Journal of Earth Science

, Volume 25, Issue 1, pp 117–125 | Cite as

Frequency extrapolation through Sparse sums of Lorentzians

  • Fredrik Andersson
  • Marcus Carlsson
  • Maarten V. de Hoop
Article

Abstract

Sparse sums of Lorentzians can give good approximations to functions consisting of linear combination of piecewise continuous functions. To each Lorentzian, two parameters are assigned: translation and scale. These parameters can be found by using a method for complex frequency detection in the frequency domain. This method is based on an alternating projection scheme between Hankel matrices and finite rank operators, and have the advantage that it can be done in weighted spaces. The weighted spaces can be used to partially revoke the effect of finite band-width filters. Apart from frequency extrapolation the method provides a way of estimating discontinuity locations.

Key Words

sparse sum Lorentzians Hankel matrices finite rank operator discontinuity location 

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Copyright information

© China University of Geosciences and Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Fredrik Andersson
    • 1
  • Marcus Carlsson
    • 1
  • Maarten V. de Hoop
    • 2
  1. 1.Centre for Mathematical SciencesLund UniversityLundSweden
  2. 2.Department of MathematicsPurdue UniversityWest LafayetteUSA

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