Recovering convex edges of an image from noisy tomographic data

Alexander Goldenshluger, Vladimir Spokoiny

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

Abstract

We consider the problem of recovering edges of an image from noisy tomographic data. The original image is assumed to have a discontinuity jump (edge) along the boundary of a compact convex set. The Radon transform of the image is observed with noise, and the problem is to estimate the edge. We develop an estimation procedure which is based on recovering the support function of the edge. It is shown that the proposed estimator is nearly optimal in order in a minimax sense. Numerical examples illustrate reasonable practical behavior of the estimation procedure.

Original languageEnglish
Pages (from-to)1322-1334
Number of pages13
JournalIEEE Transactions on Information Theory
Volume52
Issue number4
DOIs
Publication statusPublished - Apr 2006
Externally publishedYes

Keywords

  • Edge detection
  • Minimax estimation
  • Optimal rates of convergence
  • Radon transform
  • Support function

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