An iterative regularization method for total variation-based image restoration. (English) Zbl 1090.94003

Osher, Stanley; Burger, Martin; Goldfarb, Donald; Xu, Jinjun; Yin, Wotao

Multiscale Model. Simul. 4, No. 2, 460-489 (2005).

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.

MSC:

94A08	Image processing (compression, reconstruction, etc.) in information and communication theory
46N10	Applications of functional analysis in optimization, convex analysis, mathematical programming, economics
65J22	Numerical solution to inverse problems in abstract spaces
49M30	Other numerical methods in calculus of variations (MSC2010)
47N70	Applications of operator theory in systems, signals, circuits, and control theory
68U10	Computing methodologies for image processing

Keywords:

iterative regularization; total variation; Bregman distances; denoising; deblurring