Polynomial smoothing of time series with additive step discontinuities

Ivan W. Selesnick, Stephen Arnold, Venkata R. Dantham

Research output: Contribution to journalArticlepeer-review


This paper addresses the problem of estimating simultaneously a local polynomial signal and an approximately piecewise constant signal from a noisy additive mixture. The approach developed in this paper synthesizes the total variation filter and least-square polynomial signal smoothing into a unified problem formulation. The method is based on formulating an $\ell- 1$-norm regularized inverse problem. A computationally efficient algorithm, based on variable splitting and the alternating direction method of multipliers (ADMM), is presented. Algorithms are derived for both unconstrained and constrained formulations. The method is illustrated on experimental data involving the detection of nano-particles with applications to real-time virus detection using a whispering-gallery mode detector.

Original languageEnglish (US)
Article number6275507
Pages (from-to)6305-6318
Number of pages14
JournalIEEE Transactions on Signal Processing
Issue number12
StatePublished - 2012


  • Digital filters
  • filtering algorithms
  • jump detection
  • least squares approximation
  • nonlinear filters
  • polynomial smoothing
  • signal denoising
  • smoothing methods
  • sparse derivative
  • sparse signal
  • total variation

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering


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