Burger, Martin; Gilboa, Guy; Osher, Stanley; Xu, Jinjun Nonlinear inverse scale space methods. (English) Zbl 1106.68117 Commun. Math. Sci. 4, No. 1, 179-212 (2006). 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. Reviewer: Wiesław Kotarski (Sosnowiec) Cited in 2 ReviewsCited in 46 Documents MSC: 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 Keywords:iterated refinement techniques; inverse scale space method; image restoration; denoising; evolution equation Citations:Zbl 1090.94003 PDFBibTeX XMLCite \textit{M. Burger} et al., Commun. Math. Sci. 4, No. 1, 179--212 (2006; Zbl 1106.68117) Full Text: DOI