A new family of variational-form-based regularizers for reconstructing epicardial potentials from body-surface mapping

We propose a new family of regularizers for the inverse ECG problem, using a variational principle that underlies finite element approximation methods. As an alternative to traditional Tikhonov regularizers, the variational formulation has several advantages: 1)it enables a simple construction of the gradient operator (in a matrix form) over irregular meshes, which is often difficult to derive; 2)it achieves consistent regularization under multi-scale simulations by preserving the norm, which is evaluated by the resolution-independent L₂-norm rather than the discrete Euclidean norm; and 3)it allows simultaneous application of multiple constraints efficiently. Our proposed method is validated by simulation on a realistic 3D model with clinical heart data, showing that the variational formulation may improve a broader range of potential-based electrocardiographic problems.