On statistical Calderón problems

  • Kweku Abraham

    Université Paris-Saclay, Orsay Cedex, France
  • Richard Nickl

    University of Cambridge, UK
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For a bounded domain in with smooth boundary , the non-linear inverse problem of recovering the unknown conductivity determining solutions of the partial differential equation

from noisy observations of the Dirichlet-to-Neumann map , with denoting the outward normal derivative, is considered. The data consists of corrupted by additive Gaussian noise at noise level , and a statistical algorithm is constructed which is shown to recover in supremum-norm loss at a statistical convergence rate of the order as . It is further shown that this convergence rate is optimal, up to the precise value of the exponent , in an information theoretic sense. The estimator has a Bayesian interpretation in terms of the posterior mean of a suitable Gaussian process prior and can be computed by MCMC methods.

Cite this article

Kweku Abraham, Richard Nickl, On statistical Calderón problems. Math. Stat. Learn. 2 (2019), no. 2, pp. 165–216

DOI 10.4171/MSL/14