Ridgelets:: a key to higher-dimensional intermittency?

In dimensions two and higher, wavelets can efficiently represent only a small range of the full diversity of interesting behaviour. In effect, wavelets are well adapted for point-like phenomena, whereas in dimensions greater than one, interesting phenomena can be organized along lines, hyperplanes and other non-point-like structures, for which wavelets are poorly adapted. We discuss in this paper a new subject, ridgelet analysis, which can effectively deal with line-like phenomena in dimension 2, plane-like phenomena in dimension 3 and so on. It encompasses a collection of tools which all begin from the idea of analysis by ridge functions psi(u(1)x(1) + ... + u(n)x(n)) whose ridge profiles psi are wavelets, or alternatively from performing a wavelet analysis in the Radon domain. The paper reviews recent work on the continuous ridgelet transform (CRT), ridgelet frames, ridgelet orthonormal bases, ridgelets and edges and describes a new notion of smoothness naturally attached to this new representation.