An Iterative Regularization Method for Total Variation-Based Image Restoration

Abstract. 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 significant improvement over standard models, and preliminary results for deblurring/denoising are very encouraging.

• NS
  National Science Foundation

  Awards: P20MH65166, 0321917, 0312222
• UD
  U.S. Department of Energy
• AS
  Austrian Science Fund
• NI
  National Institutes of Health
• OO
  Office of Naval Research

  Award: N00014