Bandlimited signal reconstruction from leaky integrate-and-fire encoding using POCS

Abstract

Leaky integrate-and-fire (LIF) encoding is a model of neuron transfer function in biology that has recently attracted the attention of the signal processing and neuromorphic computing communities as a technique of event-based sampling for data acquisition. While LIF enables the implementation of analog-circuit signal samplers of lower complexity and higher accuracy simultaneously, the core difficulty of this technique is the retrieval of an input from its LIF-encoded output. This theoretically requires to perform the pseudo-inversion of a linear but time-varying operator of virtually infinite size. In the context of bandlimited inputs to allow finite-rate sampling, we show two fundamental contributions of the method of projection onto convex sets (POCS) to this problem: (i) single iterations of the POCS method can be used to deterministically improve input estimates from any other reconstruction method; (ii) the iteration limit of the POCS method is the pseudo-inverse of the above mentioned operator in all conditions, whether reconstruction is unique or not and whether the encoding is corrupted by noise or not. The algorithms available until now converge only under particular situations of unique of reconstruction.