2 results for Arridge, SR

  • Approximation errors and model reduction with an application in optical diffusion tomography

    Arridge, SR; Kaipio, Jari; Kolehmainen, V; Schweiger, M; Somersalo, E; Tarvainen, T; Vauhkonen, M (2006)

    Journal article
    The University of Auckland Library

    Model reduction is often required in several applications, typically due to limited available time, computer memory or other restrictions. In problems that are related to partial differential equations, this often means that we are bound to use sparse meshes in the model for the forward problem. Conversely, if we are given more and more accurate measurements, we have to employ increasingly accurate forward problem solvers in order to exploit the information in the measurements. Optical diffusion tomography (ODT) is an example in which the typical required accuracy for the forward problem solver leads to computational times that may be unacceptable both in biomedical and industrial end applications. In this paper we review the approximation error theory and investigate the interplay between the mesh density and measurement accuracy in the case of optical diffusion tomography. We show that if the approximation errors are estimated and employed, it is possible to use mesh densities that would be unacceptable with a conventional measurement model.

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  • Marginalization of uninteresting distributed parameters in inverse problems – application to diffuse optical tomography

    Kolehmainen, V; Tarvainen, T; Arridge, SR; Kaipio, Jari (2011)

    Journal article
    The University of Auckland Library

    With inverse problems there are often several unknown distributed parameters of which only one may be of interest. Since assigning incorrect fixed values to the uninteresting parameters usually leads to a severely erroneous model, one is forced to estimate all distributed parameters simultaneously. This may increase the computational complexity of the problem significantly. In the Bayesian framework, all unknowns are generally treated as random variables and estimated simultaneously and all uncertainties can be modeled systematically. Recently, the approximation error approach has been proposed for handling uncertainty and model-reduction-related errors in the models. In this approach approximate marginalization of these errors is carried out before the estimation of the interesting variables. In this paper we discuss the adaptation of the approximation error approach to the marginalization of uninteresting distributed parameters. As an example, we consider the marginalization of scattering coefficient in diffuse optical tomography.

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