Reconstructing Natural Visual Scenes From Spike Times

In this paper, we investigate neural circuit architectures encoding natural visual scenes with neuron models consisting of dendritic stimulus processors (DSPs) in cascade with biophysical spike generators (BSGs). DSPs serve as functional models of processing of stimuli up to and including the neuron´s active dendritic tree. BSGs model spike generation at the axon hillock level where neurons respond to aggregated synaptic currents. The highly nonlinear behavior of BSGs calls for novel methods of input/output (I/O) analysis of neural encoding circuits and novel decoding algorithms for signal recovery. On the encoding side we characterize the BSG I/O with a phase response curve (PRC) manifold and interpret neural encoding as generalized sampling. We provide a decoding algorithm that recovers visual stimuli encoded by a neural circuit with intrinsic noise sources. In the absence of noise, we give conditions on perfect reconstruction of natural visual scenes. We extend the architecture to encompass neuron models with on-off BSGs with self- and cross-feedback. With the help of the PRC manifold, decoding is shown to be tractable even for a wide signal dynamic range. Consequently, bias currents that were essential in the encoding process can largely be reduced or eliminated. Finally, we present examples of massively parallel encoding and decoding of natural visual scenes on a cluster of graphical processing units (GPUs). We evaluate the signal reconstruction under different noise conditions and investigate the performance of signal recovery in the Nyquist region and for different temporal bandwidths.