Exploitation of natural image statistics by biological vision systems: 1/f2 power spectra and self-similar bandpass decompositions

The second-order statistics of natural images can be well characterized by a “self-similar” 1/F² power spectrum and the bandpass decomposition in biological vision systems is characterized by a self-similar, wavelet-like structuring of the “frequency channels”. It has thus often been suggested that there might exist a systematic interrelationship between these two properties, but a complete formal derivation of this relation has not yet been provided. Using rate-distortion arguments and a complexity measure, we first show that a self-similar bandpass decomposition can achieve a desired level of distortion with a less complex system structure than required for a decomposition in bands of equal linear bandwidth. A closer analysis reveals that the true optimum decomposition is approximately self-similar but shows a systematic decrease of the log-bandwidths with increasing center frequency of the subbands. Since this effect has also been observed in neurophysiological experiments, we conclude that the typical properties of visual neurons may in fact result from an optimized exploitation of the statistical redundancies of the natural environment