Approaches for modelling and reconstruction in optical tomography in the presence of anisotropies

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dc.contributor Aalto-yliopisto fi
dc.contributor Aalto University en Heino, Jenni 2012-02-17T06:58:54Z 2012-02-17T06:58:54Z 2005-05-20
dc.identifier.isbn 951-22-7669-0
dc.identifier.issn 1795-4584
dc.description.abstract In this thesis, models for light propagation and solution methods for the inverse problem in medical optical tomography (OT) in the presence of anisotropies are developed. Light propagation is modelled using the anisotropic diffusion equation (DE) in the frequency domain. The derivation of the diffusion equation in an anisotropic case is sketched, and the relevant boundary and source conditions presented. The numerical solution is obtained using the finite element (FE) method. The numerical work is done in two dimensional space in order to facilitate the testing of the novel methods for solving the inverse problem. To verify the light propagation model, the 2D FE solution is compared to the boundary element method solution to the DE and to a Monte Carlo simulation. The main emphasis is on the solution of the inverse problem in OT in the presence of anisotropies. The anisotropic inverse problem is non-unique, and hence simultaneous reconstruction of both the anisotropic diffusion tensor and the absorption coefficient is not feasible without substantial prior knowledge. The goal in this work is to reconstruct the spatial distribution of the optical absorption coefficient and overcome the disturbing effect of the background anisotropies. At the same time, the prior knowledge available on the anisotropies is assumed to be rather limited. A few different approaches for estimating the absorption coefficient is presented. Firstly, an attempt to use a conventional isotropic reconstruction scheme is considered. In this case, the obtained estimates suffer from relative large artefacts. In the second approach the structure of the anisotropy is assumed known, and the spatially constant strength is reconstructed simultaneously with the absorption. The quality of the absorption estimate degrades quickly with the accuracy of the underlying anisotropy structure. To help this, statistical inversion methods are employed. Statistical methods provide means to model the prior information on unknown parameters through probability distributions. The anisotropy parameters are modelled using relatively loose Gaussian priors. By using Gaussian priors the posterior probability distribution of the absorption on condition of the measurements also assumes a Gaussian form. Hence the conditional mean estimates and covariances can be derived in a closed form without having to resort to numerical integration. The statistical approach is used to derive a modelling error approach, where the effect of anisotropies is treated as a modelling error and included into estimation. Implementing the statistical inversion methods enables recovering the main features in the absorption distribution. The statistical treatment of anisotropies is also applied to help the inverse problem when the boundary shape and source/measurement locations are modelled inaccurately. en
dc.format.extent 45, [app]
dc.format.mimetype application/pdf
dc.language.iso en en
dc.publisher Helsinki University of Technology en
dc.publisher Teknillinen korkeakoulu fi
dc.relation.ispartofseries TKK dissertations en
dc.relation.ispartofseries 6 en
dc.relation.haspart Jenni Heino and Erkki Somersalo. 2002. Estimation of optical absorption in anisotropic background. Inverse Problems 18, pages 559-573. [article1.pdf] © 2002 Institute of Physics Publishing. By permission.
dc.relation.haspart Jenni Heino, Simon Arridge, Jan Sikora, and Erkki Somersalo. 2003. Anisotropic effects in highly scattering media. Physical Review E 68, 031908 (8 pages). [article2.pdf] © 2003 American Physical Society. By permission.
dc.relation.haspart Ilkka Nissilä, Tommi Noponen, Jenni Heino, Timo Kajava, and Toivo Katila. 2005. Diffuse optical imaging. In: James Lin (editor), Advances in Electromagnetic Fields in Living Systems 4, pages 77-130. Springer Science, in press.
dc.relation.haspart Jenni Heino, Erkki Somersalo, and Simon Arridge. 2002. Simultaneous estimation of optical anisotropy and absorption in medical optical tomography. Proceedings of IVth International Workshop "Computational Problems of Electrical Engineering". Zakopane, Poland, pages 191-194. [article4.pdf] © 2002 Warsaw University of Technology. By permission.
dc.relation.haspart Jenni Heino and Erkki Somersalo. 2004. A modelling error approach for the estimation of optical absorption in the presence of anisotropies. Physics in Medicine and Biology 49, pages 4785-4798. [article5.pdf] © 2004 Institute of Physics Publishing. By permission.
dc.relation.haspart Jenni Heino, Erkki Somersalo, and Jari Kaipio. 2005. Compensation for geometric mismodelling by anisotropies in optical tomography. Optics Express 13, pages 296-308. [article6.pdf] © 2005 Optical Society of America (OSA). By permission.
dc.subject.other Medical sciences en
dc.subject.other Physics en
dc.title Approaches for modelling and reconstruction in optical tomography in the presence of anisotropies en
dc.type G5 Artikkeliväitöskirja fi
dc.description.version reviewed en
dc.contributor.department Department of Engineering Physics and Mathematics en
dc.contributor.department Teknillisen fysiikan ja matematiikan osasto fi
dc.subject.keyword optical tomography en
dc.subject.keyword medical imaging en
dc.subject.keyword anisotropies en
dc.subject.keyword inverse problems en
dc.subject.keyword finite elements en
dc.identifier.urn urn:nbn:fi:tkk-005182
dc.type.dcmitype text en
dc.type.ontasot Väitöskirja (artikkeli) fi
dc.type.ontasot Doctoral dissertation (article-based) en
dc.contributor.lab Laboratory of Biomedical Engineering en
dc.contributor.lab Lääketieteellisen tekniikan laboratorio fi

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