Sparsity-assisted signal smoothing

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

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
Pages149-176
Number of pages28
Edition9783319201870
DOIs
StatePublished - Jan 1 2015

Publication series

NameApplied and Numerical Harmonic Analysis
Number9783319201870
ISSN (Print)2296-5009
ISSN (Electronic)2296-5017

Fingerprint

Sparsity
Smoothing
Wavelet Denoising
Signal denoising
Fast Solvers
Gibbs Phenomenon
Computational efficiency
Linear Inverse Problems
Inverse problems
Non-convexity
Wavelet transforms
Optimization
Denoising
Direct Method
Computational Efficiency
Wavelet Transform
Iterative Algorithm
Penalty
Linear Time
Regularization

Keywords

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

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

Selesnick, I. (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. https://doi.org/10.1007/978-3-319-20188-7_6

Sparsity-assisted signal smoothing. / Selesnick, Ivan.

Applied and Numerical Harmonic Analysis. 9783319201870. ed. Springer International Publishing, 2015. p. 149-176 (Applied and Numerical Harmonic Analysis; No. 9783319201870).

Research output: Chapter in Book/Report/Conference proceedingChapter

Selesnick, I 2015, Sparsity-assisted signal smoothing. in Applied and Numerical Harmonic Analysis. 9783319201870 edn, Applied and Numerical Harmonic Analysis, no. 9783319201870, Springer International Publishing, pp. 149-176. https://doi.org/10.1007/978-3-319-20188-7_6
Selesnick I. Sparsity-assisted signal smoothing. In Applied and Numerical Harmonic Analysis. 9783319201870 ed. Springer International Publishing. 2015. p. 149-176. (Applied and Numerical Harmonic Analysis; 9783319201870). https://doi.org/10.1007/978-3-319-20188-7_6
Selesnick, Ivan. / Sparsity-assisted signal smoothing. Applied and Numerical Harmonic Analysis. 9783319201870. ed. Springer International Publishing, 2015. pp. 149-176 (Applied and Numerical Harmonic Analysis; 9783319201870).
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