Beats, kurtosis and visual coding

Techniques adapted from standard higher-order statistical methods are appli ed to natural-image data in an attempt to discover exactly what makes 'wave let' representations of natural scenes sparse. Specifically, this paper des cribes a measure known as the phase-only second spectrum, a fourth-order st atistic which quantifies harmonic beat interactions in data, and uses it to show that there are statistical consistencies in the phase spectra of natu ral scenes. The orientation-averaged phase-only second spectra of natural i mages appear to show power-law behaviour rather like image power spectra, b ut with a spectral exponent of approximately -1 instead of -2. They also ap pear to display a similar form of scale-invariance. Further experimental re sults indicate that the form of these spectra can account for the observed sparseness of bandpass-filtered natural scenes. This implies an intimate re lationship between the merits of sparse neural coding and the exploitation of non-Gaussian 'beats' structures by the visual system.