Robust online reconstruction of continuous-time signals from a lean spike train ensemble code

TL;DR

This paper introduces a deterministic framework for encoding continuous signals into biologically plausible spike trains and provides a robust, efficient reconstruction method with proven convergence, achieving high accuracy at low spike rates.

Contribution

It develops a novel signal encoding and reconstruction framework with a closed-form inverse solution and an iterative, windowed approach inspired by biological processing.

Findings

High reconstruction accuracy at one-fifth of Nyquist rate

Robustness to ill-conditioned encoding demonstrated

Outperforms state-of-the-art sparse coding in low spike regimes

Abstract

Sensory stimuli in animals are encoded into spike trains by neurons, offering advantages such as sparsity, energy efficiency, and high temporal resolution. This paper presents a signal processing framework that deterministically encodes continuous-time signals into biologically feasible spike trains, and addresses the questions about representable signal classes and reconstruction bounds. The framework considers encoding of a signal through spike trains generated by an ensemble of neurons using a convolve-then-threshold mechanism with various convolution kernels. A closed-form solution to the inverse problem, from spike trains to signal reconstruction, is derived in the Hilbert space of shifted kernel functions, ensuring sparse representation of a generalized Finite Rate of Innovation (FRI) class of signals. Additionally, inspired by real-time processing in biological systems, an efficient iterative version of the optimal reconstruction is formulated that considers only a finite window of past spikes, ensuring robustness of the technique to ill-conditioned encoding; convergence guarantees of the windowed reconstruction to the optimal solution are then provided. Experiments on a large audio dataset demonstrate excellent reconstruction accuracy at spike rates as low as one-fifth of the Nyquist rate, while showing clear competitive advantage in comparison to state-of-the-art sparse coding techniques in the low spike rate regime.