Beats, kurtosis and visual coding

Techniques adapted from standard higher-order statistical methods are applied to natural-image data in an attempt to discover exactly what makes `wavelet' representations of natural scenes sparse. Specifically, this paper describes a measure known as the phase-only second spectrum, a fourth-order statistic which quantifies harmonic beat interactions in data, and uses it to show that there are statistical consistencies in the phase spectra of natural scenes. The orientation-averaged phase-only second spectra of natural images appear to show power-law behaviour rather like image power spectra, but with a spectral exponent of approximately -1 instead of -2. They also appear to display a similar form of scale-invariance. Further experimental results indicate that the form of these spectra can account for the observed sparseness of bandpass-filtered natural scenes. This implies an intimate relationship between the merits of sparse neural coding and the exploitation of non-Gaussian `beats' structures by the visual system.