Figure 6. Spectral analysis of the proposed model compared to whitening.

Every stage of sensory representations and their transformations are illustrated (cf. Figure 3). The signal is 100-dimensional, and the fovea and periphery conditions differ only in the neural population size (100 and 10, respectively). Each is analyzed under two sensory noise levels (20 and −10 dB). The horizontal axes represent the frequency (or spectrum) of the signal and are common across all plots. The vertical axes of the open plots (e.g., original signal) are common and represent the variance of the indicated sensory representations; those of the box plots (e.g., blur) are also common and represent gain (or modulation) with the indicated transformation, where the thin horizontal line indicates unit gain. The original signal (, yellow) is assumed to have a power spectrum where f is the frequency of the signal. The blur (, black) is assumed to be low-pass gaussian. The observed signal () is shown component-wise, i.e., the blurred signal (, blue) and the sensory noise (, red). The observed signal is transformed by the neural encoding (, black). Solid and dashed lines indicate the gain as a function of frequency for the proposed and whitening model, respectively (and the same line scheme is used in the other plots). The neural representation () is also shown component-wise, i.e., the encoded signal (, blue) and neural noise (, red). The optimal decoding transform (, black) is applied to the neural representation to obtain the reconstructed signal (; blue), which is superimposed with the original signal (yellow); the percentage shows the MSE of reconstruction. Note all axes are in logarithmic scale. It is useful to recall that transforming a signal with a matrix is multiplicative, but it is simply summation in a logarithmic scale, and thus one can visually compute, for example, the blurred signal as the sum of the original signal and blur curves.