Cartoon Approximation with alpha-Curvelets

摘要

It is well-known that curvelets provide optimal approximations for so-called cartoon images which are defined as piecewise -functions, separated by a singularity curve. In this paper, we consider the more general case of piecewise -functions, separated by a singularity curve for . We first prove a benchmark result for the possibly achievable best N-term approximation rate for this more general signal model. Then we introduce what we call -curvelets, which are systems that interpolate between wavelet systems on the one hand () and curvelet systems on the other hand (). Our main result states that those frames achieve this optimal rate for , up to -factors.