Algorithms for piecewise constant signal approximations

Leif Bergerhoff, Joachim Weickert, Yehuda Dar

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

4 Scopus citations

Abstract

We consider the problem of finding optimal piecewise constant approximations of one-dimensional signals. These approximations should consist of a specified number of segments (samples) and minimise the mean squared error to the original signal. We formalise this goal as a discrete nonconvex optimisation problem, for which we study two algorithms. First we reformulate a recent adaptive sampling method by Dar and Bruckstein in a compact and transparent way. This allows us to analyse its limitations when it comes to violations of its three key assumptions: signal smoothness, local linearity, and error balancing. As a remedy, we propose a direct optimisation approach which does not rely on any of these assumptions and employs a particle swarm optimisation algorithm. Our experiments show that for nonsmooth signals or low sample numbers, the direct optimisation approach offers substantial qualitative advantages over the Dar-Bruckstein method. As a more general contribution, we disprove the optimality of the principle of error balancing for optimising data in the `2 norm.

Original languageEnglish
Title of host publicationEUSIPCO 2019 - 27th European Signal Processing Conference
PublisherEuropean Signal Processing Conference, EUSIPCO
ISBN (Electronic)9789082797039
DOIs
StatePublished - 1 Sep 2019
Externally publishedYes
Event27th European Signal Processing Conference, EUSIPCO 2019 - A Coruna, Spain
Duration: 2 Sep 20196 Sep 2019

Publication series

NameEuropean Signal Processing Conference
Volume2019-September
ISSN (Print)2219-5491

Conference

Conference27th European Signal Processing Conference, EUSIPCO 2019
Country/TerritorySpain
CityA Coruna
Period2/09/196/09/19

Keywords

  • Adaptive Signal Processing
  • Nonconvex Optimisation
  • Nonuniform Sampling
  • Particle Swarm Optimisation
  • Segmentation

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering

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