A wavelet method for unfolding sphere size distributions

Anestis Antoniadis, Jianqing Fan, Irène Gijbels

Research output: Contribution to journalArticle

10 Scopus citations

Abstract

The authors consider the problem of estimating the density of the radii of spheres in a medium, based on their observed random cross-sections. This problem is known as Wicksell's corpuscle problem. The authors first convert Wicksell's integral equation to a form suitable for the application of thresholding wavelet methods to solve ill-posed integral equations, given noisy data. They then derive the asymptotic properties of their estimators and compare them with other methods available via a Monte Carlo simulation study. They also illustrate their approach with some real data.

Original languageEnglish (US)
Pages (from-to)251-268
Number of pages18
JournalCanadian Journal of Statistics
Volume29
Issue number2
DOIs
StatePublished - Jun 2001
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Keywords

  • Abel integral equation
  • Adaptive estimation
  • Besov spaces
  • Corpuscle problem
  • Fractional integration
  • Linear estimators
  • Wavelet thresholding
  • Wavelets

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