Approximating surfaces with discontinuities

In this work, we study a method to recover surfaces with some discontinuity curves from a set of noisy data. By function with singularities, we mean that the function or its partial derivatives are discontinuous across planar curves. The method we present is well suited for correlated data on trajectories (i.e., the data are collected on given tracks as in the case for measurements gathered from ships or aircraft). We propose a method based on wavelet decomposition and splines as well.