e & i Elektrotechnik und Informationstechnik

, Volume 124, Issue 7–8, pp 248–253

Bayesian inversion method for 3D dental X-ray imaging

  • V. Kolehmainen
  • A. Vanne
  • S. Siltanen
  • S. Järvenpää
  • J. P. Kaipio
  • M. Lassas
  • M. Kalke


Diagnostic and operational tasks in dentistry require three-dimensional (3D) information about tissue. A novel type of low dose dental 3D X-ray imaging is considered. Given projection images taken from a few sparsely distributed directions using the dentist's regular X-ray equipment, the 3D X-ray attenuation function is reconstructed. This is an ill-posed inverse problem, and Bayesian inversion is a well suited framework for reconstruction from such incomplete data. The reconstruction problem is formulated in a well-posed probabilistic form in which a priori information is used to compensate for the incomplete data. A parallelized Bayesian method (implemented for a Beowulf cluster computer) for 3D reconstruction in dental radiology is presented (the method was originally presented in (Kolehmainen et al., 2006)). The prior model for dental structures consists of a weighted l1 and total variation (TV)-prior together with the positivity prior. The inverse problem is stated as finding the maximum a posterior (MAP) estimate. The method is tested with in vivo patient data and shown to outperform the reference method (tomosynthesis).


Inverse problems X-ray tomography Dental Beowulf Parallel computing 

Bayes'sche Inversion für dreidimensionale Röntgentomografie in der Zahnmedizin


Diagnostische und operative Zahnmedizin erfordert dreidimensionale (3D) Gewebeinformation. In diesem Beitrag wird eine neue Art der schwachdosierten 3D-Röntgentomografie untersucht. Die Rekonstruktion der 3D-Dämpfungsverteilung erfolgt aus nur wenigen Projektionen, die mit handelsüblichen Röntgenapparaten aufgenommen werden. Das inverse Problem ist als Bayes'sches Schätzproblem formuliert, in dem a priori Information zur Kompensation der unvollständigen Messdaten berücksichtigt wird. Zur Lösung des inversen Problems wird eine parallelisierte Bayes'sche Methode für 3D-Röntgentomografie (implementiert für einen Beowulf-Rechencluster) vorgeschlagen. Diese Art der Rekonstruktion wurde in (Kolehmainen et al., 2006) präsentiert. Das verwendete A priori-Modell besteht aus einer Kombination einer gewichteten (l1-prior, einer total variation (TV) prior und einer Positivitätsprior. Das inverse Problem kann als Suche nach dem Maximum a posterior (MAP)-Zustand betrachtet werden. Die vorgeschlagene Methode wird anhand von In vivo-Patientendaten getestet und zeigt eine signifikante Verbesserung gegenüber der üblichen Methode (tomosynthesis).


Inverses Problem Röntgentomografie Zahnmedizin Beowulf Parallelverarbeitung 


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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • V. Kolehmainen
    • 1
  • A. Vanne
    • 1
  • S. Siltanen
    • 4
  • S. Järvenpää
    • 2
  • J. P. Kaipio
    • 1
  • M. Lassas
    • 2
  • M. Kalke
    • 3
  1. 1.University of KuopioKuopioFinland
  2. 2.Helsinki University of TechnologyTKKFinland
  3. 3.PaloDEx GroupTuusulaFinland
  4. 4.Tampere University of TechnologyTampereFinland

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