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[2602.07466] Learned Finite Element-based Regularization of the Inverse Problem in Electrocardiographic Imaging
Summary
This article presents a novel framework for regularizing the inverse problem in electrocardiographic imaging by combining spatial and temporal data, enhancing the accuracy of cardiac activity reconstructions.
Why It Matters
Electrocardiographic imaging is crucial for noninvasive cardiac diagnostics. This research addresses the challenges of ill-posed inverse problems, offering improved methods that leverage both spatial and temporal dynamics, potentially leading to better clinical outcomes in cardiac health monitoring.
Key Takeaways
- Introduces a space-time regularization framework for ECGI.
- Combines spatial regularization with learned temporal patterns.
- Demonstrates improved denoising and reconstruction over traditional methods.
- Utilizes finite element discretization for unstructured cardiac meshes.
- Proves Mosco-convergence and develops a scalable optimization algorithm.
Mathematics > Numerical Analysis arXiv:2602.07466 (math) [Submitted on 7 Feb 2026 (v1), last revised 13 Feb 2026 (this version, v2)] Title:Learned Finite Element-based Regularization of the Inverse Problem in Electrocardiographic Imaging Authors:Manuel Haas, Thomas Grandits, Thomas Pinetz, Thomas Beiert, Simone Pezzuto, Alexander Effland View a PDF of the paper titled Learned Finite Element-based Regularization of the Inverse Problem in Electrocardiographic Imaging, by Manuel Haas and 5 other authors View PDF HTML (experimental) Abstract:Electrocardiographic imaging (ECGI) seeks to reconstruct cardiac electrical activity from body-surface potentials noninvasively. However, the associated inverse problem is severely ill-posed and requires robust regularization. While classical approaches primarily employ spatial smoothing, the temporal structure of cardiac dynamics remains underexploited despite its physiological relevance. We introduce a space-time regularization framework that couples spatial regularization with a learned temporal Fields-of-Experts (FoE) prior to capture complex spatiotemporal activation patterns. We derive a finite element discretization on unstructured cardiac surface meshes, prove Mosco-convergence, and develop a scalable optimization algorithm capable of handling the FoE term. Numerical experiments on synthetic epicardial data demonstrate improved denoising and inverse reconstructions compared to handcrafted spatiotemporal methods, yielding solutions ...
