NDLI: Total Variation as a Local Filter

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Total Variation as a Local Filter

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Moisan, Lionel Louchet, Ccile
Copyright Year	2011
Abstract	In the RudinOsherFatemi (ROF) image denoising model, total variation (TV) is used as a global regularization term. However, as we observe, the local interactions induced by TV do not propagate much at long distances in practice, so that the ROF model is not far from being a local filter. In this paper, we propose building a purely local filter by considering the ROF model in a given neighborhood of each pixel. We show that appropriate weights are required to avoid aliasing-like effects, and we provide an explicit convergence criterion for an associated dual minimization algorithm based on Chambolle's work. We study theoretical properties of the obtained local filter and show that this localization of the ROF model brings an interesting optimization of the bias-variance trade-off, and a strong reduction of an ROF drawback called the staircasing effect. Finally, we present a new denoising algorithm, TV-means, that efficiently combines the idea of local TV-filtering with the nonlocal means patch-based method.
Starting Page	651
Ending Page	694
Page Count	44
File Format	PDF
DOI	10.1137/100785855
e-ISSN	19364954
Journal	SIAM Journal on Imaging Sciences (SJISBI)
Issue Number	2
Volume Number	4
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2011-06-21
Access Restriction	Subscribed
Subject Keyword	local filter Optimization and variational techniques Image analysis Image processing nonlocal means variational model total variation image denoising
Content Type	Text
Resource Type	Article

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