Model agnostic signal encoding by leaky integrate and fire, performance and uncertainty

TL;DR

This paper analyzes the integrate-and-fire signal encoder's performance and uncertainty effects using a bandwidth-based approach, providing insights for initialization of reconstruction algorithms.

Contribution

It introduces a comprehensive analysis of the integrate-and-fire encoder considering uncertainty factors, extending previous exact encoding results to more realistic scenarios.

Findings

Quantifies the impact of spike location uncertainty on encoding performance

Provides a bandwidth-based framework applicable to various signal models

Uses Wasserstein distance to measure spike discrepancy effectively

Abstract

Integrate-and-fire is a resource efficient time-encoding mechanism that summarizes into a signed spike train those time intervals where a signal's charge exceeds a certain threshold. We analyze the IF encoder in terms of a very general notion of approximate bandwidth, which is shared by most commonly-used signal models. This complements results on exact encoding that may be overly adapted to a particular signal model. We take into account, possibly for the first time, the effect of uncertainty in the exact location of the spikes (as may arise by decimation), uncertainty of integration leakage (as may arise in realistic manufacturing), and boundary effects inherent to finite periods of exposure to the measurement device. The analysis is done by means of a concrete bandwidth-based Ansatz that can also be useful to initialize more sophisticated model specific reconstruction algorithms, and uses the earth mover's (Wasserstein) distance to measure spike discrepancy.