Shearlet approximation of functions with discontinuous derivatives

TL;DR

This paper shows that shearlet systems outperform wavelets in approximating functions with discontinuous derivatives, providing better approximation rates and decay estimates for shearlet coefficients near discontinuities.

Contribution

It introduces improved decay estimates for shearlet coefficients and demonstrates their superior approximation capabilities for functions with discontinuous derivatives.

Findings

Shearlet systems achieve better N-term approximation rates than wavelets.

Shearlet coefficients decay faster near discontinuity curves.

The paper provides new estimates for shearlet coefficient decay intersecting discontinuities.

Abstract

We demonstrate that shearlet systems yield superior $N$-term approximation rates compared with wavelet systems of functions whose first or higher order derivatives are smooth away from smooth discontinuity curves. We will also provide an improved estimate for the decay of shearlet coefficients that intersect a discontinuity curve non-tangentially.