Curvelet

Summary

Curvelets are a multiscale system of functions on the plane that are indexed by scale, orientation and position. At fine scales they are thin needles whose width is roughly the square of their length, a rule called parabolic scaling. This shape matches smooth curves well, so images that are smooth apart from smooth edges have sparse curvelet expansions. For such images, the best approximation with $N$ curvelets has squared error of order $N^{-2}(\log N)^3$, while $N$ wavelets give only order $N^{-1}$.