Electronic Journal of Differential Equations,
Vol. 1997(1997), No. 15, pp 1-12.

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

Author: Otmar Scherzer (Johannes-Kepler Univ., Linz Austria)


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.


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.