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Transient Artifacts Suppression in Time Series via Convex Analysis

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Signal Processing in Medicine and Biology

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Abstract

This book chapter addresses the suppression of transient artifacts in time series data. We categorize the transient artifacts into two general types: spikes and brief waves with zero baseline, and step discontinuities. We propose a sparse-assisted optimization problem for the estimation of signals comprising a low-pass signal, a sparse piecewise constant signal, a piecewise constant signal, and additive white Gaussian noise. For better estimation of the artifacts, in turns better suppression performance, we propose a non-convex generalized conjoint penalty that can be designed to preserve the convexity of the total cost function to be minimized, thereby realizing the benefits of a convex optimization framework (reliable, robust algorithms, etc.). Compared to the conventional use of ℓ 1 norm penalty, the proposed non-convex penalty does not underestimate the true amplitude of signal values. We derive a fast proximal algorithm to implement the method. The proposed method is demonstrated on the suppression of artifacts in near-infrared spectroscopic (NIRS) measures.

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Acknowledgements

The authors thank Randall Barbour for important discussions. This work was supported by NSF (grant CCF-1525398).

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Authors and Affiliations

  1. Tandon School of Engineering, New York University, Brooklyn, NY, USA

    Yining Feng & Ivan Selesnick

  2. Tandon School of Engineering, New York University, Brooklyn, NY, USA

    Baoqing Ding

  3. School of Mechanical Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi, China

    Baoqing Ding

  4. Photon Migration Technologies Corp., Glen Head, NY, USA

    Harry Graber

Authors
  1. Yining Feng
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  2. Baoqing Ding
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  3. Harry Graber
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  4. Ivan Selesnick
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Corresponding author

Correspondence to Yining Feng .

Editor information

Editors and Affiliations

  1. Department of Electrical & Computer Engineering, Temple University, Philadelphia, PA, USA

    Iyad Obeid

  2. Department of Electrical & Computer Engineering, New York University, Brooklyn, NY, USA

    Ivan Selesnick

  3. Department of Electrical & Computer Engineering, Temple University, Philadelphia, PA, USA

    Joseph Picone

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Feng, Y., Ding, B., Graber, H., Selesnick, I. (2020). Transient Artifacts Suppression in Time Series via Convex Analysis. In: Obeid, I., Selesnick, I., Picone, J. (eds) Signal Processing in Medicine and Biology. Springer, Cham. https://doi.org/10.1007/978-3-030-36844-9_4

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  • DOI: https://doi.org/10.1007/978-3-030-36844-9_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-36843-2

  • Online ISBN: 978-3-030-36844-9

  • eBook Packages: EngineeringEngineering (R0)

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