This paper proposes a data-driven model for solving the inverse problem of electrocardiography, the mathematical problem that forms the basis of electrocardiographic imaging (ECGI). We present a conditional diffusion framework that learns a probabilistic mapping from noisy body surface signals to heart surface electric potentials. The proposed approach leverages the generative nature of diffusion models to capture the non-unique and underdetermined nature of the ECGI inverse problem, enabling probabilistic sampling of multiple reconstructions rather than a single deterministic estimate. Unlike traditional methods, the proposed framework is geometry-free and purely data-driven, alleviating the need for patient-specific mesh construction. We evaluate the method on a real ECGI dataset and compare it against strong deterministic baselines, including a convolutional neural network, long short-term memory network, and transformer-based model. The results demonstrate that the proposed diffusion approach achieves improved reconstruction accuracy, highlighting the potential of diffusion models as a robust tool for noninvasive cardiac electrophysiology imaging.

翻译：本文提出了一种数据驱动模型，用于求解心电逆问题——这一数学问题是心电图成像（ECGI）技术的基础。我们提出了一个条件扩散框架，该框架能够学习从含噪声的体表信号到心表电位的概率映射。所提出的方法利用扩散模型的生成特性来捕捉ECGI逆问题的非唯一性与欠定性本质，从而实现对多个重建结果的概率采样，而非单一确定性估计。与传统方法不同，该框架无需几何建模且完全由数据驱动，避免了对患者特异性网格构建的需求。我们在真实ECGI数据集上评估了该方法，并与包括卷积神经网络、长短期记忆网络和基于Transformer模型在内的强确定性基线进行了比较。结果表明，所提出的扩散方法实现了更高的重建精度，凸显了扩散模型作为无创心脏电生理成像稳健工具的潜力。