用学习的时空先验提升心电成像逆问题的重建精度与稳定性
Learned Finite Element-based Regularization of the Inverse Problem in Electrocardiographic Imaging
- 融合有限元与学习型时序先验，建模心脏电活动的复杂时空特性
- 在合成数据上显著降低噪声影响，重建结果更贴近生理实际
- 适合从事心脏电活动反演、医学影像重建的研究者参考
心电成像（ECGI）旨在从体表电位非侵入性地重建心脏电活动，但其逆问题严重病态，需强正则化。传统方法多依赖空间平滑，忽视了具有生理意义的心脏动态时序结构。本文提出一种时空正则化框架，将空间正则化与学习型时序领域专家（FoE）先验相结合，以捕捉复杂的时空激活模式。基于非结构化心脏表面网格推导有限元离散化，证明了莫斯科收敛性，并开发了可扩展的优化算法以处理FoE项。在合成心外膜数据上的数值实验表明，该方法相比手工设计的时空方法，在降噪和逆问题重建方面均有提升，所得解既抗噪又具生理合理性。
原文摘要 · Abstract (English)
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 that are both robust to noise and physiologically plausible.
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