Publication detail

Orthogonality is superiority in piecewise-polynomial signal segmentation and denoising

NOVOSADOVÁ, M. RAJMIC, P. ŠOREL, M.

Original Title

Orthogonality is superiority in piecewise-polynomial signal segmentation and denoising

English Title

Orthogonality is superiority in piecewise-polynomial signal segmentation and denoising

Type

journal article

Language

en

Original Abstract

Segmentation and denoising of signals often rely on the polynomial model which assumes that every segment is a polynomial of a certain degree and that the segments are modeled independently of each other. Segment borders (breakpoints) correspond to positions in the signal where the model changes its polynomial representation. Several signal denoising methods successfully combine the polynomial assumption with sparsity. In this work, we follow on this and show that using orthogonal polynomials instead of other systems in the model is beneficial when segmenting signals corrupted by noise. The switch to orthogonal bases brings better resolving of the breakpoints, removes the need for including additional parameters and their tuning, and brings numerical stability. Last but not the least, it comes for free!

English abstract

Segmentation and denoising of signals often rely on the polynomial model which assumes that every segment is a polynomial of a certain degree and that the segments are modeled independently of each other. Segment borders (breakpoints) correspond to positions in the signal where the model changes its polynomial representation. Several signal denoising methods successfully combine the polynomial assumption with sparsity. In this work, we follow on this and show that using orthogonal polynomials instead of other systems in the model is beneficial when segmenting signals corrupted by noise. The switch to orthogonal bases brings better resolving of the breakpoints, removes the need for including additional parameters and their tuning, and brings numerical stability. Last but not the least, it comes for free!

Keywords

Signal segmentation; Signal smoothing; Signal approximation; Denoising; Piecewise polynomials; Orthogonality; Sparsity; Proximal splitting; Convex optimization

Released

25.01.2019

Publisher

Springer Open

Pages from

1

Pages to

15

Pages count

15

URL

Full text in the Digital Library

BibTex


@article{BUT153383,
  author="Michaela {Novosadová} and Pavel {Rajmic} and Michal {Šorel}",
  title="Orthogonality is superiority in piecewise-polynomial signal segmentation and denoising",
  annote="Segmentation and denoising of signals often rely on the polynomial model which assumes that every segment is a polynomial of a certain degree and that the segments are modeled independently of each other. Segment borders (breakpoints) correspond to positions in the signal where the model changes its polynomial representation. Several signal denoising methods successfully combine the polynomial assumption with sparsity. In this work, we follow on this and show that using orthogonal polynomials instead of other systems in the model is beneficial when segmenting signals corrupted by noise. The switch to orthogonal bases brings better resolving of the breakpoints, removes the need for including additional parameters and their tuning, and brings numerical stability. Last but not the least, it comes for free!",
  address="Springer Open",
  chapter="153383",
  doi="10.1186/s13634-018-0598-9",
  howpublished="online",
  institution="Springer Open",
  number="6",
  volume="2019",
  year="2019",
  month="january",
  pages="1--15",
  publisher="Springer Open",
  type="journal article"
}