Stable Evaluation of Diierential Operators and Linear and Nonlinear Multi{scale Ltering

Diiusion processes create multi{scale analyses, which enable the generation of simpliied 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 eeciently solve these minimization problems.