Properties of Laplacian Pyramids for Extension and Denoising

TL;DR

This paper analyzes the Laplacian pyramids algorithm for function extension and denoising, establishing convergence conditions, stability bounds, and exploring iterative denoising methods using truncated kernels.

Contribution

It provides theoretical analysis of convergence and stability for Laplacian pyramids and introduces iterative denoising techniques with truncated kernels.

Findings

Convergence conditions for Laplacian pyramids are established.

Stability bounds for the extended functions are derived.

Iterative denoising with truncated kernels effectively reduces noise.

Abstract

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.