Smoothness of nonlinear median-interpolation subdivision

We give a refined analysis of the Hoelder regularity for the limit functions arising from a subdivision scheme proposed by Donoho and Yu for triadic refinement. Although their original motivation was the design of a fast pyramid algorithm for robust removal of non-Gaussian noise, their scheme can be interpreted as a nonlinear subdivision process where new points are inserted based on local quadratic polynomial median interpolation and imputation. We introduce the analogon of the Donoho-Yu scheme for dyadic refinement, and give close-to-optimal regularity estimates for both the dyadic and triadic case.