# Properties of Laplacian Pyramids for Extension and Denoising

arXiv: https://arxiv.org/abs/1909.07974 · HTML: https://mlsanity.com/paper/1909.07974/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Sep 2019.

## Built on by (most cited first, 2 of 2)

- [Grassmannian diffusion maps based surrogate modeling via geometric harmonics](https://mlsanity.com/paper/2109.13805/) (2021)
- [StreaMRAK a Streaming Multi-Resolution Adaptive Kernel Algorithm](https://mlsanity.com/paper/2108.10411/) (2021)

## Abstract (arXiv)

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.