A Dynamic Mode Decomposition Approach to Morphological Component Analysis

Abstract: This paper introduces a novel methodology of adapting the representation of videos based on the dynamics of their scene content variation. In particular, we demonstrate how the clustering of dynamic mode decomposition eigenvalues can be leveraged to learn an adaptive video representation for separating structurally distinct morphologies of a video. We extend the morphological component analysis (MCA) algorithm, which uses multiple predefined incoherent dictionaries and a sparsity prior to separate distinct sources in signals, by introducing our novel eigenspace clustering technique to obtain data-driven MCA dictionaries, which we call dynamic morphological component analysis (DMCA). After deriving our novel algorithm, we offer a motivational example of DMCA applied to a still image, then demonstrate DMCA's effectiveness in denoising applications on videos from the Adobe 240fps dataset. Afterwards, we provide an example of DMCA enhancing the signal-to-noise ratio of a faint target summed with a sea state, and conclude the paper by applying DMCA to separate a bicycle from wind clutter in inverse synthetic aperture radar images.