Earth Mover's Distance as a Dynamics Regularizer for Sparse Signal Tracking

An important problem in statistical signal processing is understanding how to exploit signal structure in inference problems. In recent years, sparse signal models have enjoyed great success, achieving state-of-the-art performance in many applications. Some algorithms further improve performance by taking advantage of temporal dynamics for streams of observations. However, often the tracking regularizers used are based on the $\ell_p$-norm which does not take full advantage of the relationship between neighboring signal elements. In this work, we propose the use of the earth mover's distance (EMD) as an alternative tracking regularizer. We introduce the earth mover's distance dynamic filtering (EMD-DF) algorithm which includes two variants: one which uses the traditional EMD as a tracking regularizer in the $\ell_1$ sparse recovery problem for nonnegative signals, and a relaxation which allows for complex valued signals. Through experiments on simulated and real data, we conclude that EMD-DF can outperform current state-of-the-art sparse tracking algorithms.