ESAR: Event-Based Synthetic Aperture Reconstruction

Event cameras report asynchronous polarity events when changes in log--radiance exceed a fixed contrast threshold, producing signed temporal contrast measurements rather than conventional image frames. We formulate monocular event-based imaging as a synthetic-aperture inverse problem for a static ground-domain log--radiance field θ ∈ ℝNg. Instead of reconstructing a latent pixel-time volume v ∈ ℝNpNt, we impose the geometric relation v=Pθ, where P maps the fixed scene into motion-dependent latent views. Aggregating events over finite time intervals gives the linearized model [ APθ = b+η, ] where A is a temporal differencing operator, b contains signed binned event counts, and η represents measurement and modeling errors. This decomposition exposes a synthetic-aperture structure: under near-nadir motion, successive projections are approximately shifted views of a common scene, while the composite operator AP remains ill-conditioned because it combines spatial averaging with temporal differencing. We therefore use regularized inversion to recover θ. Numerical experiments on simulated data and real near-nadir Falcon Neuro event data show that the proposed θ-based formulation recovers coherent large-scale spatial structure, relative to dynamic latent-image and learned event-reconstruction baselines, while suppressing fine-scale texture.