Optimal rates for total variation denoising
Name
1603.09388.pdf
Description
Accepted version
Size
342.16 KB
Format
Adobe PDF
Checksum (MD5)
1c380f29f922b998edd6e4b589494ba7
Author(s)
Huetter, Jan-Christian Klaus
Rigollet, Philippe
Date Issued
2016
Journal
29th Annual Conference on Learning Theory, PMLR 49
Publisher
PMLR
Citation
Huetter, Jan-Christian and Philippe Rigollet. "Optimal rates for total variation denoising." 29th Annual Conference on Learning Theory, PMLR 49, (2016): 1115-1146. © 2016 J.-C. Hütter & P. Rigollet
Version
Author's final manuscript
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. Key words and phrases: Total variation regularization; TV denoising; sharp oracle inequalities; image denoising; edge Lasso; trend filtering; nonparametric regression; shape constrained regression; minimax
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
http://proceedings.mlr.press/v49/huetter16.html
