Geometry-Free Conditional Diffusion Modeling for Solving the Inverse Electrocardiography Problem

TL;DR

This work tackles the ill-posed inverse electrocardiography problem (ECGI) by introducing a geometry-free, data-driven conditional diffusion model that maps body-surface potentials to heart-surface potentials. The method learns the conditional distribution $p(\mathbf{x}_0|\mathbf{y})$ using a transformer-based denoiser within a denoising diffusion probabilistic framework, enabling multiple plausible reconstructions without relying on patient-specific geometry. Empirically, it outperforms deterministic baselines (1D-CNN, LSTM, Transformer) on a canine torso-tank dataset, achieving a temporal correlation of $0.783$, MSE of $32.83$, and MAE of $3.42$, demonstrating improved waveform morphology and amplitude recovery. This probabilistic, geometry-free approach offers uncertainty-aware ECGI reconstructions and provides a foundation for robust noninvasive cardiac imaging in settings where anatomical geometry is unavailable or unreliable.

Abstract

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.

Figures (3)

• Figure 1: Illustration of the forward and inverse problems in electrocardiography.
• Figure 2: Scheme of our conditional diffusion model for ECGI reconstruction. The reverse diffusion process progressively denoises an initial random signal $x_T$ to recover the cardiac surface potentials $x_0$, guided by observed body surface measurements $y$. At each timestep $t$, the conditional transition $p_\theta(x_{t-1} \mid x_t, y)$ incorporates the torso ECG to constrain the reconstruction toward physiologically consistent solutions.
• Figure 3: Reconstruction of 6 epicardial point signals.