Signal Coding and Perfect Reconstruction using Spike Trains
This work addresses signal processing in neural systems, offering a theoretical framework that could impact neuroscience and neuromorphic computing, though it appears incremental as it builds on existing convolve-then-threshold models.
The paper tackles the problem of coding and reconstructing signals from spike trains using a biologically plausible neuron model, and identifies conditions for perfect reconstruction with a proposed stochastic gradient descent mechanism, demonstrated through simulation experiments.
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