Real-Time Decoding of an Integrate and Fire Encoder

Neuronal encoding models range from the detailed biophysically-based Hodgkin Huxley model, to the statistical linear time invariant model specifying firing rates in terms of the extrinsic signal. Decoding the former becomes intractable, while the latter does not adequately capture the nonlinearities present in the neuronal encoding system. For use in practical applications, we wish to record the output of neurons, namely spikes, and decode this signal fast in order to drive a machine, for example a prosthetic device. Here, we introduce a causal, real-time decoder of the biophysically-based Integrate and Fire encoding neuron model. We show that the upper bound of the real-time reconstruction error decreases polynomially in time, and that the L2 norm of the error is bounded by a constant that depends on the density of the spikes, as well as the bandwidth and the decay of the input signal. We numerically validate the effect of these parameters on the reconstruction error.