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.

Keywords

DeblurringTotal variation denoisingRegularization (linguistics)Image restorationMathematicsInverse problemImage denoisingNoise reductionAlgorithmMathematical optimizationApplied mathematicsIterative methodConvergence (economics)Image processingComputer scienceImage (mathematics)Artificial intelligenceMathematical analysis

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Publication Info

Year: 2005
Type: article
Volume: 4
Issue: 2
Pages: 460-489
Citations: 1795
Access: Closed

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APA Style

                            
                                
                                    Stanley Osher, 
                                
                                    Martin Burger, 
                                
                                    Donald Goldfarb
                                
                                et al.
                            
                            (2005). 
                            An Iterative Regularization Method for Total Variation-Based Image Restoration. 
                            Multiscale Modeling and Simulation
                            , 4
                            (2)
                            , 460-489.
                            https://doi.org/10.1137/040605412
                        

Identifiers

DOI: 10.1137/040605412