Nonlinear image operators, higher-order statistics, and the AND-like combinations of frequency components

The frequency domain plays a key role in the description of signals and systems. In the classical approaches, the individual frequency components are treated as independent: In linear systems, the superposition principle restricts the filtering to an OR-like processing of independent complex exponentials. Likewise, the classical second-order statistic (the powerspectrum) measures only the occurrence of each individual frequency component, independent of whether it occurs in a systematic combination with other components or not. This basic limitation can be overcome by the extension of the classical approaches to nonlinear systems and higher-order statistics, which makes it possible to selectively address AND-like combinations of frequency components. We measure which AND combinations are statistically most relevant in natural images, and investigate how this statistical structure can be exploited by nonlinear Volterra filters.