Barlow's redundancy reduction hypothesis is applied using techniques developed from signal processing theory to derive the one-dimensional ganglion and simple cell kernels. The resulting closed-form expression for the ganglion cell kernel reduces redundancy over the entire range of signal-to-noise ratios, and resembles the phenomenological kernel. Significantly, it exhibits observed nontrivial dependence of the cell's parameters on background luminosity. The one-dimensional simple cell kernel is deduced by requiring that it maintain the redundancy reduction achieved by the ganglion cells despite the presence of intrinsic noise introduced through transmission along the optic nerve Neural update algorithms which converge to these cell profiles, starting from any initial set of synaptic strengths, are also derived. These learning algorithms turn out to be anti-Hebbian.