Considering new regularization parameter-choice techniques for choice techniques for the Tikhonov method to improve the accuracy of electrocardiographic imaging

Judit Chamorro-Servent*, Remi Dubois, Yves Coudiere

*Corresponding author for this work

Research output: Contribution to journalArticleResearchpeer-review

12 Citations (Scopus)

Abstract

The electrocardiographic imaging (ECGI) inverse problem highly relies on adding constraints, a process called regularization, as the problem is ill-posed. When there are no prior information provided about the unknown epicardial potentials, the Tikhonov regularization method seems to be the most commonly used technique. In the Tikhonov approach the weight of the constraints is determined by the regularization parameter. However, the regularization parameter is problem and data dependent, meaning that different numerical models or different clinical data may require different regularization parameters. Then, we need to have as many regularization parameter-choice methods as techniques to validate them. In this work, we addressed this issue by showing that the Discrete Picard Condition (DPC) can guide a good regularization parameter choice for the two-norm Tikhonov method. We also studied the feasibility of two techniques: The U-curve method (not yet used in the cardiac field) and a novel automatic method, called ADPC due its basis on the DPC. Both techniques were tested with simulated and experimental data when using the method of fundamental solutions as a numerical model. Their efficacy was compared with the efficacy of two widely used techniques in the literature, the L-curve and the CRESO methods. These solutions showed the feasibility of the new techniques in the cardiac setting, an improvement of the morphology of the reconstructed epicardial potentials, and in most of the cases of their amplitude.

Original languageEnglish
Article number273
JournalFrontiers in physiology
Volume10
Issue numberMAR
DOIs
Publication statusPublished - 2019

Keywords

  • Body surface potentials
  • ECG
  • Electrocardiography
  • Ill-posed
  • Inverse problem
  • MFS
  • Regularization
  • Tikhonov
  • meshless methods
  • least-squares
  • Picard
  • Applied mathematics

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