  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. 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 in this setup. Finally, a stochastic gradient descent mechanism is
proposed to achieve these conditions. Simulation experiments are presented to
demonstrate the strength and efficacy of the framework
