Abstract:

Curvelets are a recent construction of a transform with good time-frequency-direction localization, created by Cand\`es and Donoho in 1999 to address the "edge representation problem". We are ultimately interested in approximations to functions in $L_2(R^2)$ from spaces $X_n$ spanned by curvelets, and in this presentation we show our on-going efforts in that direction: some numerical experiments to help us acquire intuition and formulate conjectures, and some theoretical results that help describe regularity of a function by means of its curvelet coefficients.