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We study the reconstruction of visual stimuli from spike trains, recordingsimultaneously from the two H1 neurons located in the lobula plate of the flyChrysomya megacephala. The fly views two types of stimuli, corresponding torotational and translational displacements. If the reconstructed stimulus is tobe represented by a Volterra series and correlations between spikes are to betaken into account, first order expansions are insufficient and we have to goto second order, at least. In this case higher order correlation functions haveto be manipulated, whose size may become prohibitively large. We thereforedevelop a Gaussian-like representation for fourth order correlation functions,which works exceedingly well in the case of the fly. The reconstructions usingthis Gaussian-like representation are very similar to the reconstructions usingthe experimental correlation functions. The overall contribution to rotationalstimulus reconstruction of the second order kernels - measured by a chi-squaredaveraged over the whole experiment - is only about 8% of the first ordercontribution. Yet if we introduce an instant-dependent chi-square to measurethe contribution of second order kernels at special events, we observe an up to100% improvement. As may be expected, for translational stimuli thereconstructions are rather poor. The Gaussian-like representation could be avaluable aid in population coding with large number of neurons.

Recording from two neurons: second order stimulus reconstruction from spike trains and population coding