Particle Filtering for Nondeterministic Electrocardiographic Imaging

Abstract. Electrocardiographic imaging (ECGI) aims to noninvasively 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 severe ill-posedness, limited knowledge of biophysical properties, and unavoidable measurement noise. The Bayesian framework, which naturally incorporates uncertainty while accounting for temporal correlations, offers a principled way to address these limitations. In this work, we propose a low-dimensional representation of the cardiac activation sequence to enable the use of particle filtering. Unlike Kalman-based approaches, this Bayesian estimation method does not rely on predefined assumptions regarding the shape of the posterior distribution. This enables the production of not only activation maps but also probabilistic maps indicating the likelihood of activation at each point on the heart over time as well as pseudoprobability 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 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. Results using simulated data show that, in favorable settings, the method accurately recovers both the number and the location of the earliest activation sites and effectively discriminates true from false lines of block. Under strong model mismatch, the loss of accuracy is balanced by increased uncertainty, correctly reflecting lower confidence levels.