On minimal trajectories for mobile sampling of bandlimited fields

Karlheinz Groechenig, Jose Luis Romero, Jayakrishnan Unnikrishnan, Martin Vetterli

Publications: Contribution to journalArticlePeer Reviewed

Abstract

We study the design of sampling trajectories for stable sampling and the reconstruction of bandlimited spatial fields using mobile sensors. The spectrum is assumed to be a symmetric convex set. As a performance metric we use the path density of the set of sampling trajectories that is defined as the total distance traveled by the moving sensors per unit spatial volume of the spatial region being monitored. Focusing first on parallel lines, we identify the set of parallel lines with minimal path density that contains a set of stable sampling for fields bandlimited to a known set. We then show that the problem becomes ill-posed when the optimization is performed over all trajectories by demonstrating a feasible trajectory set with arbitrarily low path density. However, the problem becomes well-posed if we explicitly specify the stability margins. We demonstrate this by obtaining a non-trivial lower bound on the path density of an arbitrary set of trajectories that contain a sampling set with explicitly specified stability bounds.

Original languageEnglish
Pages (from-to)487-510
Number of pages24
JournalApplied and Computational Harmonic Analysis
Volume39
Issue number3
DOIs
Publication statusPublished - Nov 2015

Austrian Fields of Science 2012

  • 101014 Numerical mathematics
  • 202040 Transmission technology
  • 101002 Analysis

Keywords

  • Spatial field sampling
  • Bandlimited field sampling
  • Mobile sensing
  • Sensor trajectories
  • Path density
  • Convex spectrum
  • Beurling density
  • SPACES
  • RECONSTRUCTION
  • INTERPOLATION

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