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Publication Detail
Approximation error approach for compensating for modelling errors between the radiative transfer equation and diffusion approximation in diffuse optical tomography
  • Publication Type:
    Journal article
  • Publication Sub Type:
  • Authors:
    Tarvainen T, Kolehmainen V, Pulkkinen A, Vauhkonen M, Schweiger M, Arridge SR, Kaipio JP
  • Publisher:
    IOP Publishing
  • Publication date:
  • Pagination:
    015005, ?
  • Journal:
    Inverse Problems
  • Volume:
  • Print ISSN:
In this paper, we investigate the applicability of the Bayesian approximation error approach to compensate for the discrepancy of the diffusion approximation in diffuse optical tomography close to the light sources and in weakly scattering subdomains. While the approximation error approach has earlier been shown to be a feasible approach to compensating for discretization errors, uncertain boundary data and geometry, the ability of the approach to recover from using a qualitatively incorrect physical model has not been contested. In the case of weakly scattering subdomains and close to sources, the radiative transfer equation is commonly considered to be the most accurate model for light scattering in turbid media. In this paper, we construct the approximation error statistics based on predictions of the radiative transfer and diffusion models. In addition, we investigate the combined approximation errors due to using the diffusion approximation and using a very lowdimensional approximation in the forward problem. We show that recovery is feasible in the sense that with the approximation error model the reconstructions with a low-dimensional diffusion approximation are essentially as good as with using a very high-dimensional radiative transfer model.
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