Signal Coding and Reconstruction using Spike Trains

Anik Chattopadhyay, Arunava Banerjee

Keywords: spike trains, signal encoding, reconstruction, kernel, representer theorem, compression, convolutional matching pursuit, COMP

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, albeit with a wide variety of convolution kernels. 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. Coding experiments on a large audio dataset are presented to demonstrate the strength of the framework.

One-sentence Summary: A mathematical framework for signal encoding and decoding, based on a model of biological neurons, is formulated and its efficacy is established both via mathematical results and through simulation experiments on large corpora of audio signals.

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