Computing variations of entropy and redundancy under nonlinear mappings not preserving the signal dimension: quantifying the efficiency of V1 cortex

In computational neuroscience, the Efficient Coding Hypothesis argues that the neural organization comes from the optimization of information-theoretic goals [Barlow Proc.Nat.Phys.Lab.59]. A way to confirm this requires the analysis of the statistical performance of biological systems that have not been statistically optimized [Renart et al. Science10, Malo&Laparra Neur.Comp.10, Foster JOSA18, Gomez-Villa&Malo J.Neurophysiol.19]. However, when analyzing the information-theoretic performance, cortical magnification in the retina-cortex pathway poses a theoretical problem. Cortical magnification stands for the increase the signal dimensionality [Cowey&Rolls Exp. Brain Res.74]. Conventional mo…