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

A. Goldenshluger, V. Spokoiny

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)123-140
Number of pages18
JournalProbability Theory and Related Fields
Volume128
Issue number1
DOIs
Publication statusPublished - Jan 2004
Externally publishedYes

Keywords

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

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