Rudin–Osher–Fatemi Total Variation Denoising using Split Bregman

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P. Getreuer, “Rudin–Osher–Fatemi Total Variation Denoising using Split Bregman,” Image Processing On Line, 2012. DOI: 10.5201/ipol.2012.g-tvd.

Article permalink: http://dx.doi.org/10.5201/ipol.2012.g-tvd

@article{getreuer2012tvdenoising,
    title = {{Rudin--Osher--Fatemi} Total Variation Denoising 
             using Split {Bregman}},
    author = {Pascal Getreuer},
    journal = {Image Processing On Line},
    year = {2012},
    doi = {10.5201/ipol.2012.g-tvd},
}

Abstract

Denoising is the problem of removing noise from an image. The most commonly studied case is with additive white Gaussian noise (AWGN), where the observed noisy image f is related to the underlying true image u by f = u + η and η is at each point in space independently and identically distributed as a zero-mean Gaussian random variable.

Total variation (TV) regularization is a technique that was originally developed for AWGN image denoising by Rudin, Osher, and Fatemi. The TV regularization technique has since been applied to a multitude of other imaging problems, see for example Chan and Shen’s book. We focus here on the split Bregman algorithm of Goldstein and Osher for TV-regularized denoising.