WIAS Preprint No. 469, (1999)

Optimal discretization and Degrees of ill-posedness for inverse estimation in Hilbert scales in the presence of random noise


Authors

  • Mathé, Peter
    ORCID: 0000-0002-1208-1421
  • Pereverzev, Sergei V.

2010 Mathematics Subject Classification

  • 62G05 65J10

Keywords

  • Ill-posed problems, inverse estimation, operator equations, Gaussian noise, optimal difficulty, regularized inverse estimator, histogram estimator

DOI

10.20347/WIAS.PREPRINT.469

Abstract

The problem of minimizing the difficulty of the inverse estimation of some unknown element x0 from noisy observations yδ = Ax0 + δξ in dependence of the nature of the random noise ξ is considered. It is shown that a combination of a Tikhonov regularization estimator with a certain projection scheme is order optimal in the sense of difficulty for a wide class of operators A acting along Hilbert scales.

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