Sparsity-assisted signal smoothing

Research output: Chapter in Book/Report/Conference proceedingChapter


This chapter describes a method for one-dimensional signal denoising that simultaneously utilizes both sparse optimization principles and conventional linear time-invariant (LTI) filtering. The method, called ‘sparsity-assisted signal smoothing’ (SASS), is based on modeling a signal as the sum of a low-pass component and a piecewise smooth component. The problem is formulated as a sparse-regularized linear inverse problem. We provide simple direct methods to set the regularization and non-convexity parameters, the latter if a non-convex penalty is utilized. We derive an iterative optimization algorithm that harnesses the computational efficiency of fast solvers for banded systems. The SASS approach performs a type of wavelet denoising, but does so through sparse optimization rather than through wavelet transforms. The approach is relatively free of the pseudo-Gibbs phenomenon that tends to arise in wavelet denoising.

Original languageEnglish (US)
Title of host publicationApplied and Numerical Harmonic Analysis
PublisherSpringer International Publishing
Number of pages28
StatePublished - 2015

Publication series

NameApplied and Numerical Harmonic Analysis
ISSN (Print)2296-5009
ISSN (Electronic)2296-5017


  • Convex optimization
  • Filtering
  • Sparse optimization
  • Total variation denoising
  • Wavelet denoising

ASJC Scopus subject areas

  • Applied Mathematics

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  • Cite this

    Selesnick, I. W. (2015). Sparsity-assisted signal smoothing. In Applied and Numerical Harmonic Analysis (9783319201870 ed., pp. 149-176). (Applied and Numerical Harmonic Analysis; No. 9783319201870). Springer International Publishing.