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 Figure 3: Is the spike representation over-complete in the retina? (Left) We compared the progressive transmission of information for different degrees of over-completeness in the retina by plotting the average MSE of the residual as a function of the information to code the spike list (in logarithmic scale, propagation up to $12.5\%$ of the relative rank for clarity). The set of neurons used rotation symmetric Mexican hat filters, with scales from layer to layer growing as $\rho=\{ 2,\sqrt{2 },\sqrt[4]{2 },\sqrt[8]{2 } \}$ (and denoted on the legend respectively as 1, 2, 4 and 8). As a comparison we plotted the method used in~\citep{van-Rullen01a} (line 'Wav'). As a function of rank, the MSE decreases more rapidly for increasing degrees of over-completeness. (Right) But if we plot the trade-off of MSE with CPU usage as a function of the over-completeness, we find that for the same amount of information the adaptive dyadic strategy is optimal. One should note that the results of the method described in the text is better than the wavelet method of [van-Rullen, 01] since it is adaptative.
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