# Rudin–Osher–Fatemi Total Variation Denoising using Split Bregman

## Reference

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.