WIAS Preprint No. 909, (2004)

Recovering edges of an image from noisy tomographic data



Authors

  • Goldenshluger, Alexander
  • Spokoiny, Vladimir
    ORCID: 0000-0002-2040-3427

2010 Mathematics Subject Classification

  • 62G20 62C20 94A08

Keywords

  • Radon transform, optimal rates of convergence, support function, edge detection, minimax estimation

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 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.

Appeared in

  • IEEE Trans. Inform. Theory, 4 (2006) pp. 1322--1334.

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