How much information is carried by the power and phase spectra of natural scenes?

Abstract

The absolute efficiency of any given visual coding strategy can be estimated only if one can determine the total amount of information contained in the visual signal. In this study, we use a new technique, developed by Chandler and Field (2007) for estimating information (entropy, redundancy) in image sets, to calculate: (1) the information provided by the power and phase spectra of natural scenes, and (2) the amount of mutual information provided by these spectra. By using both raw natural scenes and scenes with strategically altered statistics, we show that for 8×8-pixel patches, approximately 53% of the information in scenes is carried by the power spectrum (which includes information due to variations in mean luminance, contrast, etc.); 61% of the information is carried by the phase spectrum; and 14% is jointly carried by the power and phase (mutual information; 53% + 61% − 14% = 100%). This dependency between power and phase is also demonstrated psychophysically by using montages created from the 8×8-pixel patches. We discuss how these results change as a function of patch size; how variations in mean and contrast contribute to the information carried by the power spectrum; and the implications of these results for visual coding.