Intertwining Operators for Mollification: Theoretical and Numerical Aspects

Pierre Maréchal*

In the variational approach to the regularisation by mollification, the main difficulty appears when generating, from real data, what we may call 'regularized data', that is, data in accordance with the objective of the reconstruction (generally a limited resolution object). Theoretically, we need to obtain exact or approximate intertwining operators, or merely (and more reasonably) a routine simulating their application. We shall explore the potential benefits of using the proximal point algorithm in this context, and show some applications.

Mathematics Subject Classification: 47A52

Keywords: Mollification, intertwining operators, proximal point algorithm.

Minisymposion: Iterative Methods for Ill-Posed Problems