Journal of Applied Mathematics
Volume 2005 (2005), Issue 2, Pages 127-152

Determination of a power density by an entropy regularization method

Olivier Prot,1,2 Maïtine Bergounioux,2 and Jean Gabriel Trotignon1

1UMR 6115, LPCE/CNRS, 3A Avenue de la Recherche Scientifique, Orléans Cedex 2 45071, France
2UMR6628, MAPMO/CNRS, Université d'Orléans, BP 6759, Orléans Cedex 2 45067, France

Received 11 January 2004; Revised 18 September 2004

Copyright © 2005 Olivier Prot et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The determination of directional power density distribution of an electromagnetic wave from the electromagnetic field measurement can be expressed as an ill-posed inverse problem. We consider the resolution of this inverse problem via a maximum entropy regularization method. A finite-dimensional algorithm is derived from optimality conditions, and we prove its convergence. A variant of this algorithm is also studied. This second one leads to a solution which maximizes entropy in the probabilistic sense. Some numerical examples are given.