Curvelets and Curvilinear Integrals

Let C(t):I@?R^2 be a simple closed unit-speed C^2 curve in R^2 with normal [formula](t). The curve C generates a distribution @C which acts on vector fields [formula](x"1, x"2):R^2@?R^2 by line integration according to[formula] We consider the problem of efficiently approximating such functionals. Suppose we have a vector basis or frame @F=[formula] with dual @F*=[formula]; then an m-term approximation to @C can be formed by selecting m terms (@m"i:1=