Polyspectra and cumulants have recently gained an increasing interest as tools for the analysis of higher-order statistics. Since images from the natural environment contain a considerable amount of statistical dependencies at a level beyond the second order we have analyzed the bi- and trispectra of such natural images. Our results indicate the presence of strong statistical dependencies between those frequency components which are aligned to each other. This is in accordance with a strong contribution from intrinsically one-dimensional image features like straight edges and lines. Since linear filter decomposition are limited in their potential for exploiting higher-order dependencies we consider which types of nonlinear Volterra-Wiener filters might be suitable for an efficient exploitation of these dependencies. It turns out that a nonlinear predictive scheme closely related to cortical end-stopping can substantially reduce the statistical dependencies in the resulting representation. The function of these operators can thus be regarded as part of a general higher-order whitening strategy underlying the function of biological vision systems.