Recovering convex edges of an image from noisy tomographic data

Alexander Goldenshluger, Vladimir Spokoiny

Research output: Contribution to journalArticlepeer-review


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
Issue number4
StatePublished - Apr 2006

Bibliographical note

Funding Information:
Manuscript received December 23, 2004; revised August 29, 2005. The work of A. Goldenshluger was supported in part by the Israel Science Foundation under Grant 300/04. A. Goldenshluger is with the Department of Statistics, Haifa University, Haifa 31905, Israel (e-mail: [email protected]). V. Spokoiny is with the Weierstrass Institute of Applied Analysis and Stochas-tics, D-10117 Berlin, Germany (e-mail: spokoiny@wias-berlin. de). Communicated by P. L. Bartlett, Associate Editor for Pattern Recognition, Statistical Learning and Inference. Digital Object Identifier 10.1109/TIT.2006.871053


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

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


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