Independent Component Analysis, as well as Sparse Component Analysis has been recently applied to naturally-occurring data to uncover hidden fundamental components. This body of work has been motivated by the idea that natural images are what living organisms see as they develop, and that perhaps living organism develop as they do because of the statistical properties of the images they are exposed to.

These studies show systems of components spatially localized, oriented and bandpass (selective to structure at different scales) and have been compared to the basis elements of the wavelet transform, and Gabor functions with highly anisotropic Gaussian windows. Nevertheless, none of these systems have been able to span the full the image space, and the question of what the computed components compare to basis elements in existing systems of harmonic analysis remain unanswered.

Our claim is that recent work on the independent components of images can best be interpreted in the light of recent constructions in harmonic analysis- such ridgelet and curvelets. These mathematical objects exhibit surprising similarities to the results of ICA on certain naturally-occurring data.