Properties of Laplacian Pyramids for Extension and Denoising

We analyze the Laplacian pyramids algorithm of Rabin and Coifman for extending and denoising a function sampled on a discrete set of points. We provide mild conditions under which the algorithm converges, and prove stability bounds on the extended function. We also consider the iterative application of truncated Laplacian pyramids kernels for denoising signals by non-local means.