Optimal rates for total variation denoising

Jan-Christian Hütter; Philippe Rigollet

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arXiv · 1603.09388

Optimal rates for total variation denoising

Jan-Christian Hütter·Philippe Rigollet

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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.

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Jan-Christian Hütter, Philippe Rigollet. 2016-03-30. Optimal rates for total variation denoising. https://arxiv.org/abs/1603.09388

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