Finite element-based space-time total variation-type regularization of the inverse problem in electrocardiographic imaging

Reconstructing cardiac electrical activity from body surface electric potential measurements results in the severely ill-posed inverse problem in electrocardiography. Many different regularization approaches have been proposed to improve numerical results and provide unique results. This work presents a novel approach for reconstructing the epicardial potential from body surface potential maps based on a space-time total variation-type regularization using finite elements, where a first-order primal-dual algorithm solves the underlying convex optimization problem. In several numerical experiments, the superior performance of this method and the benefit of space-time regularization for the reconstruction of epicardial potential on two-dimensional torso data and a three-dimensional rabbit heart compared to state-of-the-art methods are demonstrated.

• Publication year

  2024

• Venue

  SIAM Journal on Scientific Computing

• Publication date

  2024-08-21

• Fields of study

  Medicine, Computer Science, Engineering, Mathematics

• Identifiers
  DOI 10.48550/arXiv.2408.11573arXiv 2408.11573
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• Reconstruction of the local contractility of the cardiac muscle from deficient apparent kinematics

  2024cited by this paper
• Digital Twinning of Cardiac Electrophysiology Models From the Surface ECG: A Geodesic Backpropagation Approach

  2023cited by this paper
• Basis and applicability of noninvasive inverse electrocardiography: a comparison between cardiac source models

  2023cited by this paper
• Learning cardiac activation maps from 12-lead ECG with multi-fidelity Bayesian optimization on manifolds

  2022cited by this paper
• A computational model of rabbit geometry and ECG: Optimizing ventricular activation sequence and APD distribution

  2022influential reference
• A Patchwork Method to Improve the Performance of Current Methods for Solving the Inverse Problem of Electrocardiography

  2022cited by this paper
• Inverse problems in blood flow modeling: A review

  2022cited by this paper
• PDE-Aware Deep Learning for Inverse Problems in Cardiac Electrophysiology

  2021cited by this paper
• Space–time shape uncertainties in the forward and inverse problem of electrocardiography

  2020cited by this paper
• SciPy 1.0: fundamental algorithms for scientific computing in Python

  2019cited by this paper
• Validation and Opportunities of Electrocardiographic Imaging: From Technical Achievements to Clinical Applications

  2018cited by this paper
• Evaluation of Fifteen Algorithms for the Resolution of the Electrocardiography Imaging Inverse Problem Using ex-vivo and in-silico Data

  2018cited by this paper
• Evaluation of a Rapid Anisotropic Model for ECG Simulation

  2017cited by this paper
• ECG signal performance de-noising assessment based on threshold tuning of dual-tree wavelet transform

  2017cited by this paper
• CuPy : A NumPy-Compatible Library for NVIDIA GPU Calculations

  2017cited by this paper
• The cardiovascular system: Mathematical modelling, numerical algorithms and clinical applications *

  2017cited by this paper
• Partial Differential Equations

  2016cited by this paper
• Application of robust Generalised Cross-Validation to the inverse problem of electrocardiology

  2016cited by this paper
• Noninvasive reconstruction of cardiac electrical activity: update on current methods, applications and challenges

  2015cited by this paper
• Mathematical cardiac electrophysiology/ Piero Colli Franzone, Luca F. Pavarino, Simone Scacchi

  2014cited by this paper
• Noninvasive Transmural Electrophysiological Imaging Based on Minimization of Total-Variation Functional

  2014cited by this paper
• Direct methods in the theory of elliptic equations

  2012cited by this paper
• Application of L1-norm regularization to epicardial potential reconstruction based on gradient projection

  2011cited by this paper
• A First-Order Primal-Dual Algorithm for Convex Problems with Applications to Imaging

  2011cited by this paper
• Finite-Element-Based Discretization and Regularization Strategies for 3-D Inverse Electrocardiography

  2011cited by this paper
• Bidomain ECG Simulations Using an Augmented Monodomain Model for the Cardiac Source

  2011cited by this paper
• Total Variation Regularization in Electrocardiographic Mapping

  2010cited by this paper
• Convex optimization

  2010cited by this paper
• Ranking the Influence of Tissue Conductivities on Forward-Calculated ECGs

  2010cited by this paper
• Resolution Strategies for the Finite-Element-Based Solution of the ECG Inverse Problem

  2010cited by this paper
• Comparison of Bayesian MAP Estimation and Kalman Filter Methods in the Solution of Spatio-Temporal Inverse ECG Problem

  2009cited by this paper
• Spatio-Temporal Solutions in Inverse Electrocardiography

  2009cited by this paper
• Application of L1-Norm Regularization to Epicardial Potential Solution of the Inverse Electrocardiography Problem

  2009cited by this paper
• Boundary Element Computations in the Forward and Inverse Problems of Electrocardiography: Comparison of Collocation and Galerkin Weightings

  2008cited by this paper
• Evaluation of cortical current density imaging methods using intracranial electrocorticograms and functional MRI

  2007cited by this paper
• Why is the Cauchy problem severely ill-posed?

  2007cited by this paper
• Computing the electrical activity in the heart

  2006cited by this paper
• Application of the Method of Fundamental Solutions to Potential-based Inverse Electrocardiography

  2006cited by this paper
• Lead field computation for the electrocardiographic inverse problem - finite elements versus boundary elements

  2005cited by this paper
• A new spatiotemporal regularization approach for reconstruction of cardiac transmembrane potential patterns

  2004cited by this paper
• Decomposition of images by the anisotropic Rudin‐Osher‐Fatemi model

  2004cited by this paper
• Noninvasive electrocardiographic imaging for cardiac electrophysiology and arrhythmia

  2004cited by this paper
• Comparison of potential- and activation-based formulations for the inverse problem of electrocardiology

  2003cited by this paper
• The temporal prior in bioelectromagnetic source imaging problems

  2003cited by this paper
• Mathematical models and numerical methods for the forward problem in cardiac electrophysiology

  2002cited by this paper
• Handbook of Image and Video Processing

  2000cited by this paper
• Inverse electrocardiographic transformations: dependence on the number of epicardial regions and body surface data points.

  1994cited by this paper
• The Mathematical Theory of Finite Element Methods

  1994cited by this paper
• Nonlinear total variation based noise removal algorithms

  1992cited by this paper
• The use of temporal information in the regularization of the inverse problem of electrocardiography

  1992cited by this paper
• The Analysis of Linear Partial Differential Operators IV

  1985cited by this paper
• Generalized cross-validation as a method for choosing a good ridge parameter

  1979cited by this paper
• Solutions of ill-posed problems

  1977cited by this paper
• Lectures on Cauchy's Problem in Linear Partial Differential Equations

  1924cited by this paper

• Learned Finite Element-based Regularization of the Inverse Problem in Electrocardiographic Imaging

  2026cites this paper