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 $\theta \in \mathbb{R}^{N_g}$. Instead of reconstructing a latent pixel-time volume $v \in \mathbb{R}^{N_pN_t}$, we impose the geometric relation $v=P\theta$, where $P$ maps the fixed scene into motion-dependent latent views. Aggregating events over finite time intervals gives the linearized model $$AP\theta = b+\eta,$$ where $A$ is a temporal differencing operator, $b$ contains signed binned event counts, and $\eta$ 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 $\theta$. Numerical experiments on simulated data and real near-nadir Falcon Neuro event data show that the proposed $\theta$-based formulation recovers coherent large-scale spatial structure, relative to dynamic latent-image and learned event-reconstruction baselines, while suppressing fine-scale texture.