Stable Evaluation of Differential Operators and Linear and Nonlinear Multi-scale Filtering
Date
1997-09-10
Authors
Scherzer, Otmar
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
Diffusion 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.
Description
Keywords
Nondifferntiable optimization problems, Regularization, Inverse problems, Image reconstruction, Bounded variation norm
Citation
Scherzer, 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.
Rights
Attribution 4.0 International
Rights Holder
This work is licensed under a Creative Commons Attribution 4.0 International License.