A Dynamic Mode Decomposition Approach to Morphological Component Analysis

TL;DR

The paper addresses the challenge of separating video content into morphologically distinct components by leveraging dynamics-based representations. It introduces Dynamic Morphological Component Analysis (DMCA), which builds data-driven dictionaries from the dynamics of video frames using sliding Dynamic Mode Decomposition (DMD) and then partitions DMD modes into dictionaries via eigenspace clustering, enabling sparse, multi-dictionary reconstruction without training data. Key contributions include the DMCA algorithm itself, demonstrations on non-Gaussian video denoising, sea-state target separation, and ISAR clutter suppression, plus a motivating still-image example. The approach offers interpretable, physics-informed dictionaries that adapt to scene dynamics and complements data-driven learning methods by providing robust, task-oriented separation in challenging imaging scenarios.

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.

Figures (12)

• Figure 1: Still image of a mandrill summed with a grid inputted to DMCA.
• Figure 2: DMCA reconstructed image of the mandrill.
• Figure 3: DMCA reconstructed texture layer.
• Figure 4: Plot of DMD eigenvalues magnitude squared in relation to the position of the DMD window they are extracted from.
• Figure 5: Noise removal results from Adobe 240fps dataset.