Consistent recovery of stimuli encoded with a neural ensemble

We consider the problem of reconstructing finite energy stimuli from a finite number of contiguous spikes. The reconstructed signal satisfies a consistency condition: when passed through the same neuron, it triggers the same spike train as the original stimulus. The recovered stimulus has to also minimize a quadratic smoothness criterion. We show that under these conditions, the problem of recovery has a unique solution and provide an explicit reconstruction algorithm for stimuli encoded with a population of integrate-and-fire neurons. We demonstrate that the quality of reconstruction improves as the size of the population increases. Finally, we demonstrate the efficiency of our recovery method for an encoding circuit based on threshold spiking that arises in neuromorphic engineering.