Beyond Rate Coding: Signal Coding and Reconstruction Using Lean Spike Trains

Recent years have seen a growing interest in spike based encoding of continuous time signals–a hallmark of biological computation. In this context, we present a mathematical framework for signal representation, leveraging a simple but robust mechanistic model of a biologically plausible spiking neuron. 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. Reconstruction is posited as a convex optimization minimizing energy. Formal conditions under which perfect and approximate reconstruction of the signal from the spike trains is possible are then identified. The strength of the framework is shown in experiments on a large audio dataset, demonstrating good reconstruction at a spike rate of one fifth the Nyquist rate. Comparison against a benchmark sparse coding technique, viz convolutional orthogonal matching pursuit, shows competitive results in reconstruction with orders of magnitude improvement in runtime efficiency.