An Iterative Regularization Method for Total Variation-Based Image Restoration

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 regul...

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Bibliographic Details
Published in:Multiscale modeling & simulation 2005-01, Vol.4 (2), p.460-489
Main Authors: Osher, Stanley, Burger, Martin, Goldfarb, Donald, Xu, Jinjun, Yin, Wotao
Format: Article
Language:English
Subjects:
Decomposition
Inverse problems
Noise
Regularization methods
Signal processing
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Summary: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.
ISSN:1540-3459
1540-3467
DOI:10.1137/040605412