On the sampling sparsity of analog-to-spike conversion based on leaky integrate-and-fire

Abstract In contrast to the traditional principle of periodic sensing, neuromorphic engineering pursues a paradigm shift towards bio-inspired event-based sensing, where events are primarily triggered by a change in the perceived stimulus. We show in a rigorous mathematical way that information encoding by means of Threshold-Based Representation based on either Leaky Integrate-and-Fire or Send-on-Delta is linked to an analog-to-spike conversion that guarantees maximum sparsity while satisfying an approximation condition based on the Alexiewicz norm.