Smoothness of Nonlinear Median-Interpolation Subdivision

We give a refined analysis of the Holder regularity for the limit functions arising from a nonlinear pyramid algorithm proposed by Donoho and Yu [6,7,14] for triadic refinement. Although the motivation of [6,7] was an application to 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.