Properties of Laplacian Pyramids for Extension and Denoising
This work addresses theoretical analysis for signal processing methods, but appears incremental as it builds on existing Laplacian pyramids algorithms.
The paper tackles the problem of extending and denoising functions sampled on discrete points using Laplacian pyramids, providing conditions for convergence and stability bounds, and applies truncated kernels for denoising via non-local means.
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.