The Finite Element Method and Balancing Principle for Magnetic Resonance Imaging

  • Larisa BeilinaEmail author
  • Geneviève Guillot
  • Kati Niinimäki
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 328)


This work considers a finite element method in combination with balancing principle for a posteriori choice of the regularization parameter for image reconstruction problem appearing in magnetic resonance imaging (MRI). The fixed point iterative algorithm is formulated and it’s performance is demonstrated on the image reconstruction from experimental MR data.


MRI Fredholm integral equation of the first kind Finite element method Regularization Balancing principle 


65R20 65R32 



The research of LB was supported by the Swedish Research Council grant VR 2018-03661 and by the French Institute in Sweden, FRÖ program. The research of KN was supported by the French Institute in Sweden, TOR program.


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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Larisa Beilina
    • 1
    Email author
  • Geneviève Guillot
    • 2
  • Kati Niinimäki
    • 3
    • 4
  1. 1.Department of Mathematical SciencesChalmers University of Technology and University of GothenburgGothenburgSweden
  2. 2.IR4M UMR8081, CNRS, Université Paris-Sud, Université Paris-SaclayOrsayFrance
  3. 3.IR4M UMR8081, CNRS, Université Paris-Sud, Université Paris-Saclay, SHFJOrsayFrance
  4. 4.Xray DivisionPlanmeca OyHelsinkiFinland

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