Optimal rates for total variation denoising
Statistics Theory
2016-06-17 v3 Statistics Theory
Abstract
Motivated by its practical success, we show that the two-dimensional 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, H\"older 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.
Keywords
Cite
@article{arxiv.1603.09388,
title = {Optimal rates for total variation denoising},
author = {Jan-Christian Hütter and Philippe Rigollet},
journal= {arXiv preprint arXiv:1603.09388},
year = {2016}
}
Comments
30 pages, 3 figures