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Optimal rates for total variation denoising

Author(s)
Huetter, Jan-Christian Klaus; Rigollet, Philippe
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Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/
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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
Date issued
2016
URI
https://hdl.handle.net/1721.1/125674
Department
Massachusetts Institute of Technology. Department of Mathematics
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
ISSN
2640-3498

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