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On the shape–from–moments problem and recovering edges from noisy Radon data
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  • Published: 04 November 2003

On the shape–from–moments problem and recovering edges from noisy Radon data

  • A. Goldenshluger1 &
  • V. Spokoiny2 

Probability Theory and Related Fields volume 128, pages 123–140 (2004)Cite this article

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Abstract.

We consider the problem of reconstructing a planar convex set from noisy observations of its moments. An estimation method based on pointwise recovering of the support function of the set is developed. We study intrinsic accuracy limitations in the shape–from–moments estimation problem by establishing a lower bound on the rate of convergence of the mean squared error. It is shown that the proposed estimator is near–optimal in the sense of the order. An application to tomographic reconstruction is discussed, and it is indicated how the proposed estimation method can be used for recovering edges from noisy Radon data.

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Author information

Authors and Affiliations

  1. Department of Statistics, University of Haifa, Haifa, 31905, Israel

    A. Goldenshluger

  2. Weierstrass Institute of Applied Analysis and Stochastics, Mohrenstrasse 39, Dy-10117, Berlin, Germany

    V. Spokoiny

Authors
  1. A. Goldenshluger
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  2. V. Spokoiny
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Corresponding author

Correspondence to A. Goldenshluger.

Additional information

Mathematics Subject Classification (2000): 62C20, 62G20, 94A12

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Cite this article

Goldenshluger, A., Spokoiny, V. On the shape–from–moments problem and recovering edges from noisy Radon data. Probab. Theory Relat. Fields 128, 123–140 (2004). https://doi.org/10.1007/s00440-003-0303-1

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  • Received: 03 December 2002

  • Revised: 11 September 2003

  • Published: 04 November 2003

  • Issue Date: January 2004

  • DOI: https://doi.org/10.1007/s00440-003-0303-1

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Keywords

  • Minimax estimation
  • Optimal rates of convergence
  • Shape
  • Moments
  • Support function
  • Radon transform
  • Tomography
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