Finite element approximation of regularized solutions of the inverse potential problem of electrocardiography and applications to experimental data

DOI10.1007/BF02576202zbMath0623.65136OpenAlexW1968442289MaRDI QIDQ1091789

C. Viganotti, Piero Colli Franzone, Bruno Taccardi, Luciano Guerri

Publication date: 1985

Published in: Calcolo (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02576202

zbMATH Keywords

error estimatesfinite elementsCauchy problemTikhonov-Phillips regularizationLaplace-Beltrami operatoroptimal control problemill-posed problemexperimental dataMorozov's discrepancy principleelectrocardiographyDirichlet data

Mathematics Subject Classification ID

Optimality conditions for problems involving partial differential equations (49K20) Medical applications (general) (92C50) Inverse problems for PDEs (35R30) Second-order elliptic equations (35J15) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Applications to the sciences (65Z05) Potentials and capacities, extremal length and related notions in higher dimensions (31B15) Numerical methods for ill-posed problems for initial value and initial-boundary value problems involving PDEs (65M30)

Related Items (15)

Nonuniform spatial mesh adaptation using a posteriori error estimates: Applications to forward and inverse problems ⋮ Regularization of the inverse problem in electrocardiography: A model study ⋮ Convergence of an Alternating Method to Solve the Cauchy Problem for Poisson's Equation ⋮ The inverse problem of electrocardiography: A solution in terms of single- and double-layer sources on the epicardial surface ⋮ The cardiovascular system: Mathematical modelling, numerical algorithms and clinical applications ⋮ A Tikhonov regularization method for Cauchy problem based on a new relaxation model ⋮ Numerical linear algebra for reconstruction inverse problems. ⋮ A model study of instability of the inverse problem in electrocardiography ⋮ The inverse problem in electrocardiography on a spherical model ⋮ Improving Tikhonov regularization with linearly constrained optimization: Application to the inverse epicardial potential solution ⋮ Uniqueness and convergence of numerical solution of the Cauchy problem for the Laplace equation by a charge simulation method ⋮ Smooth fitting with a method for determining the regularization parameter under the genetic programming algorithm ⋮ Computational issues of importance to the inverse recovery of epicardial potentials in a realistic heart-torso geometry ⋮ A mathematical procedure for solving the inverse potential problem of electrocardiography. Analysis of the time-space accuracy from in vitro experimental data ⋮ Inverse electrocardiographic transformations: Dependence on the number of epicardial regions and body surface data points

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