Electron. J. Diff. Eqns., Vol. 1997(1997), No. 15, pp 1-12.

Stable evaluation of differential operators and linear and nonlinear multi-scale filtering

Otmar Scherzer

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.

Submitted July 8, 1997. Published September 10, 1997.
Math Subject Classification: 65J10, 65J15, 65K10, 35J60, 26A45.
Key Words: Nondifferntiable optimization problems, regularization, inverse problems, image reconstruction, bounded variation norm.

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Otmar Scherzer
Institut fur Industriemathematik, Universitat Linz,
Altenberger Str. 69, A--4040 Linz, Austria
E-Mail address: scherzer@indmath.uni-linz.ac.at
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