What is . . . a curvelet?
Emmanuel J. Candès · CaltechAUTHORS (California Institute of Technology) · 2003
Energized by the success of wavelets, the last two decades saw the rapid development of a new field, computational harmonic analysis, which aims to develop new systems for effectively representing phenomena of scientific interest. The curvelet transform is a recent addition to the family of mathematical tools this community enthusiastically builds up. In short, this is a new multiscale transform with strong directional character in which elements are highly anisotropic at fine scales, with effective support shaped according to the parabolic scaling principle length 2 ∼ width. To fix ideas (although this is a distortion of reality) it is useful to think about curvelets as obtained by applying parabolic dilations, rotations, and translations to a specifically shaped function ψ; they are indexed by a scale parameter a (0 <a<1), a location b, and an orientation θ and are nearly of the form ψa,b,θ(x) =a −3/4 ψ(DaRθ(x − b)),