Journal of Mathematical Imaging and Vision

, Volume 59, Issue 3, pp 456–480 | Cite as

Demystifying the Asymptotic Behavior of Global Denoising

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Abstract

In this work, we revisit the global denoising framework recently introduced by Talebi and Milanfar. We analyze the asymptotic behavior of its mean-squared error restoration performance in the oracle case when the image size tends to infinity. We introduce precise conditions on both the image and the global filter to ensure and quantify this convergence. We also make a clear distinction between two different levels of oracle that are used in that framework. By reformulating global denoising with the classical formalism of diagonal estimation, we conclude that the second-level oracle can be avoided by using Donoho and Johnstone’s theorem, whereas the first-level oracle is mostly required in the sequel. We also discuss open issues concerning the most challenging aspect, namely the extension of these results to the case where neither oracle is required.

Keywords

Diagonal estimation Global denoising Wiener filtering Asymptotic study 

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.LTCITélécom ParisTechParisFrance
  2. 2.CNRS MAP5Université Paris DescartesParisFrance

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