foreground components. However, When fore-ground/background separation is performed on noisy video, noisy background/foreground components are obtained because the DMD mode is degraded by noise. This paper proposes a novel noise removal method for the DMD mode of a noisy video. Specifically, we formulate a minimization problem that simultaneously reduces the noise of the DMD mode and the re-constructed video. The proposed minimization problem is solved by an algorithm based on Plug-and-Play alternating direction method of multipliers (PnP-ADMM). The experimental results demonstrate the advantages of the proposed method compared with a conventional noise removal method.