ESAR: Event-Based Synthetic Aperture Reconstruction

Abstract

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 $\hat{I}¸\in {\mathbb{R}}^{N_g}$. Instead of reconstructing a latent pixel-time volume $v\in {\mathbb{R}}^{N_p{N}_t}$, we impose the geometric relation $v=P\hat{I}¸$, 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 $\hat{I}\cdot$ 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 $\hat{I}¸$. Numerical experiments on simulated data and real near-nadir Falcon Neuro event data show that the proposed $\hat{I}¸$-based formulation recovers coherent large-scale spatial structure, relative to dynamic latent-image and learned event-reconstruction baselines, while suppressing fine-scale texture.

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