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

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.

Keywords

• Nondifferntiable optimization problems
• regularization
• inverse problems
• image reconstruction
• bounded variation norm.