Optimal Rates for Total Variation Denoising
Abstract
Motivated by its practical success, we show that the 2D total variation denoiser satisfies a sharp oracle inequality that leads to near optimal rates of estimation for a large class of image models such as bi-isotonic, Hölder smooth and cartoons. Our analysis hinges on properties of the unnormalized Laplacian of the two-dimensional grid such as eigenvector delocalization and spectral decay. We also present extensions to more than two dimensions as well as several other graphs.
Cite
Text
Hü. "Optimal Rates for Total Variation Denoising." Annual Conference on Computational Learning Theory, 2016.Markdown
[Hü. "Optimal Rates for Total Variation Denoising." Annual Conference on Computational Learning Theory, 2016.](https://mlanthology.org/colt/2016/hu2016colt-optimal/)BibTeX
@inproceedings{hu2016colt-optimal,
title = {{Optimal Rates for Total Variation Denoising}},
author = {Hü, Jan-Christian},
booktitle = {Annual Conference on Computational Learning Theory},
year = {2016},
pages = {1115-1146},
url = {https://mlanthology.org/colt/2016/hu2016colt-optimal/}
}