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The Radon transform inversion using moments

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  • Mnatsakanov, Robert M.
  • Li, Shengqiao

Abstract

The problem of recovering the multivariate probability density function f from the moments of its Radon transform Rf is studied. The approximation of the Radon transform Rf itself is obtained from the moments of f. Under the mild conditions on f the uniform rates of convergence for the proposed constructions are established.

Suggested Citation

  • Mnatsakanov, Robert M. & Li, Shengqiao, 2013. "The Radon transform inversion using moments," Statistics & Probability Letters, Elsevier, vol. 83(3), pages 936-942.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:3:p:936-942
    DOI: 10.1016/j.spl.2012.11.026
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    References listed on IDEAS

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    1. Mnatsakanov, Robert M., 2008. "Hausdorff moment problem: Reconstruction of probability density functions," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1869-1877, September.
    2. Mnatsakanov, Robert M., 2011. "Moment-recovered approximations of multivariate distributions: The Laplace transform inversion," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 1-7, January.
    3. Gilliam, D. S. & Hall, P. & Ruymgaart, F. H., 1993. "Rate of Convergence of the Empirical Radon Transform," Journal of Multivariate Analysis, Elsevier, vol. 44(1), pages 115-145, January.
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