Interpolation and denoising of nonuniformly sampled data using wavelet-domain processing

In this paper, we link concepts from nonuniform sampling, smoothness function spaces, interpolation, and denoising to derive a suite of multiscale, maximum-smoothness interpolation algorithms. We formulate the interpolation problem as the optimization of finding the signal that matches the given samples with smallest norm in a function smoothness space. For signals in the Besov space B-q(alpha)(L-p), the optimization corresponds to convex programming in the wavelet domain; for signals in the Sobolev space W-alpha(L-2), the optimization reduces to a simple weighted least-squares problem. An optional wavelet shrinkage regularization step makes the algorithm suitable for even noisy sample data, unlike classical approaches such as bandlimited and spline interpolation.