Recovering convex boundaries from blurred and noisy observations

Research output: Contribution to journalArticlepeer-review


We consider the problem of estimating convex boundaries from blurred and noisy observations. In our model, the convolution of an intensity function f is observed with additive Gaussian white noise. The function f is assumed to have convex support G whose boundary is to be recovered. Rather than directly estimating the intensity function, we develop a procedure which is based on estimating the support function of the set G. This approach is closely related to the method of geometric hyperplane probing, a well-known technique in computer vision applications. We establish bounds that reveal how the estimation accuracy depends on the ill-posedness of the convolution operator and the behavior of the intensity function near the boundary.

Original languageEnglish
Pages (from-to)1375-1394
Number of pages20
JournalAnnals of Statistics
Issue number3
StatePublished - Jun 2006


  • Boundary estimation
  • Convex sets
  • Deconvolution
  • Geometric probing
  • Image analysis
  • Rates of convergence
  • Support function

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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