We introduce a new iterative regularization procedure for inverse problems based on the use of Bregman distances, with particular focus on problems arising in image processing. We are motivated by the problem of restoring noisy and blurry images via variational methods, by using total variation regularization. We obtain rigorous convergence results, and effective stopping criteria for the general procedure. The numerical results for denoising appear to give signifcant improvement over standard models and preliminary results for deblurring/denoising are very encouraging.

@Article{OBGXY05,
  author       = {Osher, S. and Burger, M. and Goldfarb, D. and Xu, J. and Yin, W.},
  title        = {An iterative regularization method for total variation based image restoration},
  journal      = {SIAM Multiscale Mod. Simul.},
  volume       = {4},
  pages        = {460-489},
  year         = {2005},
  url          = \{/2005/OBGXY05},
}