Optimal rates for total variation denoising

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Jan-Christian Hütter, Philippe Rigollet ;
29th Annual Conference on Learning Theory, PMLR 49:1115-1146, 2016.

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.

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