Interpolation and Denoising of Nonuniformly Sampled Data using Wavelet-domain Processing
Choi, Hyeokho; Baraniuk, Richard G.
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," (Lp)t,h e optimization corresponds to convex programming in the wavelet domain; for signals in the Sobolev space We(&), 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.