Efficient reconstruction algorithms for three-dimensional tomographic imaging

Helle Majander

Research output: ThesisDoctoral ThesisCollection of Articles


This thesis considers nonlinear parameter estimation problems arising from tomographic imaging modalities governed by elliptic partial differential equations. These are ill-posed inverse problems and hence their solution requires regularization or, in the Bayesian framework, incorporation of prior information about the to-be-reconstructed spatially varying parameter. In particular, if the parameter is known to have distinct inclusions in a constant background, we quantify such information by assuming that after discretization the parameter follows an edge-enhancing prior distribution. Moreover, we study how to recover from different kinds of errors in the data, since even small ones can be enough to ruin the reconstruction for an illposed tomographic imaging problem. We consider the solution of the investigated inverse problem to be the maximum a posteriori estimate for the parameter of interest, which can be found by solving a minimization problem. We propose to search for the minimizer by an iterative algorithm based on combining linearizations of the forward model, lagged diffusivity steps and a priorconditioned Krylov subspace method (LSQR). By presenting examples from electrical impedance tomography (EIT), diffuse optical tomography (DOT) and quantitative photoacoustic tomography (QPAT), we demonstrate that such a method can be implemented efficiently enough to be feasible for solving large-scale three-dimensional problems. In addition, we use a conformal invariance result for the complete electrode model (CEM) of EIT to compensate for geometric modeling errors.
Translated title of the contributionTehokkaita rekonstruktioalgoritmeja kolmiulotteiseen tomografiseen kuvantamiseen
Original languageEnglish
QualificationDoctor's degree
Awarding Institution
  • Aalto University
  • Hyvönen, Nuutti, Supervising Professor
  • Hyvönen, Nuutti, Thesis Advisor
Print ISBNs978-952-60-7007-0
Electronic ISBNs978-952-60-7006-3
Publication statusPublished - 2016
MoE publication typeG5 Doctoral dissertation (article)


  • parameter estimation problem
  • tomographic imaging
  • edge-enhancing regularization
  • modeling errors
  • priorconditioning
  • LSQR
  • electrical impedance tomography
  • complete electrode model
  • diffuse optical tomography
  • quantitative photoacoustic tomography


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