An Iterative Regularization Method and Inverse Scale Space for Image Restoration

Stanley Osher

Stanley Osher (joint with Martin Burger, Donald Goldfarb, Jinjun Xu and Wotao Yin)

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 criteria for the general procedure. The numerical results for denoising and deblurring appear to give significant improvement over standard models. By taking the regularization parameter ery small and the number
of iteration steps large we are led to a new paradigm for restoration based on inverse scale space flows, instead of variational methods.

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