Particle Filtering for Non-Deterministic Electrocardiographic Imaging
arXiv:2509.19404v2 Announce Type: replace-cross Abstract: Electrocardiographic imaging (ECGI) aims to non-invasively reconstruct activation maps of the heart from temporal body surface potentials. While most existing approaches rely on inverse and optimization techniques that may yield satisfactory reconstructions, they typically provide a single deterministic solution, overlooking the inherent uncertainty of the problem stemming from its very ill-posed nature, the poor knowledge of biophysical features and the unavoidable presence of noise in the measurements. The Bayesian framework, which naturally incorporates uncertainty while also accounting for temporal correlations across time steps, can be used to address this limitation. In this work, we propose a low-dimensional representation of the activation sequence that enables the use of particle filtering, a Bayesian filtering method that does not rely on predefined assumptions regarding the shape of the posterior distribution, in contrast to approaches like the Kalman filter. This allows to produce not only activation maps but also probabilistic maps indicating the likelihood of activation at each point on the heart over time, as well as pseudo-probability maps reflecting the likelihood of a point being part of an earliest activation site. Additionally, we introduce a method to estimate the probability of the presence of a conduction lines of block on the heart surface. Combined with classical reconstruction techniques, this could help discriminate artificial from true lines of block in activation maps. We support our approach with a numerical study based on simulated data, demonstrating the potential of our method.