Scherzer, Otmar2018-11-042018-11-041997-09-10Scherzer, O. (1997). Stable evaluation of differential operators and linear and nonlinear multi-scale filtering. <i>Electronic Journal of Differential Equations, 1997</i>(15), pp. 1-12.1072-6691https://hdl.handle.net/10877/7772Diffusion processes create multi--scale analyses, which enable the generation of simplified pictures, where for increasing scale the image gets sketchier. In many practical applications the ``scaled image'' can be characterized via a variational formulation as the solution of a minimization problem involving unbounded operators. These unbounded operators can be evaluated by regularization techniques. We show that the theory of stable evaluation of unbounded operators can be applied to efficiently solve these minimization problems.Text12 pages1 file (.pdf)enAttribution 4.0 InternationalNondifferntiable optimization problemsRegularizationInverse problemsImage reconstructionBounded variation normArticleThis work is licensed under a Creative Commons Attribution 4.0 International License.