Adaptive rates for total variation image denoising
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Date
2020-12
Publication Type
Journal Article
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yes
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Abstract
We study the theoretical properties of image denoising via total variation penalized least-squares. We define the total vatiation in terms of the two-dimensional total discrete derivative of the image and show that it gives rise to denoised images that are piecewise constant on rectangular sets. We prove that, if the true image is piecewise constant on just a few rectangular sets, the denoised image converges to the true image at a parametric rate, up to a log factor. More generally, we show that the denoised image enjoys oracle properties, that is, it is almost as good as if some aspects of the true image were known. In other words, image denoising with total variation regularization leads to an adaptive reconstruction of the true image. (© 2020 Microtome Publishing)
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published
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Journal / series
Volume
21
Pages / Article No.
247
Publisher
Microtome Publishing
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Edition / version
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Date created
Subject
total variation; image denoising; fused Lasso; oracle inequalities
Organisational unit
03717 - van de Geer, Sara (emeritus) / van de Geer, Sara (emeritus)
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