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

arXiv: https://arxiv.org/abs/2408.05950 · HTML: https://mlsanity.com/paper/2408.05950/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 35 references that are in the map.
- First posted on arXiv 12 Aug 2024.

## Builds on (most cited first, 3 of 3)

- [General-purpose Tagging of Freesound Audio with AudioSet Labels: Task Description, Dataset, and Baseline](https://mlsanity.com/paper/1807.09902/) (2018)
- [Convolutional Dictionary Learning: A Comparative Review and New Algorithms](https://mlsanity.com/paper/1709.02893/) (2017)
- [Learning to represent signals spike by spike](https://mlsanity.com/paper/1703.03777/) (2017)

## Abstract (arXiv)

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.