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Nonlinear inverse scale space methods. (English) Zbl 1106.68117
In the paper two new types of nonlinear processes based on PDE evolutions for image simplification and regularization are presented. Both extend the Bregman iteration procedure introduced in [S. Osher, M. Burger, D. Goldfarb, J. Xu and W. Yin, Multiscale Model Simul. 4, 460–489 (2005; Zbl 1090.94003)] to a time-continuous inverse scale-space formulation, creating stable flows. The inverse flow can be computed directly for 1D signals, yelding high quality restorations. For 2D images a relaxation technique using two evolution equations is introduced. Properties of these new types of flows are investigated. Also some tests carried out on the well-known benchmark images (“Cameraman”, “Sailboat”) showing excellent denoising capabilities of flows are presented. The bibliography contains 35 items.

68U10 Computing methodologies for image processing
47A52 Linear operators and ill-posed problems, regularization
49M30 Other numerical methods in calculus of variations (MSC2010)
65J22 Numerical solution to inverse problems in abstract spaces
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