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Transient Artifacts Suppression in Time Series via Convex Analysis

  • Yining FengEmail author
  • Baoqing Ding
  • Harry Graber
  • Ivan Selesnick
Chapter
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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 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.

Keywords

Sparse signal processing Fused lasso Non-convex regularization Artifact reduction Convex optimization Morphological component analysis 

Notes

Acknowledgements

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

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Yining Feng
    • 1
    Email author
  • Baoqing Ding
    • 2
    • 3
  • Harry Graber
    • 4
  • Ivan Selesnick
    • 1
  1. 1.Tandon School of EngineeringNew York UniversityBrooklynUSA
  2. 2.Tandon School of EngineeringNew York UniversityBrooklynUSA
  3. 3.School of Mechanical EngineeringXi’an Jiaotong UniversityXi’anChina
  4. 4.Photon Migration Technologies Corp.Glen HeadUSA

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