Abstract
We show that regularization methods can be regarded as scale-spaces where the regularization parameter serves as scale. In analogy to nonlinear diffusion filtering we establish continuity with respect to scale, causality in terms of a maximum/minimum principle, simplifica- tion properties by means of Lyapunov functionals and convergence to a constant steady-state. We identify nonlinear regularization with a single implicit time step of a diffusion process. This implies that iterated regu- larization with small regularization parameters is a numerical realization of a diffusion filter. Numerical experiments in two and three space dimen- sions illustrate the scale-space behaviour of regularization methods.
Keywords
- Regularization Parameter
- Regularization Method
- Extremum Principle
- Total Variation Regularization
- Lyapunov Functional
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Radmoser, E., Scherzer, O., Weickert, J. (1999). Scale-Space Properties of Regularization Methods. In: Nielsen, M., Johansen, P., Olsen, O.F., Weickert, J. (eds) Scale-Space Theories in Computer Vision. Scale-Space 1999. Lecture Notes in Computer Science, vol 1682. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48236-9_19
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DOI: https://doi.org/10.1007/3-540-48236-9_19
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