# Signal Coding and Perfect Reconstruction using Spike Trains

## TL;DR

This paper introduces a new mathematical framework for encoding and perfect reconstruction of signals using biologically plausible spike trains, leveraging convex optimization and stochastic gradient descent.

## Contribution

It presents a novel model for signal coding and reconstruction with formal conditions for perfect recovery, applicable to neural spike train analysis.

## Key findings

- Framework enables perfect signal reconstruction under certain conditions
- Convex optimization effectively reconstructs signals from spike trains
- Simulation results demonstrate the method's robustness and efficacy

## Abstract

In many animal sensory pathways, the transformation from external stimuli to spike trains is essentially deterministic. In this context, a new mathematical framework for coding and reconstruction, based on a biologically plausible model of the spiking neuron, is presented. The framework considers encoding of a signal through spike trains generated by an ensemble of neurons via a standard convolve-then-threshold mechanism. Neurons are distinguished by their convolution kernels and threshold values. Reconstruction is posited as a convex optimization minimizing energy. Formal conditions under which perfect reconstruction of the signal from the spike trains is possible are then identified in this setup. Finally, a stochastic gradient descent mechanism is proposed to achieve these conditions. Simulation experiments are presented to demonstrate the strength and efficacy of the framework