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Demystifying the asymptotic behavior of global denoising

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.
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Contributor : Antoine Houdard Connect in order to contact the contributor
Submitted on : Tuesday, March 21, 2017 - 5:51:19 PM
Last modification on : Tuesday, December 8, 2020 - 9:39:45 AM
Long-term archiving on: : Thursday, June 22, 2017 - 2:00:54 PM


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Antoine Houdard, Andrès Almansa, Julie Delon. Demystifying the asymptotic behavior of global denoising. Journal of Mathematical Imaging and Vision, Springer Verlag, 2017, ⟨10.1007/s10851-017-0716-6⟩. ⟨hal-01340822v3⟩



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