Nonlinear Approximation of Functions by Sums of Wave Packets∗

We consider the problem of approximating functions by sums of wave packets. Our objective is to find sparse decompositions of image functions, over a finite range of scales. We also address the naturally connected task of approximating the wavefront set, computationally. We formulate the problem in terms of Hankel operators, Hankel matrices and their low-rank approximations, and develop an algebraic structure associated with the decomposition of functions into wave packets.