Earth Mover's Distance as a Dynamics Regularizer for Sparse Signal Tracking (bibtex)
by , , , and
Abstract:
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 Lp-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 L1 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.
Reference:
Earth Mover's Distance as a Dynamics Regularizer for Sparse Signal TrackingN. Bertrand, A. Charles, J. Lee, P. Dunn and C.J. Rozell. 2019. Under review.
Bibtex Entry:
@Article{bertrand.18b,
  author = {Bertrand, N. and Charles, A. and Lee, J. and Dunn, P. and Rozell, C.J.},
  title = {{Earth Mover's Distance} as a Dynamics Regularizer for Sparse Signal Tracking},
  year = 2019,
  abstract = {
  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 Lp-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 L1 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.
  },
  note = {Under review.},
  url = {http://arxiv.org/abs/1806.04674}
}
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