Optimal sampling and curve interpolation via wavelets

We propose a wavelet-based method for determining optimal sampling positions and inferring underlying functions based on the samples when it is known that the underlying function is Lipschitz. We first propose a Lipschitz regularity-based statistical model for data which are sampled from a Lipschitz curve. And then we propose a wavelet-based interpolation method for generating a Lipschitz curve given a set of points, and derive the optimal sampling positions.