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Comptes Rendus Mathématique
Volume 352, n° 11
pages 917-921 (novembre 2014)
Doi : 10.1016/j.crma.2014.09.009
Received : 1 July 2014 ;  accepted : 12 September 2014
Localization of extended current source with finite frequencies
Localisation de sources étendues à partir d'un nombre fini de fréquences
 

Abdul Wahab a , Amer Rasheed a , Rab Nawaz b , Saman Anjum a
a COMSATS Institute of Information Technology, G. T. Road, 47040, Wah Cantt., Pakistan 
b COMSATS Institute of Information Technology, Park Road, Chak Shahzad, 44000, Islamabad, Pakistan 

Abstract

A phase conjugation algorithm for localizing the spatial support of an extended radiating current source from boundary measurements of the electric field over a finite set of frequencies is presented. An imaging function using a full frequency bandwidth is established and analyzed. It is subsequently adopted to the case of finite frequency measurements. Finally, the algorithm is blended with  -regularization in order to deal with the artifacts associated with finite frequency data.

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Résumé

Dans cette note, nous présentons un algorithme de conjugaison de phase pour la reconstruction d'une source étendue à partir de mesures de champ électrique obtenues pour un ensemble fini de fréquences. Nous commençons par introduire et analyser une fonctionnelle d'imagerie à partir de mesures obtenues pour un intervalle de fréquences. Ensuite, nous proposons une régularisation   d'une telle fonctionnelle d'imagerie afin d'éliminer les artefacts dus à l'aspect discret et limité des fréquences utilisées.

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