Efficient Tracking of Sparse Signals via an Earth Mover's Distance Dynamics Regularizer

TL;DR

This paper introduces a novel Earth Mover's Distance-based regularizer for tracking sparse signals, improving geometric awareness and computational efficiency in dynamic filtering tasks.

Contribution

It proposes a Beckmann formulation for EMD that reduces complexity and demonstrates its effectiveness in imaging and neurophysiology signal tracking.

Findings

Significant reduction in computational complexity with the new formulation.

Improved tracking accuracy in imaging applications.

Effective handling of geometrical relationships in sparse signals.

Abstract

Tracking algorithms such as the Kalman filter aim to improve inference performance by leveraging the temporal dynamics in streaming observations. However, the tracking regularizers are often based on the $\ell_p$-norm which cannot account for important geometrical relationships between neighboring signal elements. We propose a practical approach to using the earth mover's distance (EMD) via the earth mover's distance dynamic filtering (EMD-DF) algorithm for causally tracking time-varying sparse signals when there is a natural geometry to the coefficient space that should be respected (e.g., meaningful ordering). Specifically, this paper presents a new Beckmann formulation that dramatically reduces computational complexity, as well as an evaluation of the performance and complexity of the proposed approach in imaging and frequency tracking applications with real and simulated neurophysiology data.