Abstract

Total variation (TV) regularization, introduced by Rudin, Osher, and Fatemi [1], is a technique often used in digital image processing for denoising, as well as a multitude of other imaging problems. The total variation of the image minimized subject to some fidelity constraints (i.e., some measures to ensure a close match to the noisy image) is remarkably effective at smoothing away noise in flat regions while preserving important details such as edges. Because of these advantages, many numerical methods were proposed to iteratively approximate the regularized minimization problem, which is today known as the ROF model. In this talk, we will briefly introduce the ROF model and focus on the split Bregman algorithm of Goldstein and Osher [2] for TV-regularized denoising.

References

[1] L. I. Rudin, S. Osher, and E. Fatemi, Nonlinear total variation based noise removal algorithms, Physica D, 60 (1992), pp. 259-268.

[2] T. Goldstein and S. Osher, The split Bregman method for L1 regularized problems, SIAM Journal on Imaging Sciences, 2 (2009), pp. 323-343.

[3] P. Getreuer, Rudin-Osher-Fatemi total variation denoising using split Bregman, Image Processing On Line, 2 (2012), pp. 74-95.