Journal of Applied Mathematics 
Volume 2005 (2005), Issue 2, Pages 127-152
doi:10.1155/JAM.2005.127

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

Abstract

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.