Computational and theoretical models in diffuse imaging

Topi Kuutela

Research output: ThesisDoctoral ThesisCollection of Articles

Abstract

In this thesis, aspects of parameter estimation problems associated with diffuse imaging modalities are studied. Both considered modalities, electrical impedance tomography (EIT) and diffuse optical tomography (DOT), correspond to ill-posed inverse problems governed by elliptic partial differential equations, with the goal of reconstructing a material parameter field inside an examined body from measurements on the surface of the body. The ill-posedness of these problems is particularly evident in their sensitivity to modeling errors. This thesis studies computational and theoretical models with which some of the reconstruction artifacts can be reduced. The logarithmic forward map of EIT has been previously introduced to facilitate the use of linearization in the parameter estimation problem. The first theoretical contribution of this thesis is proving the Fréchet differentiability of the logarithmic forward map, and establishing its regularity. Curiously the Fréchet derivative is found to be more regular than the logarithmic forward map itself. The second theoretical contribution consists of extensions to the series reversion technique in EIT. Numerical methods with higher order convergence rates can be constructed via series reversion using only directional derivatives, which are cheap to compute for the forward map of EIT. In this thesis, the series reversion method is extended to simultaneously cover the domain conductivity and the electrode contact reconstructions and to also allow arbitrary parametrizations for the reconstructed quantities. The error in electrode locations is known to be one of the most significant error sources for EIT reconstruction problems. A computationally simple method to compensate for the electrode location error in the reconstruction process is presented and numerically evaluated in this thesis. The method is based on an extension to the smoothened complete electrode model in which the contact conductivity between the electrodes and the measured domain is not considered a constant but instead a function on the boundary. The viability of this method is demonstrated by two-dimensional reconstructions based on real-world measurements and by three-dimensional numerical experiments as a part of the study on the generalized series reversion. Finally, this thesis includes a careful evaluation of the effect of anatomical variation in frequency-domain DOT. The variation is studied numerically using 166 segmented neonatal head anatomies with the two commonly used computational models for DOT, the diffusion approximation and Markov chain Monte Carlo. Furthermore, a new segmentation method is presented to separate cerebrospinal fluid into two physiologically plausible types, one present in between the skull and the brain while the other found in the sulci of the brain.
Translated title of the contributionLaskennallisia ja teoreettisia menetelmiä diffuusiin kuvantamiseen
Original languageEnglish
QualificationDoctor's degree
Awarding Institution
  • Aalto University
Supervisors/Advisors
  • Hyvönen, Nuutti, Supervising Professor
  • Hyvönen, Nuutti, Thesis Advisor
Publisher
Print ISBNs978-952-64-1144-6
Electronic ISBNs978-952-64-1145-3
Publication statusPublished - 2023
MoE publication typeG5 Doctoral dissertation (article)

Keywords

  • inverse problem
  • parameter estimation problem
  • forward modeling
  • electrical impedance tomography
  • diffuse optical tomography
  • complete electrode model
  • modeling errors
  • series reversion

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